Credit Without Ground Truth: Auditing Step-Level Credit Assignment in LLM Agents Against Executed Replay

# Credit Without Ground Truth: Auditing Step-Level Credit Assignment in LLM Agents Against Executed Replay
Source: [https://arxiv.org/html/2608.19760](https://arxiv.org/html/2608.19760)
Heady ZhangAffiliation:University of Southern CaliforniaAffiliation:Los Angeles, CA, USAEmail:[haiyuez@usc\.edu](mailto:)

###### Abstract

Audited against causal ground truth from executed replay in a single\-agent tool environment \(ALFWorld\), none of the step\-level credit signals used to train LLM agents — LLM\-judge scores, outcome\-conditioned logprob ratios, or the policy’s own confidence — identifies which steps causally matter better than chance\. Existing evaluations grade these signals against annotated step*correctness*; we audit them against step*contribution*— what re\-sampling the policy’s own alternatives at each decision point and rolling forward actually changes about the outcome — and the two come apart\. The ground truth itself is structured: causal contribution is sparse \(30\.5% of decision points where ground truth is defined carry measurable effect\), and measurability is model\-dependent — the fraction of points with no policy\-supported counterfactual differs by a factor of two \(13\.1% vs\. 26\.8%\) between two similar\-scale policies\. The failure mode is identifiable: implicit credit echoes the policy’s fluency \(median rank correlation\+0\.75\+0\.75, replicating at\+0\.70\+0\.70in a second family under a corrected instrument\), while conditioning on the outcome adds no causal information \(partial correlation−0\.004\-0\.004, Qwen\)\. A confidence\-only router recovers pivotal steps at chance level, but cuts judge cost by13\.113\.1% per turn \(14\.014\.0% per trajectory\)\. In a seven\-arm pre\-registered training experiment, no arm reliably outperforms the untrained policy, and the checkpoints’ apparent instrument signature is fully explained by training dose — sparser credit retains fewer examples, an order\-of\-magnitude spread in optimizer steps — not credit content\. Comparisons of credit rules must therefore match effective sample size, or they measure dose, not credit\.

Figure 1:The audit verdict: in both model families, credit is indistinguishable from its own shuffled control\.Each family’s rank\-fidelity estimate against executed\-replay ground truth \(median within\-trajectory Spearman vs\.AreplayA\_\{\\mathrm\{replay\}\}, Section[2](https://arxiv.org/html/2608.19760#S2); filled markers\) beside its*own*marginal\-matched shuffled control \(open markers, paired within family; the figure plots rank fidelity only — the precision\-at\-pivotal lift discussed in Section[4](https://arxiv.org/html/2608.19760#S4)is a different statistic and is not plotted\): Qwen2\.5\-7B implicit0\.01930\.0193\[−0\.109,0\.081\]\[\-0\.109,0\.081\]\(neff=37n\_\{\\mathrm\{eff\}\}\{=\}37of 50; own control\[0\.005,0\.114\]\[0\.005,0\.114\]\) and judge0\.11420\.1142\[0\.027,0\.168\]\[0\.027,0\.168\]\(n=37n\{=\}37, 32 computable; own control\[−0\.049,0\.117\]\[\-0\.049,0\.117\]\), dataruns/collect\_v2/analysis\_summary\.json; Llama\-3\.1\-8B implicit under the corrected instrument−0\.043\-0\.043\[−0\.125,−0\.016\]\[\-0\.125,\-0\.016\]\(n=21n\{=\}21trajectories retained of 28; own control\[−0\.102,\+0\.024\]\[\-0\.102,\+0\.024\]\), dataruns/xfam\_ext/redo/redo\_family\_analysis\.json, coverage 88\.3%[1](https://arxiv.org/html/2608.19760#footnote1)\. Under the frozen controls\-first verdict order, every family–control pair overlaps under the controls\-first order: verdict H3 \(placebo\-level, frozen verdict order, Section[4](https://arxiv.org/html/2608.19760#S4)\) throughout; the binding comparison is each family against its own control\.## 1Introduction

Agentic reinforcement learning is converging on a bet: train LLM agents through long tool\-use episodes by scoring each step, not just the outcome\. Step\-level credit signals — LLM judges scoring turns, outcome\-conditioned log\-probability ratios, the policy’s own confidence — are moving from evaluation harnesses into training loops\([Tan et al\. 2025](https://arxiv.org/html/2608.19760#bib.bib8);[Li et al\. 2026b](https://arxiv.org/html/2608.19760#bib.bib3);[Tan et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib7);[Chen et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib1);[Zhang et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib11)\), and surveys catalogue dozens of methods built on them\([Zhang 2026](https://arxiv.org/html/2608.19760#bib.bib10)\)\. The bet rests on an assumption that, to our knowledge, no one has tested: that the credit these signals assign to a step tracks what the step actually contributed to the outcome\. C3 audits multi\-agent credit against its own replay advantages\([Chen et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib1)\); grading signals already in LLM\-agent training use against an external, executed causal ground truth is a different object \(Appendix[L](https://arxiv.org/html/2608.19760#A12)\)\.

Existing evaluations measure something else: step\-level benchmarks grade credit signals against*annotated step correctness*\([Zhang et al\. 2025](https://arxiv.org/html/2608.19760#bib.bib9);[Liu et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib4)\)\. But a correct step can contribute nothing \(the trajectory was already determined\) and an incorrect one can be pivotal \(it opened the state from which recovery happened\); correctness and contribution are different quantities, and only the second is what a training loop pays for\. Auditing the signals the field actually trains on, at the level they operate requires ground truth for contribution itself\.

We build that ground truth by executed replay\. At each decision point of a collected trajectory, we re\-sample alternative actions the policy itself supports, roll each forward to completion, and measure the shift in the outcome distribution — a per\-step causal effect with a per\-estimate noise floor and an explicit resolution bound\. Nothing in the construction consults the credit signals under audit\.

The ground truth itself is the first surprise: causal contribution is sparse — under a third of decision points carry any measurable effect — and*measurability is model\-dependent*: the no\-counterfactual fraction differs by a factor of two between two similar\-scale policies\. Against it, the audit’s null survives every probe: neither credit family ranks steps better than its own marginal\-matched shuffled control, in either model family, under either instrument generation\. The mechanism is identifiable: implicit credit largely echoes the policy’s own fluency \(median rank correlation\+0\.75\+0\.75, replicated across families\), and conditioning on the outcome adds no causal information\. In a seven\-arm pre\-registered training experiment, apparent differences between credit rules are fully accounted for by training*dose*— sparser credit buys fewer optimizer steps — not by what the credit says\.

Our contributions, by type:

1. 1\.Measurement\.A measurability map of causal ground truth in a replayable single\-agent tool environment: contribution is sparse, and measurability itself is model\-dependent in both directions — steps are unmeasurable either because the policy supports no alternative or because the outcome is already absorbed\.
2. 2\.Audit\.In a replayable single\-agent tool environment, no off\-the\-shelf signal — judge scores, implicit outcome\-conditioned logprob ratios, outcome conditioning itself, or the policy’s own confidence — identifies which steps causally matter better than chance\.
3. 3\.Mechanism\.The implicit family’s scores are a fluency echo, replicated across two model families on three pre\-registered supports; the outcome\-conditioned increment carries no causal information, with the primary evidence on the Qwen policy\.
4. 4\.Decision rule \(cost\-only\)\.A frozen confidence\-routing rule that cuts judge calls by13\.113\.1% per turn and14\.014\.0% per trajectory — the two granularities move oppositely and are always reported together — with chance\-level pivotal recall, and prospective deployment of the router is not evaluated\.
5. 5\.Protocol\.A named toolset for credit comparisons: dose matching, measured perturbation strength for controls, an MDE ladder for reading training nulls, and a four\-dimension integrity taxonomy with its incident catalogue\.

Our method\-level contributions are the decision rule and the protocols, not an end\-to\-end system\.

## 2Measuring causal ground truth by executed replay

Our instrument is executed replay: at each decision point of a collected trajectory we re\-execute the environment under sampled alternative actions and measure how the outcome distribution shifts\. We instantiate it in ALFWorld, a replayable single\-agent tool environment, with Qwen2\.5\-7B\-Instruct as the policy: 50 trajectories on a task list frozen before collection, sampled at temperature 0\.7 under the HCAPO method’s published ALFWorld agent template\([Tan et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib7)\), extracted verbatim from the paper’s appendix\. Environment determinism was verified before collection and re\-verified on every host that touched the data \(one trajectory hash, four independent environments\)\. A concurrent formalization of the same instrument validates it under planted effects\([Shah 2026](https://arxiv.org/html/2608.19760#bib.bib5)\); the contrast is in Appendix[L](https://arxiv.org/html/2608.19760#A12)\.

The audited signals are the two families of step\-level credit that agentic RL pipelines train on\. The*implicit*family is HCAPO’s outcome\-conditioned token log\-probability ratioρt\\rho\_\{t\}, computed exactly as published; its scorer is the policy checkpoint itself, by HCAPO’s design, and the instrument constants, the hindsight\-injection construction, and the matched*policy*scoring mode are detailed in Appendix[G](https://arxiv.org/html/2608.19760#A7)\.

Ground truth at a turn is a contrast between two outcome distributions, never a single continuation\. At every action turnttwe re\-execute the factual action at least three times and sampleK=4K\{=\}4distinct admissible alternatives from the same policy snapshot at the collection temperature \(within at most 300 seeded draws\), rolling each alternative to terminal at least three times; the replay advantage isAreplay​\(t\)=mean⁡\(outcome∣factual replays at​t\)−mean⁡\(outcome∣alternative rollouts at​t\)A\_\{\\mathrm\{replay\}\}\(t\)=\\operatorname\{mean\}\(\\text\{outcome\}\\mid\\text\{factual replays at \}t\)\-\\operatorname\{mean\}\(\\text\{outcome\}\\mid\\text\{alternative rollouts at \}t\)\. The realized continuation of the original trajectory is never used as the factual estimate\. When four distinct admissible alternatives cannot be sampled from the policy, the policy\-supported counterfactual is*undefined*at that turn; such turns are excluded and counted rather than imputed\. Under Qwen2\.5\-7B this leaves 1,768 complete turns of 2,034 intervened; the excluded fraction is itself a finding \(Section[3](https://arxiv.org/html/2608.19760#S3)\)\. Prefix\-restore determinism held across the full sweep: zero divergences over its 20,538 replay rollouts\.

The same factual replicas give the estimator its noise floor and its resolution\. Per turn,σfloor​\(t\)\\sigma\_\{\\mathrm\{floor\}\}\(t\)is the standard deviation of the outcome across factual replays, and a turn is*pivotal*exactly whenAreplay​\(t\)≠0A\_\{\\mathrm\{replay\}\}\(t\)\\neq 0under the literal stored value — no significance filter, no floor threshold\. Because outcomes are discrete and replicas few, exact zeros are common: 69\.5% of complete turns carryAreplay=0A\_\{\\mathrm\{replay\}\}=0, and for the 1,184 turns where both arms are all\-zero the data exclude only\|Δ​p\|\>0\.632\|\\Delta p\|\>0\.632at one\-sided 95% confidence\. Every zero in this paper is therefore a resolution\-bounded statement — “indistinguishable from the factual action at the achieved sampling resolution” — and never a claim of no causal effect\.

Fidelity is scored where credit is consumed: within trajectories\. For each family we compute the within\-trajectory Spearman correlation between the credit values andAreplayA\_\{\\mathrm\{replay\}\}, aggregated as the median across trajectories with a 10,000\-resample bootstrap interval; trajectories on which the statistic is degenerate \(fewer than four complete turns, or constantAreplayA\_\{\\mathrm\{replay\}\}\) are excluded from this computation only, symmetrically across families, and counted\. Random, uniform, and within\-trajectory shuffled credit — the shuffle preserves each trajectory’s marginal exactly — run through the identical pipeline in the same batch\. The verdict order is frozen, and its controls gate comes first: a family whose interval overlaps that of its own shuffled control is placebo\-level regardless of its point estimate\. Three structural bias tests accompany the verdicts under a Holm correction over all six family\-level hypotheses; one of them, T3, carries a registered directional prediction — positive for the implicit family — that fluent, high\-probability actions receive inflated credit regardless of causal effect\.

Thresholds, exclusion rules, and the verdict order were frozen and signed before collection under immutable tags; every number here is regenerated by script from raw artifacts, never transcribed; checkpoints are content\-verified shard\-by\-shard before any stage loads them \(Section[8](https://arxiv.org/html/2608.19760#S8)\)\. The audit is repeated in a second model family, Llama\-3\.1\-8B\-Instruct\. For the implicit family the swap changes the measured object, the scoring instrument, and the ruler at once — HCAPO’s scorer*is*the policy, and replay truth is defined over the policy’s own action distribution — so the cross\-family run tests the system\-level claim, that a policy’s own implicit credit does not track its own causal ground truth, under a second system; it cannot and does not evaluate the scoring instrument apart from the policy\. The Llama arm collected 28 trajectories, of which 27 enter the analysis set after one exclusion\. Its replay layer was re\-executed in full under a corrected instrument after a chat\-template defect was found and quantified \(Section[8](https://arxiv.org/html/2608.19760#S8)\); the re\-execution’s coverage is stated once here111Coverage 88\.3% \(1,082/1,225 parseable turns\)\. Missingness is concentrated exclusively in long \(≥\\geq44\-turn\) trajectories \(13/28 partially covered; short/medium buckets 100%\)\. The 143 turns outside the analysis set — 142 never generated at the cap trip\+\+1 unparseable — were not re\-run, by pre\-registered precedent \(∼\\sim1% expected conversion\)\. Length\-sensitive quantities inherit this caveat \(gate disclosure: Section[8](https://arxiv.org/html/2608.19760#S8)\)\.and inherited by every Llama\-side quantity in the paper\.

## 3The structure of causal ground truth

### 3\.1The measurability map

Before asking whether credit tracks causal contribution, we ask where causal contribution can be measured at all — and the answer is that the ground truth is sparse and mostly silent\. Under Qwen2\.5\-7B, 30\.5% of complete turns are pivotal \(n=1,768n\{=\}1\{,\}768\): fewer than a third of decision points have any measurable causal effect on the outcome at all\. The dynamics are strongly absorbing —σfloor=0\\sigma\_\{\\mathrm\{floor\}\}=0at 86\.0% of complete turns — and every turn withAreplayA\_\{\\mathrm\{replay\}\}exactly zero carries the resolution bound of Section[2](https://arxiv.org/html/2608.19760#S2): the data exclude only\|Δ​p\|\>0\.632\|\\Delta p\|\>0\.632there\. Most of the trajectory is causally inert; a credit signal earns its keep only by finding the minority of turns that are not\.

### 3\.2Measurability is model\-dependent — in both directions

Under the same environment, the sameK=4K\{=\}4alternatives, and the same 15\-rollout budget, the policy\-supported counterfactual is undefined at 13\.1% of intervened turns for Qwen2\.5\-7B \(n=2,034n\{=\}2\{,\}034\) but at 26\.8% for Llama\-3\.1\-8B \(n=1,082n\{=\}1\{,\}082; corrected instrument[1](https://arxiv.org/html/2608.19760#footnote1)\) — a factor of 2\.05, with non\-overlapping intervals\. And where ground truth*is*defined, the same comparison reverses: the family that is harder to measure carries more causal signal, 38\.3% of Llama’s complete turns pivotal against Qwen’s 30\.5%\. The full three\-rate map is Figure[5](https://arxiv.org/html/2608.19760#A10.F5)in Appendix[J](https://arxiv.org/html/2608.19760#A10); the two divergences run in opposite directions\. The Wilson 95% intervals are\[11\.7,14\.6\]%\[11\.7,14\.6\]\\%\(Qwen\) and\[24\.2,29\.5\]%\[24\.2,29\.5\]\\%\(Llama\)\. The mechanism is concentration, not capability: at some decision points Llama’s probability mass is too tight for four distinct admissible alternatives to be sampled within budget\. This is a scope condition on replay methodology itself\.

The pivotal reversal’s precision: 38\.3% of Llama’s complete turns \(n=792n\{=\}792; corrected instrument[1](https://arxiv.org/html/2608.19760#footnote1)\) against Qwen’s 30\.5% \(n=1,768n\{=\}1\{,\}768\)\. The absorbing structure, by contrast, transfers approximately —σfloor=0\\sigma\_\{\\mathrm\{floor\}\}=0at 80\.6% versus 86\.0% of turns\. Measurability structure therefore varies with the model in both directions: the family that is harder to define counterfactuals for is the one with more causal signal where counterfactuals exist\. It is a property of the \(policy, environment\) pair — not an environment constant, and not a statement that either family is uniformly harder to audit\. Concurrent work reports a similar sparsity pattern\([Shen et al\. 2025](https://arxiv.org/html/2608.19760#bib.bib6)\); ours differs in kind: zeros are noise\-floored and resolution\-bounded, and measurability itself is bidirectionally model\-dependent \(Appendix[L](https://arxiv.org/html/2608.19760#A12)\)\. Figure[4](https://arxiv.org/html/2608.19760#A10.F4)in Appendix[J](https://arxiv.org/html/2608.19760#A10)shows both divergences\.

The exclusions are not random, and the direction of their bias is measured rather than assumed\. The turns without a policy\-supported counterfactual are systematically the low\-entropy ones, so exclusion correlates with the implicit family’s own predictor: for Qwen, the included\-minus\-excluded difference in mean policy log\-probability is−0\.70\-0\.70\(n=1,768n\{=\}1\{,\}768\), the interval excluding zero\. We report this selection check for Qwen only\. For Llama, what the corrected instrument re\-establishes is the exclusion*rate*just stated; the selection\-check*correlation*was computed on pre\-correction inputs and cannot be recomputed — a permanent state, disclosed in Appendix[B](https://arxiv.org/html/2608.19760#A2)\. The analysis sets are therefore right\-truncated on the fluency axis, with the direction of the truncation measured for Qwen, and Section[4](https://arxiv.org/html/2608.19760#S4)states what this range restriction does to the fidelity estimates\.

An occupancy\-style predictor built from the policy’s own action statistics ranks turns correctly while missing the aggregate level — the ranking is trustworthy, the level is not \(Appendix[J](https://arxiv.org/html/2608.19760#A10)\)\.

## 4The fidelity audit: implicit credit against its own ground truth

Table 1:Both credit families are placebo\-level at within\-trajectory credit ranking under the frozen verdict order \(H3\): each is indistinguishable from its own marginal\-matched shuffled control\.The implicit estimate is centred on zero; the judge estimate is weak, possibly nonzero, yet indistinguishable from its own control — the families are reported separately and earn the same verdict class\. Estimator: median within\-trajectory Spearman vs\.AreplayA\_\{\\mathrm\{replay\}\}, 10k bootstrap \(estimator note: Appendix[A](https://arxiv.org/html/2608.19760#A1)\); controls: marginal\-matched within\-trajectory shuffles; instruments: original \(Qwen\), corrected \(Llama; coverage 88\.3%[1](https://arxiv.org/html/2608.19760#footnote1)\); data:runs/collect\_v2/analysis\_summary\.json,runs/xfam\_ext/redo/redo\_family\_analysis\.json\. Sign agreement: per\-step vs trajectory\-median splits, Wilson 95%; implicit267/527=50\.7%267/527=50\.7\\%\[46\.4,54\.9\]\[46\.4,54\.9\], judge84/139=60\.4%84/139=60\.4\\%\[52\.1,68\.2\]\[52\.1,68\.2\];neffn\_\{\\mathrm\{eff\}\}= trajectories retained by the frozen exclusion rules\.The audit question is whether the credit a trained scorer assigns to each step tracks the causal contribution that executed replay measures for that same step — and the answer, everywhere the audit reaches, is that it does not\. Coverage differs by signal, and we scope it per signal: implicit credit is audited in both model families and under both instrument generations; judge fidelity in one family \(Qwen\); the confidence signal in one family \(Qwen\)\.

Three measurements that share no estimator, no test statistic, and no failure mode — rank fidelity against a marginal\-matched shuffled control, per\-step sign agreement against chance, and partial correlation with the causal increment after conditioning out fluency — agree on the same null: the first two in both families, the third on the registered Qwen set \(corrected\-instrument partials: Appendix[D](https://arxiv.org/html/2608.19760#A4)\)\.

For the Qwen policy under the original instrument, the family\-level rank fidelity of implicit credit is read under the frozen verdict order, and the controls gate fires before any effect gate is reached: the verdict is H3 \(Table[1](https://arxiv.org/html/2608.19760#S4.T1); Figure[1](https://arxiv.org/html/2608.19760#S0.F1)\)\. Per\-step sign agreement sits at chance\. The audit’s negative result is not that credit anti\-tracks its ground truth; it is that nothing distinguishes the trained scorer’s ranking from the same scores with their step\-assignment destroyed\.

One face of the judge signal does clear chance, and we state it plainly before locating its limit: per\-step sign agreement for the judge family is84/139=60\.484/139=60\.4% \(Wilson 95%\[52\.1,68\.2\]\[52\.1,68\.2\];runs/collect\_v2/analysis\_summary\.json\), an interval excluding 50%\. It does not amount to identifying which steps causally matter — a rank\-and\-concentration claim — and the two families fail it differently \(registered exploratory, per family,n=35n\{=\}35trajectories each, of 50 loaded;runs/collect\_v2/r12\_precision\_at\_pivotal\.json\): the implicit family’s precision\-at\-pivotal lift is0\.9400\.940\[0\.760,0\.997\]\[0\.760,0\.997\], an interval lying entirely below the chance line of1\.01\.0, while the judge’s1\.0001\.000\[0\.935,1\.001\]\[0\.935,1\.001\]contains it\. The judge’s per\-step sign signal buys no concentration on the turns that mattered; the implicit family’s ranking is, if anything, mildly anti\-concentrated\. Agreement with the anchor judge is reported in Appendix[J](https://arxiv.org/html/2608.19760#A10)\.

The Llama replication was run twice: once under the original instrument, and in full again under the corrected instrument after the chat\-template defect of Section[8](https://arxiv.org/html/2608.19760#S8)was found\. Under the corrected instrument the verdict class is unchanged: the family estimate and its own marginal\-matched shuffled control overlap, under the frozen order the controls gate fires first, and the verdict is H3, matching Qwen’s \(Figure[1](https://arxiv.org/html/2608.19760#S0.F1), which carries both intervals\)\. Descriptively, the family point estimate is negative with a confidence interval excluding zero \(−0\.043\-0\.043,\[−0\.125,−0\.016\]\[\-0\.125,\-0\.016\];n=21n\{=\}21trajectories retained of 28[1](https://arxiv.org/html/2608.19760#footnote1)\), and it is indistinguishable from its own marginal\-matched shuffle \(−0\.010\-0\.010,\[−0\.102,\+0\.024\]\[\-0\.102,\+0\.024\]\) — we note the sign and draw no claim from it, since the gate that binds is the control comparison, not the zero crossing\. Sign agreement between implicit credit and replay is0\.4490\.449\(\[0\.393,0\.505\]\[0\.393,0\.505\];n=301n\{=\}301turn pairs[1](https://arxiv.org/html/2608.19760#footnote1)\) — chance\-level, the third measure returning the same answer as the first two\.

That the null itself replicates is established by the pre\-registered transfer criterion\. T3 replicates across model families under the corrected instrument: on the registered primary \(full\) set, the cross\-family median \(\+0\.7008\+0\.7008\[0\.6482,0\.7683\]\[0\.6482,0\.7683\],n=27n\{=\}27, coverage 88\.3%[1](https://arxiv.org/html/2608.19760#footnote1)\) satisfies the pre\-registered point criterion — it lies within KS1’s registered CI\[0\.647,0\.793\]\[0\.647,0\.793\]\. The corrected interval’s lower edge,0\.64820\.6482, clears the registered band’s exact lower bound \(0\.64740\.6474\) by0\.00080\.0008— the cross\-family replication holds on both the point criterion and the full interval, with essentially zero margin, which we state proactively\. The second, independent criterion also holds: re\-run under a script frozen before execution, the shuffled control for T3 is−0\.0155\-0\.0155\(\[−0\.1290,\+0\.0844\]\[\-0\.1290,\+0\.0844\],n=27n\{=\}27\), non\-overlapping with the observed interval, so the control criterion fires; we note its shuffling procedure executes in a remote frozen script and its control value is read from the archived artifact rather than recomputed locally\. And the full\-set family difference, re\-run by the recovered original bootstrap on the corrected inputs, spans zero for 40/40 seeds \(seed\-11 primary−0\.0188\-0\.0188\[−0\.1178,\+0\.0954\]\[\-0\.1178,\+0\.0954\];nxfam=27n\_\{\\mathrm\{xfam\}\}\{=\}27vsnKS1=47n\_\{\\mathrm\{KS1\}\}\{=\}47\)[1](https://arxiv.org/html/2608.19760#footnote1)— the families do not measurably differ on the statistic whose replication the criterion certifies\.

The two instrument generations bracket the result\. The defect that forced the re\-run moved the measurability map materially \(Section[8](https://arxiv.org/html/2608.19760#S8)\); it did not move a single verdict class\. Fidelity is H3 against the shuffled control under the broken template and under the fixed one, at pilot power and atn=21n\{=\}21; sign agreement is chance\-level in both; the transfer criterion holds in both\. A result that survives its own instrument being repaired is the closest an audit of this kind comes to an internal replication\.

Two readings are excluded by construction\. The null is not an artifact of unmeasurable ground truth — every fidelity quantity above is computed only over turns where replay truth is defined \(Section[3](https://arxiv.org/html/2608.19760#S3)\)\. And it is not a statement that the scorer’s outputs are uninformative: they are strongly structured, just not by causal contribution — which raises the question Section[5](https://arxiv.org/html/2608.19760#S5)answers, of what they are structured by\.

## 5Mechanism: credit echoes fluency, not effect

If the credit does not track causal effect, what does it track? We registered the answer before the data, and it was confirmed: implicit credit rises with the policy’s own probability of the action it is scoring — credit, in this family, is largely an echo of fluency\. The structural test against policy log\-probability is the implicit family’s one pre\-registered positive prediction, and it survived multiplicity correction \(median rank correlation\+0\.752\+0\.752, CI\[0\.647,0\.793\]\[0\.647,0\.793\],n=47n\{=\}47trajectories; Holm\-adjustedp=0\.0002p\{=\}0\.0002\)\.

The decomposition makes the echo quantitative\. Regressing implicit credit jointly on the action’s fluency \(its mean policy log\-probability\) and on the causal increment replay measures, fluency carries roughly two and a third times the weight of the increment for the Qwen policy \(standardised0\.9550\.955against0\.4020\.402;n=1,768n\{=\}1\{,\}768\), and once fluency is conditioned out, the partial correlation between credit and the causal increment is−0\.004\-0\.004\(p=0\.87p\{=\}0\.87\)\. Nothing of the causal signal survives the conditioning; the increment’s apparent weight in the joint model is the shadow fluency casts on it\.

One trajectory shows the mechanism whole\. In trajectoryseed017, the policy issues the same action —*take cloth 1 from toilet 1*— four consecutive times, the environment answering the first attempt with*Nothing happens\.*; at turns 12, 16, and 20 the scorer’s confidence in these repetitions exceeds0\.99990\.9999\. Replay judges the same turns pivotal, with causal increments of\+0\.333\+0\.333,−0\.167\-0\.167, and\+0\.250\+0\.250\. A policy stuck in a loop is maximally confident, because the next token is maximally predictable — and a credit signal that echoes that confidence will spend its certainty on exactly the steps where the trajectory has stopped going anywhere\.

Nor does the conditioning on outcome rescue the signal\. The scorer’s hindsight increment — what seeing the outcome adds to the policy’s own log\-probability — is uncorrelated with the causal increment on the registered Qwen set, with the corrected\-instrument Llama estimators disagreeing \(Appendix[D](https://arxiv.org/html/2608.19760#A4)\): knowing how the trajectory ended changes the score, but not in the direction of what each step contributed\.

The cross\-family run is the check on this mechanism, and its headline is stability of the dominance structure rather than any single coefficient: the fluency\-dominance ratio is template\- and family\-robust \(KS1 2\.37; xfam old 2\.29→\\rightarrowcorrected 2\.35\)\. Whatever the template regime and whichever the family, the same ordinary\-least\-squares \(OLS\) regression places roughly two and a third times the weight on fluency that it places on the causal increment[1](https://arxiv.org/html/2608.19760#footnote1)\.

The corrected\-instrument partial correlations — both estimators, their disagreement, and the selection caveat together — are in Appendix[D](https://arxiv.org/html/2608.19760#A4)\. This section rests on the Qwen analysis, where the conditioning null is measured on the registered set; the Llama arm’s role is the one its ratio plays — showing that fluency dominance, the structure the mechanism needs, survives a family swap and an instrument repair\.

A scorer that pays out for predictability is not thereby harmless: whether the echo damages the policy it trains is a separate, empirical question, and Section[6](https://arxiv.org/html/2608.19760#S6)takes it up with the scorer placed inside a live training loop\.

## 6The training layer: credit signals inside a live training loop

The audit’s natural objection is that fidelity to replay might not matter if the credit still trains a better policy\. We closed the loop: seven training arms — outcome\-only, implicit credit, judge credit, their shuffled and inverted controls, and a reduced\-resolution replay\-truth arm — trained under common random numbers \(CRN\) and evaluated on 128 held\-out tasks; the full seven\-arm table is Table[3](https://arxiv.org/html/2608.19760#A5.T3)in the appendix\. No arm reliably beats the untrained base policy \(0\.4220\.422;54/12854/128\), and every one of the six pre\-registered confirmatory comparisons came back inconclusive under the frozen±3\\pm 3pp equivalence band with Holm correction; none of the three verdict lines fired\. We report this as inconclusive, not as “no difference”: implicit credit trained2\.32\.3pp below its own shuffled control \(Holmp=0\.43p\{=\}0\.43\) and7\.07\.0pp below outcome\-only training \(p=0\.91p\{=\}0\.91\), and neither gap is resolvable at this power\. What the experiment rules out is any effect large enough to survive its own design; what it cannot do is certify equivalence\.

The power shortfall is itself a pre\-registration finding: the frozen proxy inverted, leaving the minimum detectable effect at≈11\.8\{\\approx\}11\.8pp against the registered±3\\pm 3pp band \(Section[7](https://arxiv.org/html/2608.19760#S7)’s reading rule\); the full account is a pre\-registration\-instrument failure story, Appendix[A](https://arxiv.org/html/2608.19760#A1)\.

One arm\-seed carries an instrument note rather than a result — a format collapse, not a competence collapse; the note, with its integrity lesson, is in Appendix[G](https://arxiv.org/html/2608.19760#A7)\.

Yet the checkpoints are not interchangeable\. On held\-out states the seven arms’ policies agree in their discrete choices — measured gaps\+0\.41\+0\.41pp \(p=0\.343p\{=\}0\.343, Stage 1\) and\+0\.50\+0\.50pp \(p=0\.185p\{=\}0\.185, Stage 2\) against the frozen A3B bar of≥5\\geq 5pp atp<0\.05p<0\.05— while their full action*distributions*separate cleanly: between\-arm Jensen–Shannon divergence exceeds within\-arm by2\.6×2\.6\\times\(0\.05200\.0520against0\.01980\.0198; restricted\-permutationp=0\.0001p\{=\}0\.0001\) — credit moved where the policies put their probability, without \(yet\) moving what they do\.

The frozen record’s own summary of this experiment is one sentence, and we quote it rather than paraphrase:*“Credit source leaves a measurable signature in the policy’s output distribution — arms cluster by instrument family \(rho\-based vs judge\-based\), not by information content — yet this signature does not reach greedy action selection: checkpoints agree on actions at the same rate whether or not they share a credit rule\.”*Two caveats travel with the sentence wherever it appears\. The masked arm moved far less than any other \(adapter norm1\.371\.37against≈4\.7\{\\approx\}4\.7for the dense arms\), so its position in any clustering is confounded with how little it moved — the divergence result survives removing it entirely \(0\.02120\.0212within\-arm against0\.04210\.0421between\-arm;n=16n\{=\}16andn=80n\{=\}80checkpoint pairs\)\. And the Stage\-2 canonicalizer initially normalized raw generations without first extracting the action, producing spuriously unique strings; the error is retained on the record, and every number here is from the corrected pass\. Two further checkpoints with elevated canonicalization\-failure counts were flagged per the pre\-registration rather than silently averaged in, and the format\-collapsed arm\-seed \(Appendix[G](https://arxiv.org/html/2608.19760#A7)\) was excluded from all primary analysis by pre\-registration\.

The phrase*not by information content*is licensed by a pre\-registered partition comparison, fixed before the checkpoint\-pair matrix was computed: the instrument partition separates the checkpoints in both stages \(500\-state bank:\+0\.0346\+0\.0346,p=0\.0002p\{=\}0\.0002;nW=30n\_\{W\}\{=\}30/nB=141n\_\{B\}\{=\}141cross\-arm pairs\), the information partition in neither \(−0\.0126\-0\.0126,p=0\.9777p\{=\}0\.9777;36/13536/135\); the full two\-stage decomposition, with its estimator and turn\-1 notes, is in Appendix[H](https://arxiv.org/html/2608.19760#A8)\. What the weights remember, then, is which instrument scored them — and the dose analysis below shows that even this signature is fully accounted for by how many optimizer steps each instrument’s credit sparsity bought\.

The instrument signature has a mundane explanation, and the explanation survives a positive control\. Credit rules that zero out many turns drop those turns from the training batch — one filter line in the update step — so sparser credit buys fewer optimizer steps and smaller parameter displacement\. Controlling for realised parameter\-change magnitude removes the instrument correspondence entirely \(partial Mantelρ=\+0\.078\\rho\{=\}\+0\.078on realised credit scale,p=0\.774p\{=\}0\.774\), against the positive control’s zero\-order association — credit sparsity — which the same test certifies at\+0\.912\+0\.912\(p=0\.0001p\{=\}0\.0001;n=21n\{=\}21arm pairs, non\-independent, both tests\)\. The mediation evidence carries its own strength label: the pair set is small and non\-independent, the association is robust to removing the sparsest arm; the design remains a partial\-correlation design — no∥Δ​W∥\\lVert\\Delta W\\rVert\-matched comparison exists — and the mediation claim is stated at that strength\. The matched comparison was permanently cancelled by ruling, for three recorded reasons in the ruled order — science first, resources last: the partial correlation already answers the question; the design has an inherent flaw \(∥Δ​W∥\\lVert\\Delta W\\rVertoverlap across arms exists only across rounds, so caliper matching necessarily introduces a round confound, and round covaries with training volume\); and cost against a calendar in which writing had not started\. The ruling ships verbatim in Appendix[K\.5](https://arxiv.org/html/2608.19760#A11.SS5)\. What the weights remember about their credit instrument is, on this evidence, how much training its sparsity allowed — dose, not doctrine\.

The natural rescue for the null — that the substrate, not the credit, was at fault — was given its own experiment and returned a negative of its own\. With the three diagnosed substrate defects repaired, outcome\-only training diverged in every configuration tried: at the original hyperparameters, at reduced learning rate \(5​e−5→2​e−55\\mathrm\{e\}\{\-\}5\\to 2\\mathrm\{e\}\{\-\}5\), and at five\-fold tighter gradient clipping \(1\.0→0\.21\.0\\to 0\.2\), each run’s pre\-clip gradient norm escaped one to several batches before KL breached its guardrail, under per\-step norm clipping throughout\. Divergence insensitive to two orthogonal stabiliser knobs, originating below the clip, indicates accumulated directional drift rather than oversized single steps: the stabiliser family and the corrected advantage signal are structurally mismatched\. The method line was closed by the frozen criterion — no configuration reached evaluation — and the trainability of the corrected substrate is not established\. The null of the training study \(tag KS2\) therefore cannot be laundered into a substrate complaint; the complaint was tested and failed to train at all\.

Finally, the practitioner’s shortcut fails first as a detector and only then earns its keep as a cost rule\. A confidence\-only router — frozen in advance as a replay\-free decision rule, its threshold an order statistic on the policy’s own confidence, its inputs free at inference time — routes low\-confidence turns to the judge and recovers11\.911\.9% of pivotal turns \(Wilson 95%\[9\.4,14\.9\]\[9\.4,14\.9\];n=540n\{=\}540\), against the13\.113\.1% of all turns it routes: chance\-level recall, the mechanism being exactly Section[5](https://arxiv.org/html/2608.19760#S5)’s — the stuck, pivotal steps are the high\-confidence ones, so a confidence threshold is aimed away from them \(exploratory, pre\-registered as such\)\. The two13\.113\.1% figures coincide by definition: the routing threshold was set so the routed fraction equals the no\-counterfactual rate by construction \(ROUTE\_NUMBERS\.md:8\-\-9\)\. The rule’s safety has two layers, only one by construction: on high\-confidence steps the policy\-gradient signal is inert \(∇log⁡π≈0\\nabla\\log\\pi\\approx 0\); the absorbing\-step half is an audit finding —σfloor\\sigma\_\{\\mathrm\{floor\}\}is replay\-derived, invisible to the router ex ante\. As a cost mechanism the same threshold is well\-behaved: it cuts judge calls by13\.113\.1% at per\-turn and14\.014\.0% at per\-trajectory granularity, and neither may be read alone\. We release the rule with its negative result attached — a rule that travels without its evaluation will be used for the thing it cannot do \(sweep and cost account: Appendix[J](https://arxiv.org/html/2608.19760#A10), Figure[3](https://arxiv.org/html/2608.19760#A10.F3)\)\. Entropy separates critical from non\-critical states at the distribution level \([Shen et al\. 2025](https://arxiv.org/html/2608.19760#bib.bib6): Cliff’sδ=0\.42\\delta=0\.42\); that separation and chance\-level recall at a cost\-matched threshold are not in conflict \(Appendix[L](https://arxiv.org/html/2608.19760#A12)\)\.

## 7What to do differently tomorrow

The audit’s negative results convert into named, practitioner\-facing artifacts, each of which exists because one of our own comparisons would have misled us without it:dose matching before any credit comparison\(any update step that drops zero\-weight examples lets the credit rule silently set the training dose — our arms’ optimizer steps ranged from112112to88per round under identical budgets\);measured perturbation strength for every control\(a control named “shuffle” is not automatically an equal\-strength manipulation, and unmeasured it invalidated our own first family dissociation\);a routing rule that knows what it is for\(a cost mechanism, not a detector — full treatment in Section[6](https://arxiv.org/html/2608.19760#S6)\); andreading a training\-loop null\(every equivalence claim travels with the registered margin,±3\\pm 3pp,*and*the design’s minimum detectable effect,≈11\.8\{\\approx\}11\.8pp at 128 held\-out tasks, single seed — a null reported with its margin but not its detection floor invites “no effect” where the design can only say “no effect this large”\)\. The reporting tables, the one\-sentence reading rules, the frozen rule text, and the full MDE ladder are in Appendices[C](https://arxiv.org/html/2608.19760#A3)and[F](https://arxiv.org/html/2608.19760#A6)\.

## 8Evidence decay and an integrity taxonomy

Auditing credit signals produced a second record we did not plan for: a catalogue of integrity failures in our own pipeline, written down as they happened\. Sorting them yields four distinct questions an integrity check can answer — whether the object checked is the object the system loads, whether the bytes were correct when they were written, whether every item is still readable now, and whether the check preserves the evidence needed to act on it — and one recurring mistake\.*No single check covers all four dimensions; the failure mode throughout is assuming one check answers another’s question\.*

The catalogue then made a prediction, and its own next failure confirmed it: we recorded, before the next audit ran, that the next incident should land on one of the two never\-tested defences — and it did \(the pack\-vs\-repository check; the full arc, with the second defence still an open prediction, is in Appendix[A](https://arxiv.org/html/2608.19760#A1), beside the closure rule that caught its sibling failure\)\.

The most consequential failure ran the whole arc: a metadata inconsistency, noticed by a person rather than by a check, led to a static trace, an A/B quantification, and a full re\-replay confirming the move in the predicted direction \(magnitudes:12\.012\.0pp predicted,REDO\_REPORT\.md:19;12\.312\.3pp measured,REDO\_REPORT\.md:19\)\. All verdict classes were unchanged under the corrected instrument; the map rates moved materially\. The lesson is narrower than*verify your inputs*\. Every replica of the affected artefact was byte\-identical and every hash matched, because the defect was semantic: two instruments that are the same file are not thereby the same instrument\.

The same re\-replay met a pre\-registered gate and failed it\. Our protocol required at least2020of2727trajectories to be complete before the analysis could run; the run finished with1515of2828complete, and the analysis was withheld\. It was released afterwards at the adjudication layer rather than by the process that had stopped — in two separately recorded steps, on grounds quantified in Appendix[A](https://arxiv.org/html/2608.19760#A1), and on the condition that every quantity derived from the run carry the partial\-coverage label it carries throughout this paper\. The stop and the two releases are separately recorded, in that order, in the project’s decision record, whose entry also records that the binding threshold was a task\-brief invention whose trajectory\-level wording conflicted with the frozen pipeline’s turn\-level inclusion rule — the gate that fired was itself an unvalidated instrument\. We report the miss because a threshold that is reinterpreted when it binds is not a threshold, and because the label alone does not tell a reader that a gate was crossed to earn it\.

## 9Limitations, and what would change our mind

Every scope condition below is one we measured rather than assumed: the audit runs in a single environment with a binary outcome, and every claim is scoped accordingly\. The training\-loop experiments are single\-family and single\-scale \(Qwen2\.5\-7B, LoRA \(low\-rank adaptation\), offline\); the cross\-family arm formally replicates the structural result under the corrected instrument, not the training loop\. KS2 lacks a validated positive control, which is why its null is reported as inconclusive; three convergent checks — an expert\-cloning arm at−10\.9\-10\.9pp on held\-out evaluation \(exact McNemarp=0\.0488p\{=\}0\.0488,n=128n\{=\}128tasks,29/1529/15discordant\), measured behavioural displacement, and off\-policy fit — bound how badly the harness could be lying, without substituting for the control\. The cross\-family analysis set excludes26\.826\.8% of intervened turns \(n=1,082n\{=\}1\{,\}082; corrected instrument[1](https://arxiv.org/html/2608.19760#footnote1)\)\. The truncation’s direction is measured for Qwen only: excluded turns are high\-probability \(included\-minus\-excluded mean policy log\-probability−0\.70\-0\.70,n=1,768n\{=\}1\{,\}768\), which attenuates the correlation there; the Llama counterpart cannot be recomputed \(Appendix[B](https://arxiv.org/html/2608.19760#A2)\), so cross\-family conservativity is qualitative — and the families truncate unequally \(Qwen excludes13\.113\.1%,n=2,034n\{=\}2\{,\}034\)\. The fidelity estimates run at small effectivenn, with wide intervals stated wherever they appear\. Every zero\-ground\-truth statement carries its sampling resolution bound\. One mid\-run batch\-composition correction \(skip undefined turns, keep trajectories\) is disclosed with its byte\-level regression verification\. And the family\-by\-length interaction our design intended to test is unmeasurable in this data — the realized length distribution put4242of5050trajectories in the long bucket \(Qwen; the two shorter buckets kept 2 and 3 after amendments\) — so that motivating axis is dead here and inherited by future work\.

Our audit is confined to a single environment\. We note, however, that ALFWorld is not an arbitrary choice: it is a primary evaluation venue for the credit methods we audit \-\-\- the implicit\-credit instrument family we test reports its state\-of\-the\-art results on this very benchmark\.222The implicit\-credit instrument family we adapt\([Tan et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib7)\)and the closest step\-credit method\([Zhang et al\. 2026](https://arxiv.org/html/2608.19760#bib.bib11)\)report their headline results on ALFWorld\. StepOPSD evaluates at 1\.7B/3B model scale against our 7B/8B policies; any comparison carries that scale gap\. It is cited as an evaluation venue only\.Our audit therefore meets these methods on their own evaluative ground; the burden of showing that step\-level credit tracks causal contribution*elsewhere*falls on settings where such credit has not yet demonstrated success either\.

### Reproducibility statement

Every number in this paper is generated, not transcribed: a single script regenerates the complete ledger from raw artifacts, two independent regenerations must agree byte\-for\-byte before any release, and each ledger row carries its value, itsnn, and its source path\. Where a row’s provenance is composite, the chain is demonstrated rather than asserted — perturbing each source artifact separately and showing each column follows its own source\. All thresholds, exclusion rules, verdict orders, and analysis plans were frozen under signed, hash\-pinned pre\-registration tags before the data they govern existed, and the frozen files ship verbatim in the supplement, under the verified environment pins \(alfworld 0\.4\.2, textworld 1\.7\.0, numpy 2\.4\.6, scipy 1\.17\.1, pyyaml 6\.0\.3\)\. We release, through an anonymized repository: the replay archive \(29,402 files\), per\-turn and per\-trajectory summaries, credit and log\-probability dumps, trained adapters, evaluation outputs, the generator, and the ledger itself\. Two quantities are released as\-is with their deaths on record rather than recomputed: the common\-support medians, whose generating procedure was never archived and whose inputs predate the instrument correction — re\-deriving them would require new code we did not authorise\. One recomputation is released with its recovery story: the full\-set difference bootstrap, whose original script was recovered, committed as received, shown to reproduce the original run byte\-identically, and only then run on corrected inputs\. The integrity incidents of Section[8](https://arxiv.org/html/2608.19760#S8), including the ones our own checks missed, are catalogued in the appendix with their detection channel and their fix; we regard that catalogue as part of the reproducibility surface, since a number that cannot survive its own pipeline’s history is not reproducible in any sense that matters\.

## AI Use Statement

AI systems contributed substantively to this project: operating experimental pipelines under pre\-registered protocols, drafting prose, auditing drafts for consistency against frozen claim wording, and executing the generation of the number ledger from archived artifacts\. Authority remained with the human authors under pre\-registered governance: every experimental adjudication, threshold freeze, stopping criterion, and claim\-strength decision was made by human ruling, and every number in the main text traces to archived, hash\-verified artifacts; the central ledger regenerates byte\-identically from a single script\. Appendix[B](https://arxiv.org/html/2608.19760#A2)retains superseded values precisely because their artifacts are dead — they are disclosed, not recomputed\. The LLM judge and the policy models audited in this paper are its research subjects, and are distinct from any AI assistance used in its preparation; no experimental data, measurement, or verdict was produced by writing assistance\. Errors arising from AI assistance during this project are themselves documented and taxonomized in Section[8](https://arxiv.org/html/2608.19760#S8)\.

## Ethics Statement

This work audits the validity of machine\-generated training signals against executed environment replay in a synthetic household\-task environment \(ALFWorld\)\. It involves no human subjects, no personal data, and no sensitive content; the audited models are publicly released open\-weight checkpoints used under their licenses\. We report negative results about widely used credit signals so that training practice is not misdirected by unvalidated per\-step scores; we see no ethical risks specific to this study beyond those general to research on agent training\.

## References

- Chen et al\. \(2026\)Yanjun Chen, Yirong Sun, Hanlin Wang, Jinghan Wang, Xinming Zhang, Xiaoyu Shen, Wenjie Li, and Wei Zhang\.Exact is easier: Credit assignment for cooperative LLM agents\.*arXiv preprint arXiv:2603\.06859*, 2026\.
- Li et al\. \(2026a\)Mukai Li, Qingcheng Zeng, Tianqing Fang, Zhenwen Liang, Linfeng Song, Qi Liu, Haitao Mi, and Dong Yu\.Verified critical step optimization for LLM agents\.*arXiv preprint arXiv:2602\.03412*, 2026a\.
- Li et al\. \(2026b\)Zhongyi Li, Wan Tian, Jinju Chen, Huiming Zhang, Yang Liu, Yikun Ban, and Fuzhen Zhuang\.Counterfactual credit policy optimization for multi\-agent collaboration\.*arXiv preprint arXiv:2603\.21563*, 2026b\.
- Liu et al\. \(2026\)Jiale Liu, Huajun Xi, Shaokun Zhang, Yifan Zeng, Tianwei Yue, Chi Wang, Jian Kang, Qingyun Wu, and Huazheng Wang\.Who&when pro: Can LLMs really attribute failures in AI agents?*arXiv preprint arXiv:2607\.09996*, 2026\.
- Shah \(2026\)Jaineet Shah\.Causal agent replay: Counterfactual attribution for LLM\-agent failures\.*arXiv preprint arXiv:2606\.08275*, 2026\.
- Shen et al\. \(2025\)Leyang Shen, Yang Zhang, Chun Kai Ling, Xiaoyan Zhao, and Tat\-Seng Chua\.CARL: Criticality\-aware agentic reinforcement learning\.*arXiv preprint arXiv:2512\.04949*, 2025\.v3, 2026\-05\.
- Tan et al\. \(2026\)Hui\-Ze Tan, Xiao\-Wen Yang, Hao Chen, Jie\-Jing Shao, Yi Wen, Yuteng Shen, Weihong Luo, Xiku Du, Lan\-Zhe Guo, and Yu\-Feng Li\.Hindsight credit assignment for long\-horizon LLM agents\.*arXiv preprint arXiv:2603\.08754*, 2026\.
- Tan et al\. \(2025\)Weiting Tan, Xinghua Qu, Ming Tu, Meng Ge, Andy T\. Liu, Philipp Koehn, and Lu Lu\.Process\-supervised reinforcement learning for interactive multimodal tool\-use agents\.*arXiv preprint arXiv:2509\.14480*, 2025\.
- Zhang et al\. \(2025\)Zhang et al\.Who&when: Multi\-agent failure attribution\.*arXiv preprint arXiv:2505\.00212*, 2025\.ICML 2025 Spotlight\.
- Zhang \(2026\)Chenchen Zhang\.From reasoning to agentic: Credit assignment in reinforcement learning for large language models\.*arXiv preprint arXiv:2604\.09459*, 2026\.
- Zhang et al\. \(2026\)Yanfei Zhang, Xu Lin, and Chenglin Wu\.StepOPSD: Step\-aware online preference distillation for agent reinforcement learning\.*arXiv preprint arXiv:2605\.27140*, 2026\.

## Appendix AIntegrity: the four dimensions, the incident chain, and evidence decay

This appendix expands Section[8](https://arxiv.org/html/2608.19760#S8)\. The taxonomy, verbatim from the governance record:

Table 2:The four dimensions of the integrity taxonomy, each with the incident that named it and the defence adopted\.*No single check covers all four dimensions; the failure mode throughout is assuming one check answers another’s question\.*#### Semantic instrument identity \(extension clause\)\.

The chat\-template defect of Section[8](https://arxiv.org/html/2608.19760#S8)adds an extension to the Identity row: tokenizer and template belong to the*instrument’s*identity, and no manifest, hash, or closure rule can see a mismatch of this kind — two instruments that are the same file are not thereby the same instrument\.

#### The prediction arc, in full\.

Two of the four defences had never met the failure they exist to catch; we recorded, before the next audit ran, that the next incident should land on one of the two\. It did: the release pack had been verified repeatedly — every time against its own manifest rather than against the repository it was cut from, a check of internal consistency, not of being the thing we claim to ship\. The prediction predates the confirming diff, and the second untested defence remains an open prediction, stated as one rather than retired\.

#### The cleanest instance\.

A generator met a configuration failure and recorded it with our marker for a number that cannot be traced — the same marker a genuinely untraceable number receives\. The verdict survived; the reason it was reached did not, and the two conditions, which call for opposite responses, were indistinguishable by the time anyone read the output\.

#### Evidence decay \(the Persistence instance, retention inverted\)\.

An inventory check passes at 29,402 files discovered against 29,402 expected while one file is unreadable \[Tier 3,ALL\_EXPERIMENTS\_RECORD\.md:2037\]; the archive verification run records 29,401 match / 0 mismatch / 0 missing / 1 named unreadable \[Tier 3,ALL\_EXPERIMENTS\_RECORD\.md:2206\-2207\]\. The derived summary survives, so the number stays traceable while its re\-derivation is lost; the verified tarball is accordingly the*primary*copy of the replay evidence and the volume secondary\.

#### The withheld\-then\-released analysis: coverage, cost, and the pillar corrected by its own run\.

The gate paragraph of Section[8](https://arxiv.org/html/2608.19760#S8)has its pillars quantified here: this run covered1,082/1,225=88\.3%1\{,\}082/1\{,\}225=88\.3\\%of parseable turns \[Tier 3,REDO\_STATUS\.md:20\]; the original XFAM\-v1 analysis had itself proceeded at1,129/1,225=92\.1%1\{,\}129/1\{,\}225=92\.1\\%\[Tier 3,REDO\_STATUS\.md:41\]\. The second pillar as worded at the stop — the record’s claim that the frozen v3\.2 rule “would retain all 28” trajectories \[Tier 3,REDO\_STATUS\.md:38\-\-41\] — was corrected by the executed analysis, which retained 26 of 28 \[Tier 3,REDO\_REPORT\.md:27\]; the record’s claim overstates by two\. The release stands either way, since 26 clears the 20\-trajectory threshold under both readings, and the divergence is recorded in the decision record rather than smoothed here\. There were two releases, not one, on the same day and in sequence: the salvage ruling released the*analysis*; the under\-review annotations on the affected claim text were released only later, by a separate close\-out item, after its own condition passed\. The ruling\-mandated missingness disclosure is likewise reported with its structure visible: per\-bucket coverage is B111/11=1\.00011/11=1\.000\[0\.741,1\.000\]\[0\.741,1\.000\], B217/17=1\.00017/17=1\.000\[0\.816,1\.000\]\[0\.816,1\.000\], B30\.8810\.881\[0\.861,0\.898\]\[0\.861,0\.898\], overall0\.8830\.883, with all 142 missing and 1 unparseable turns falling exclusively in long\-bucket \(B3\) trajectories of length≥44\\geq 44\[Tier 3,REDO\_REPORT\.md:55\-\-70\]\. The stated flag criterion — a bucket is marked insufficient\-coverage when its Wilson 95% CI excludes the overall rate — fires for no bucket; that is not evidence of balanced coverage, because B3 dominates the universe and its CI contains the overall rate by construction, so the flag is structurally incapable of firing for the only bucket with missing data\. The missing turns sit at the cap\-trip end of long trajectories and are plausibly harder than average; the B3\-level numbers inherit that caveat\. Context of the stop: generation halted at the 13 GPU\-hour cap trip with 1,083 summaries written, 13\.17 GPU\-hours metered against a $40 cap \[Tier 3,REDO\_STATUS\.md:14,16\]\.

#### Two 2026\-08\-14 additions\.

\(i\) The packaging\-boundary defect of the main text is filed to the Retention family; mechanism:*closure\-rule blind spot — future citation*\. \(ii\) A comparator defect, self\-reported by the execution side: a column\-diff tool split rows on every pipe, including one escaped inside a field, and reported a correct ledger as FAILED\. The ledger was right; the checker was wrong\. This is a live instance of this section’s own meta\-requirement — the checks are themselves unvalidated instruments — and the better instance precisely because the error ran in the harmless direction: a comparator that calls a correct ledger FAIL will, another day, call a wrong one PASS\.

#### Fail\-closed, worked example\.

A task required re\-running a frozen procedure that did not exist and never had; the session stopped and escalated rather than reconstructing the specification from prose \[Tier 3,E051\_RERUN\_BLOCKED\.md:1\-\-6\]\. It pairs with the comparator instance above: one is a check that failed safe, one is a task that refused to improvise\.

#### A frozen power proxy, inverted\.

The KS2 adaptive rule computed power from the outcome\-only arm’s between\-seed spread, treated as an upper bound on the paired spread; realised paired spreads ran7\.67\.6to3535times that proxy — the anchor arm happened to be the most stable one, so the bound was inverted, not conservative, and the rule reported full power for a study underpowered at the registered band\. It was executed verbatim and escalated rather than adapted mid\-run: a power calculation frozen before the data is only as conservative as its proxy, and ours taught us which proxy not to freeze\.

#### Reference closure is not need closure\.

One failure is about the checks rather than the data\. Our closure rule verifies that every artefact cited by a governance document is in the release pack; it did not catch a directory left out entirely, because nothing cited it yet — the citation arrived a batch later, with the analysis that needed it\. The rule guarantees reference closure, not need closure\. We added no check, because need closure is not mechanically decidable and the defence that worked was already in place: the session that could not find the artefacts stopped and escalated instead of substituting a neighbouring one\.

#### A length check against a float\-saturated flow\.

A length check anchored to a document endpoint assumes the flow is incompressible: that removing content moves the anchor\. The assumption fails in float\-saturated regions — where a page range’s area is jointly allocated to floats and text, text removals re\-balance around the committed floats and release no page fraction, so the endpoint reads zero movement across full edit rounds while a word\-level diff certifies the removals as real\. The check’s unit \(endpoint position\) and the edit’s unit \(words\) live in different layers, and the discrepancy was resolved only by a downstream deletion probe, which localized the responsive region\. The instance is typographic; the pattern is not: a checker whose invariant lives below the layer being edited will silently report stasis\.

#### Defence status\.

Each dimension names a defence, and each defence is reported with its own validation status rather than a blanket claim \(statuses as frozen at the taxonomy’s 2026\-08\-09 ruling\):

The taxonomy was derived from incidents, so its validation is likewise incident\-supplied\. Two of its four defences have met a known\-positive only because a real failure happened to supply one; the other two have never been tested against the failure they are designed to catch, and hold by design rather than by demonstration\.We report the taxonomy as a way of reasoning about integrity checks, not as four validated instruments — claiming otherwise would be the same category of error this appendix catalogues\. No synthetic known\-positives were constructed for the two untested rows: writing is the critical path, and the limitation stated plainly is worth more than a hurried test\. We recorded that the next incident should land on identity or diagnosability, the two defences that had never met a known\-positive\. Recorded before the diff was run, the prediction was confirmed by e58 \(the pack\-vs\-repository check\), which supplied identity’s known\-positive; diagnosability remains outstanding as a live prediction\. The table is shown as frozen at its ruling date, with e58’s confirmation carried by the arc rather than by a silent status edit — an append\-only record updates by appending\.

#### A trim that outlived its premise\.

One typographic entry belongs with the rest: a negative vertical space inserted between a table caption and its body during an early compression round became a defect once the caption later grew — the table’s top rule came to overlap the caption’s final line\. The lesson generalises beyond typography: a compensation tuned to one state of an artefact is not annotated with the state it assumed, so it silently becomes wrong when the artefact changes under it\.

#### A note on identifiers\.

PC3\-series incident ids carry the PC3\- prefix; incident identifiers \(lowercase e52–e58\) and experiment identifiers \(uppercase E052–E058\) are different series that collide numerically and are never resolved into one another — renumbering an append\-only record would itself be an integrity edit of the class this appendix catalogues\. \(The prefix rule was an oral ruling first written to the record on 2026\-08\-19, after an exhaustive search — 189 governance documents, every local project root, and all unpacked archives — returned no earlier written instance; the record gains the rule by ruling, dated, rather than by a reconstructed memory of it\.\)

#### The week the taxonomy was tested\.

Five incidents in three days exercised every dimension of the catalogue, and the chain is reproduced verbatim in Appendix K\.5; what belongs here is what each one did to the record\. e52 \(persistence\): three heartbeat lines NUL\-zeroed in place, length unchanged — the file was sealed unrepaired, and append\-type logs joined the periodic read\-back that had previously covered only newly created governance files\. e53 \(a gate doing its job\): the pre\-registered MDE gate hard\-stopped a training diagnostic at zero GPU when the requirednnexceeded the frozen cap and the 5 pp target proved structurally unreachable on the intended held\-out split; a carve\-out that would have let the run proceed was computed, labelled not\-adopted because its motivation post\-dated seeing the failing number, and escalated — the amendment that resolved it re\-based the held\-out table and left the threshold untouched\. e54 \(diagnosability\): a filesystem stall under concurrent small\-file writes was diagnosed at the syscall level before any restart, and an intermediate misreading — a dead process taken for a finished one because a fresh file existed — is retained with its lesson: an exit code and a census, not the presence of output, decide success\. e55 \(identity, the e34/e46 shape again\): a dependency was declared missing after being checked in an interpreter the pipeline never uses; the false report nearly caused a substrate change, and the discipline it minted — existence checks run in the interpreter that will do the work, interpreter path recorded with the conclusion — is now standing\. e56 \(a scope breach, recorded rather than excused\): a sealed training script was modified in place instead of copied; the compensations were an opt\-in flag preserving every existing invocation, a bit\-exact regression of the default path against committed records, and the explicit note that “unchanged since seal” is no longer assertable for that file\. e57 \(a nominal dose that was not the delivered dose\): a control arm’s effective optimizer\-facing sample was roughly half its nominal collection because degenerate rollout groups carry zero advantage; the step target was still met, so no gate fired, but the gap is recorded as part of the arm’s interpretation rather than as a post\-hoc caveat\. Alongside the incident series, the record keeps a channel for assertions that entered through conversation rather than from a verified source — four relayed\-assertion instances and one unsourced reasoning error as of this submission’s record close, counted and classed separately because no lookup discipline could have caught the latter — each corrected by an appended entry, never by deletion\.

#### Estimator note \(Table[1](https://arxiv.org/html/2608.19760#S4.T1)\)\.

The shuffled control’s own interval may exclude zero without carrying signal: under marginal matching, the median of within\-trajectory rank correlations over small turn counts is not constrained to centre on zero — which is why the verdict gate is the family\-versus\-its\-own\-control comparison, not either interval’s position relative to zero\.

## Appendix BSuperseded and disclosed values

#### E051 full\-set difference, as published\.

The originally published value\+0\.0432\+0\.0432\[−0\.0903,\+0\.2044\]\[\-0\.0903,\+0\.2044\]has no artifact, no script, and therefore no recorded procedure and no recorded seed; it is disclosed here and not printed in the main text\. The main\-text disclosed re\-computation is the seeded one \(\+0\.0319\+0\.0319\[−0\.0903,\+0\.2000\]\[\-0\.0903,\+0\.2000\], script in repo, seed 11\) — a re\-runnable computation of the same quantity, not a reproduction of the original run — whose script was later shown to regenerate its artifact byte\-identically, and whose corrected\-instrument successor \(−0\.0188\-0\.0188\[−0\.1178,\+0\.0954\]\[\-0\.1178,\+0\.0954\]\) is what Section[4](https://arxiv.org/html/2608.19760#S4)reports\. That the two historical intervals share a lower bound suggests procedural similarity but does not constitute proof, and no same\-procedure comparison between them is computable\.

#### Common\-support medians\.

The common\-support medians \(\+0\.7673\+0\.7673cross\-family,\+0\.6757\+0\.6757KS1\) are released as\-is with their deaths on record: the generating procedure was never archived and cannot be rebuilt, and the cross\-family side’s inputs predate the instrument correction\. No re\-derivation was authorised; no claim rests on them\.

#### The Llama selection check\.

The included\-minus\-excluded log\-probability check of Section[3](https://arxiv.org/html/2608.19760#S3)exists for Qwen only: the Llama counterpart would need the corrected\-instrument analysis set, whose membership was not separably recorded, so the check does not exist for Llama and cannot be reconstructed\.

#### Pre\-redo instrument values\.

All pre\-redo Llama\-side quantities \(the pre\-redo T3 values, the pre\-redo measurability rates, and their derivatives\) are retained in the ledger under explicit SUPERSEDED / NOT\-citable labels and appear nowhere in this paper’s claims, except where a pre\-correction value is quoted, explicitly labeled, solely to demonstrate robustness across the instrument fix\.

#### E057\.

The contaminated\-era family\-residual observation is void and is recorded here in one line only\.

## Appendix CThe protocol, in full

#### The dose\-matching table\.

One reporting table per credit comparison: surviving examples, optimizer steps, tokens updated, realised parameter displacement \(free for LoRA adapters via the trace identity, no materialisation\), and the measured strength of every control — with the behavioural measure in the last column\. The reading rule is one sentence: if the behavioural column is monotone in the dose columns, the comparison has measured dose, not credit\. In our own arms, optimizer steps ranged from112112to88per round under identical budgets\.

#### Measured strength, worked\.

Within\-trajectory shuffling changed90\.490\.4% of positions for our continuous credit but only26\.026\.0% for the tie\-heavy discrete judge scores, so comparing the two families against “their shuffles” confounded information destruction with perturbation magnitude\. Every control should ship with its fraction\-changed, displacement, and rank\-correlation against the original; our inversion control’s assumed−1\-1correlation held exactly, but held*because we finally checked*\.

## Appendix DCross\-family descriptive partials

The partial correlations under the corrected instrument are reported descriptively, both estimators side by side: after conditioning on fluency, the Pearson partial correlation between implicit credit and the causal increment is−0\.086\-0\.086\(p=0\.015p\{=\}0\.015,n=792n\{=\}792; Llama, corrected instrument\), while the Spearman partial is−0\.019\-0\.019\(p=0\.591p\{=\}0\.591,n=792n\{=\}792\)[1](https://arxiv.org/html/2608.19760#footnote1)\. We draw no confirmatory claim from the nominally significant Pearson value: the recomputation was not registered, the two estimators disagree, and the missing turns are concentrated non\-randomly in the longest trajectories \(Section[8](https://arxiv.org/html/2608.19760#S8)\), so a selection effect cannot be excluded\.

## Appendix EThe seven\-arm results table

Table[3](https://arxiv.org/html/2608.19760#A5.T3)reports the full seven\-arm outcome that Section 6 summarizes: final\-round win rates per arm and seed, and the six pre\-registered confirmatory comparisons under the frozen±3\\pm 3pp equivalence band with Holm correction\. Every comparison is inconclusive; no verdict line fires\. The arm 5 seed 2 evaluation carries the format\-collapse instrument note of Appendix G and was excluded from all primary analysis by pre\-registration; it is printed here for completeness and flagged wherever a mean or SD includes it\.

Table 3:Seven\-arm training outcome: every pre\-registered confirmatory comparison is inconclusive under the frozen±3\\pm 3pp band \(C1–C4 TOST equivalence; C5–C6 one\-sided superiority; Holm over the six\), and no arm reliably beats the untrained base policy \(0\.422; 54/128\)\.Top: final\-round win rates on the frozen 128 held\-out tasks \(greedy;n=128n\{=\}128per arm\-seed; seed\-paired CRN seeds \{0,1,2\}\)\.†\\daggerarm 5 seed 2 is the format\-collapse instrument note of Appendix G, excluded from primary analysis by pre\-registration; the printed arm\-5 mean and SD include it and inherit the flag, and the registered\-exploratory sensitivity dropping it leaves all six comparisons inconclusive\. Bottom: paired comparisons; the design’s minimum detectable effect at thisnnand seed count is≈\\approx11\.8 pp \(Appendix F\), so “inconclusive” is the frozen reading, never “no difference”\. Data:runs/ks2/eval/final/<arm\>/<seed\>/eval\.json\(win rates\),runs/ks2/eval/r1/base\_control/s0/eval\.json\(base\),runs/ks2/CONFIRMATORY\_RESULT\.json\(comparisons\)\.

## Appendix FThe MDE ladder

Minimum detectable effects for the paired binary design of Section[6](https://arxiv.org/html/2608.19760#S6), at the registered±3\\pm 3pp band; every MDE carries its\(n,split\)\(n,\\mathrm\{split\}\)label, since the MDE moves with both\.

## Appendix GInstrument details and notes

#### The implicit instrument, in detail\.

The ratioρt\\rho\_\{t\}is computed by Eqs\. 6–7 of the HCAPO paper exactly, with the published constants \(Ttemp=5\.0T\_\{\\mathrm\{temp\}\}\{=\}5\.0, clip\[0\.8,1\.2\]\[0\.8,1\.2\]\)\. Hindsight conditioning is a single outcome\-injection line appended to the prompt — our addition, not HCAPO’s; the*policy*scoring mode uses the identical prompt without it, which keeps Section[5](https://arxiv.org/html/2608.19760#S5)’s fluency contrast clean\. Deviation note: KS1 rollouts run at temperature 0\.7, frozen in the pre\-registration; HCAPO’s published rollout temperature is 1\.0, and the deviation is a KS1 design choice, logged\.

The judge\-family adaptation preserves the TARL judge’s prompt structure\([Tan et al\. 2025](https://arxiv.org/html/2608.19760#bib.bib8)\), response contract, and\{1,0,−1\}\\\{1,0,\-1\\\}scale\. TARL’s published judge receives ground\-truth tool\-call annotations; ALFWorld has none, so the judge runs without them — a disclosed deviation from TARL’s regime, and the condition under which such judges are actually used during training\.

One arm carries an instrument note rather than a result\. The inverted\-credit arm’s third seed collapsed to near\-zero evaluation not because inverted credit destroyed the policy’s competence but because training degraded its output format:87\.787\.7% of that seed’s actions embedded the action tag inside the action text, making them inadmissible to the environment, where every other arm\-seed sits at or near zero\. The format gate passed it, because the gate tests for loops and command\-likeness, not tag placement — an integrity lesson \(Section[8](https://arxiv.org/html/2608.19760#S8)\) arriving through the training layer\.

## Appendix HThe pre\-registered partition decomposition \(E031\(b\)\)

The phrase*not by information content*is licensed by a comparison that was fixed in advance rather than chosen afterwards\. The pre\-registration froze two competing partitions of the seven training arms — one grouping them by which instrument produced the credit, one grouping them by whether the credit carried task information — together with the criterion that decides between them, before the checkpoint\-pair matrix was computed\. The instrument partition won in both stages on both criteria: on the 500\-state bank, mean between\-partition JS exceeds mean within\-partition JS by\+0\.0346\+0\.0346\(p=0\.0002p=0\.0002;nW=30n\_\{W\}\{=\}30within\-partition andnB=141n\_\{B\}\{=\}141between\-partition cross\-arm checkpoint pairs\), while the information partition separates the same checkpoints in neither stage \(Table[4](https://arxiv.org/html/2608.19760#A8.T4)\)\. What the weights remember is which instrument scored them — Section[6](https://arxiv.org/html/2608.19760#S6)’s reading; the decomposition below is its full evidential basis\.

Table 4:The pre\-registered instrument partition separates the checkpoints; the information partition does not\.Each row reports mean between\-partition minus mean within\-partition JS divergence over cross\-arm checkpoint pairs, under the partition named in column 1; positive means checkpoints sharing a group are more similar to each other than to the other group\. Partitions, criterion, and the reading to record were frozen ina3b\-prereg\-v1before the matrix was seen; each partition’sppis a restricted permutation test under the pre\-registered within\-seed scheme \(10,000 draws\), the scheme attribution following the pre\-registration\. Both partitions divide the same 171 cross\-arm pairs; the split differs, so the two rows carry differentnW/nBn\_\{W\}/n\_\{B\}\. Data:a3b\_stage1\_structure\.json,a3b\_stage2\_structure\.json\.
## Appendix IRelease inventory

Items released through the anonymized repository \(counts from the sealed final\-state record\):

## Appendix JSupplementary figures

Figure 2:Perturbation strength does not order the checkpoints’ distributional positions: the position readout is not a dose meter for information destruction along the magnitude axis\.Each contrast pair’s JS position relative to the within\-arm band \(%\), across training rounds r1–r3 \(marker shade\), against the measured strength of its perturbation — fraction of credit positions actually changed: shuffle\-ρ\\rho0\.90430\.9043, shuffle\-judge0\.26020\.2602, inversion1\.00001\.0000\(n=288n\{=\}288trajectories each;runs/pc2/a3b\_perturbation\_strength\.json\)\. Position values are the nine round\-by\-contrast cells ofruns/pc2/a3b\_position\_monotonicity\.json; the pre\-registered monotonicity test returnsp=0\.9413p\{=\}0\.9413\(10k perm;n=6n\{=\}6adjacent comparisons; grid3×33\{\\times\}3, randomization unit = contrast,k=3k\{=\}3\)\. Four qualifiers ride this figure, per its record: the strongest perturbations sit in a saturated regime of the readout; separation is monotone in information*destruction*; the non\-monotonicity is confined to the magnitude axis; and the judge\-shuffle pair carries no positional signal\.#### The cost account\.

At the registered threshold,4343of5050baseline judge calls remain; the two cost granularities move in opposite directions across the sweep \(Figure[3](https://arxiv.org/html/2608.19760#A10.F3)\), so neither substitutes for the other\. Two disclosures travel with these numbers: the per\-trajectory denominator 50 is the frozen value and the flattering one — the analysis set spans 48 trajectories \(seed010 and seed020 have no complete turns\), and the 48\-based figure is0\.10420\.1042; and the confidence input is a per\-token geometric mean, which runs high for multi\-token actions\. Route to save money, not to find the steps that matter\.

Figure 3:\[Exploratory — R\_ROUTE\] The confidence router recovers pivotal turns at chance level at every pre\-registered threshold — its recall never exceeds the matched random\-routing baseline; its two cost granularities move in opposite directions, so neither may be read alone\.Left: recall of pivotal turns \(pivotal==storedAreplay≠0A\_\{\\mathrm\{replay\}\}\\neq 0; zeros are resolution\-bounded, Section[2](https://arxiv.org/html/2608.19760#S2)\) across the six pre\-registered threshold multipliers, with Wilson 95% band \(n=540n\{=\}540pivotal turns atθ∗\\theta^\{\*\}\); the dashed curve is the matched random\-routing baseline \(the routed fraction\), and the dotted line marks the baseline0\.13070\.1307at the registered thresholdθ∗\\theta^\{\*\}, against recall0\.11850\.1185\[0\.0939,0\.1485\]\[0\.0939,0\.1485\]— chance\-level, never exceeding the matched baseline at any of the six multipliers\. Right: judge\-call reduction at per\-turn and per\-trajectory granularity; the curves cross directions across the sweep, and neither curve may be read as a single unlabelled cost figure\. Sweep is sensitivity only; the single main result is multiplier 1\.0\. Data:route\_pack/artifacts/route\_theta\_sweep\.json,route\_pack/route\_retrospective\.json\(frozen prereg1814166…\)\.Figure 4:Measurability of causal ground truth is model\-dependent in both directions: the family with more undefined counterfactuals is the one with more causal signal where they exist\.Bars: fraction of turns with no policy\-supported counterfactual \(Qwen13\.113\.1%\[11\.7,14\.6\]\[11\.7,14\.6\],n=2,034n\{=\}2\{,\}034intervened; Llama26\.826\.8%\[24\.2,29\.5\]\[24\.2,29\.5\],n=1,082n\{=\}1\{,\}082; corrected instrument[1](https://arxiv.org/html/2608.19760#footnote1)\) and fraction of complete turns that are pivotal \(Qwen30\.530\.5%\[28\.4,32\.7\]\[28\.4,32\.7\],n=1,768n\{=\}1\{,\}768; Llama38\.338\.3%\[34\.9,41\.7\]\[34\.9,41\.7\],n=792n\{=\}792\); Wilson 95% intervals; the two divergences run in opposite directions\. The absorbing axis is near\-flat across families and is reported here rather than plotted:σfloor=0\\sigma\_\{\\mathrm\{floor\}\}\{=\}0at86\.086\.0%\[84\.3,87\.6\]\[84\.3,87\.6\]of Qwen’s and80\.680\.6%\[77\.7,83\.2\]\[77\.7,83\.2\]of Llama’s complete turns; everyAreplay=0A\_\{\\mathrm\{replay\}\}\{=\}0turn carries the resolution bound of Section[2](https://arxiv.org/html/2608.19760#S2)\(unexcluded\|Δ​p\|≤0\.632\|\\Delta p\|\\leq 0\.632at one\-sided 95%\)\. Data:measurability\_counts\_\{ks1,xfam\_redo\}\.json; full three\-axis map: Figure[5](https://arxiv.org/html/2608.19760#A10.F5)\(appendix\)\.Figure 5:Where per\-step causal ground truth can be measured depends on the model — in both directions\.For each family, three fractions of the replay map: turns with no policy\-supported counterfactual \(Qwen2\.5\-7B 13\.1%,n=2,034n\{=\}2\{,\}034intervened turns; Llama\-3\.1\-8B 26\.8%,n=1,082n\{=\}1\{,\}082, corrected instrument[1](https://arxiv.org/html/2608.19760#footnote1)\), pivotal turns \(Areplay≠0A\_\{\\mathrm\{replay\}\}\\neq 0: 30\.5%,n=1,768n\{=\}1\{,\}768; 38\.3%,n=792n\{=\}792\), and absorbing turns \(σfloor=0\\sigma\_\{\\mathrm\{floor\}\}\{=\}0: 86\.0%,n=1,768n\{=\}1\{,\}768; 80\.6%,n=792n\{=\}792\)\. Error bars are Wilson 95% intervals throughout — Qwen:\[11\.7,14\.6\]\[11\.7,14\.6\],\[28\.4,32\.7\]\[28\.4,32\.7\],\[84\.3,87\.6\]\[84\.3,87\.6\]; Llama:\[24\.2,29\.5\]\[24\.2,29\.5\],\[34\.9,41\.7\]\[34\.9,41\.7\],\[77\.7,83\.2\]\[77\.7,83\.2\]respectively\. The large divergence is the first bar — Llama lacks a policy\-supported counterfactual at twice Qwen’s rate — yet the pivotal fraction runs the*other*way, so neither family is uniformly harder to audit\. All zero\-valuedAreplayA\_\{\\mathrm\{replay\}\}turns are resolution\-bounded \(\|Δ​p\|≤0\.632\|\\Delta p\|\\leq 0\.632, Section[2](https://arxiv.org/html/2608.19760#S2)\)\. Data:measurability\_counts\_ks1\.json,measurability\_counts\_xfam\_redo\.json\.These rates are reported as an observation, not as a predictor, and the observation is a single\-family one: for Qwen, an occupancy\-style model built from the policy’s own action statistics ranks turns correctly — observed completion rises from 0\.650 to 0\.981 across its predicted deciles — while missing the aggregate level by 20 percentage points, so the ranking is trustworthy and the level is not; the predictor’s uniform\-residual assumption makes it an upper bound and therefore optimistic by construction, and no pre\-GPU estimate of the measurable fraction is claimed for either family\.

Figure 6:An occupancy\-style model of the policy’s own action statistics ranks turns by measurability but does not level\-calibrate\.KS1/Qwen; the cross\-family replicate is reported numerically in §5\. Single\-family presentation is the figure’s specification: the predictor is reported as a one\-family observation, and the ranking\-vs\-level contrast \(observed completion rising0\.650→0\.9810\.650\\to 0\.981across predicted deciles against a 20\-percentage\-point aggregate level miss\) is stated in Section[3](https://arxiv.org/html/2608.19760#S3)\.n=2,034n\{=\}2\{,\}034intervened turns; dataruns/ks1xfam/measurability\_predictor\.json\(ks1key\)\.
#### Pre\-registered secondaries of the judge audit, reported\.

Agreement of the primary judge \(Qwen2\.5\-72B\) with the anchor judge \(GPT\-4\.1, the audited method family’s own judge, frozen 11\-trajectory selection\) is exact74\.174\.1% \(Wilson 95%\[68\.0,79\.4\]\[68\.0,79\.4\],n=224n\{=\}224turns\), Cohen’sκ=0\.496\\kappa=0\.496, pooled Spearman0\.4840\.484\(runs/collect\_v2/judge\_anchor\_agreement\.json\) — the judge\-family credit signal is substantially judge\-model\-sensitive\. The self\-preference check \(self\-minus\-crossρ\\rhoscorer\) detected none:−0\.011\-0\.011, CI\[−0\.077,0\.064\]\[\-0\.077,0\.064\]\(runs/collect\_v2/sec7\_self\_preference\.json\)\. The family×\\timeslength interaction registered alongside them is not testable in this run \(Section[9](https://arxiv.org/html/2608.19760#S9)\)\.

## Appendix KPre\-registrations, prompts, and diagnostics \(verbatim\)

#### Rendering policy\.

Every document in this appendix is included*verbatim*from its frozen source; nothing is summarized and nothing is reflowed\. Two rendering tiers apply\. \(i\) English\-major sources are typeset below via a recorded, content\-preserving glyph transliteration for the PDF engine \(§→\\lx@sectionsign\{\\to\}S,Δ→\\Delta\{\\to\}Delta,ρ→\\rho\{\\to\}rho,→⁣→\\rightarrow\\,\{\\to\}\-\>,≤/≥→\\leq/\\geq\{\\to\}<=/\>=,±⁣→\\pm\{\\to\}\+/\-,×⁣→\\times\{\\to\}x, ✓\-class marks→\{\\to\}\[OK\], crosses→\{\\to\}\[X\]/\[FAIL\], isolated CJK tokens→\{\\to\}\[ZH\]\); the byte\-exact file, whose sha256 is stated per item, is authoritative and ships in the supplementary pack\. \(ii\) Chinese\-major sources \(the R\_ROUTE pre\-registration, the PC3 verdict, the DECISIONS excerpt body\) ship byte\-exact in the supplementary pack with sha256 and size stated here; where the paper needs their structured content readable, an English rendering that passed the element\-by\-element faithfulness check of the assembly record is given, and labelled as a rendering\. \(iii\) Double\-blind redaction: author names in sign\-off and ruling blocks are rendered as \[AUTHOR\-1\] in this PDF and in the supplementary files; the stated sha256 hashes refer to the unredacted originals retained by the authors, and the unredacted files ship with the camera\-ready\.

### K\.1Pre\-registrations, with amendments and signed tags

#### KS1 \(the audit\)\.

\#KILLSHOT\_PREREG\-\-\-KS1,projectcredit\-validity\-paradox\(v2,dual\-familyaudit\)

Status:PRESENTEDFORSIGN\-OFF\.Datacollectionblockeduntil\[AUTHOR\-1\]signs\(S9\)\.

Supersedes:v1skeleton\(handoffS4\)\.DirectionperratifiedOptionB\(2026\-07\-31\)\.

\#\#1\.Question

Twofamiliesofper\-stepcreditareusedtotrainLLMagents:

\-\*\*judgefamily\*\*\(explicitLLM\-judgeturnscores;known\-inaccurateonattributiontasks,accuracylength\-dependent\)

\-\*\*implicitfamily\*\*\(outcome\-conditionedlogprobratios,HCAPOEqs\.6\-\-7;nevervalidatedagainstcausalgroundtruth\)

KS1reconcilesbothagainstenvironment\-replaygroundtruthinareplayablesingle\-agenttoolenvironment,pertrajectory\-lengthbucket,andissuesaper\-familyH\-branchverdict\.

\#\#2\.Environment/models\(frozen\)

\|Item\|Value\|

\|\-\-\-\|\-\-\-\|

\|Environment\|ALFWorld\(TextWorldbackend\),determinismverifiedbeforeanycollection\|

\|Policy\|Qwen2\.5\-7B\-Instruct\(HFrevisionpinnedatharnesscommit\),vLLM,temp0\.7samplingforrollouts\|

\|Implicit\-creditscorer\|Samepolicycheckpoint\(faithfultoHCAPO\);logprobevaldeterministic\|

\|Cross\-familyimplicitcontrol\|Llama\-3\.1\-8B\-Instructasrho\_tscorer\|

\|Judge\(primary\)\|Qwen2\.5\-72B\-Instruct\(DECISIONA,ratified2026\-07\-31;deviationfromTARL’sGPT\-4\.1judgeloggedinPROVENANCESb\)\|

\|Judgeanchorcontrol\|GPT\-4\.1on12trajectories\-\-\-4perlengthbucket,lowestseedswithineachbucket\(frozenoncebucketsareknown\)\|

\|n\|50trajectories,seeds0\-\-49,fixedtasklistcommittedbeforecollection\|

\|Replaytruth\|atturnt:K=4alternativeactionsresampledfromsamepolicysnapshot,eachrolledtoterminal\>=3x;\*\*plusthefactualactiona\_tre\-executed\>=3xateveryintervenedturn\*\*;alloutcomedistributionsrecorded\|

\#\#3\.Metriccards

\#\#\#3\.1replay\_credit\(groundtruth\)

\-Definition:replayadvantageA\_replay\(t\)=mean\(outcome\|factual\-actionreplaysatt,\>=3\)\-mean\(outcome\|alternativerolloutsatt,K=4x\>=3\)\.Bothtermsarereplaydistributions;thesinglerealizedcontinuationisneverusedasthefactualestimate\.

\-Tool:harness‘replay\.py‘\(version=gitSHAatrun\)\.

\-Denominator:turnswith\>=Kx3completedreplays;incompleteturnsexcludedandcounted\.

\-Failuremodes:truncation/timeout\(bucketedseparately,S6\);envnon\-determinism\(blockedbysmoketest\)\.

\#\#\#3\.2implicit\_credit\(rho\_t\)

\-Definition:HCAPOEqs\.6\-\-7exactly\-\-\-pi\_hind\(a\_t\)=exp\(meantokenlogprobofa\_t\|s\_t,s\_final\),self\-normalizedbytrajectorymeanpi\_hind,clippedto\[C\_min,C\_max\]=HCAPOdefaults\(frompaperappendix;ifunpublished,C=\[0\.5,2\.0\]andloggedinPROVENANCE\)\.

\-Tool:‘score\_implicit\.py‘,readstrajectorystoreonly\.

\-Denominator:allactionturns\.

\-Failuremodes:prompt\-templatemismatchvsHCAPOappendixtemplates\(mitigated:templatesreconstructedfrompaperAppendixC\.2;deviationlogged\)\.

\#\#\#3\.3judge\_credit

\-Definition:TARL\-styleper\-turnscorefromLLMjudgegiventhecompletetrajectory\+outcome\.Scale:TARL’spublishedscale\(adoptedverbatimfromarXiv:2509\.14480prompt;adaptationforALFWorldactionvocabularylogged\)\.\*\*DeviationfromTARL\(logged,PROVENANCESb\):noground\-truthtool\-callannotationsexistforALFWorld,sojudgerunsinthew/o\-goldregime\.\*\*

\-Prompt:verbatim,appendix\-ready,committedas‘prompts/judge\_credit\_v1\.txt‘beforeanyscoring\.

\-Tool:‘score\_judge\.py‘,readstrajectorystoreonly\.

\-Denominator:allactionturns;unparseablejudgeoutputscountedandreported\(notsilentlyretriedmorethan2x\)\.

\#\#\#3\.4rank\_fidelity\(perfamily\)

\-Definition:within\-trajectorySpearmanrho\(primary\)andKendalltau\(secondary\)between\{rho\_t\}or\{judgescore\_t\}and\{A\_replay\(t\)\},computedpertrajectory,aggregatedasmedianwithbootstrap95%CI\(10kresamples\)\.

\-Also:signagreementrate\(creditabove/belowitstrajectorymedianvsA\_replayabove/belowitstrajectorymedian\),WilsonCIwhenn<50\.

\*\*Amendmentv3\.2\(signed2026\-07\-31,pre\-analysis\):trajectorieswith<4completeturnsare

excludedfromrank\_fidelitycomputationforbothfamiliessymmetrically\(completenessis

family\-independent\);excludedtrajectoriesarecountedandreportedperlengthbucket\.

Rationale:Spearmanon<4pointsisdegenerate\.Nothresholdortestspecaltered\.\*\*

\*\*Amendmentv3\.3\(signed2026\-08\-01,day\-11REVISEDrulingR5’;thiswordingsupersedesthe

draftwordingcarriedbytagks1\-prereg\-v3\.3\-signed\-\-\-authoritativeformistagged

ks1\-prereg\-v3\.3r2\-signed\):trajectorieswhoseA\_replayisconstantacrossallcompleteturns

areexcludedFROMrank\_fidelityCOMPUTATIONONLY,forbothfamiliessymmetrically,because

within\-trajectorySpearmanismathematicallyundefinedonaconstantvariable\.Thisisnota

data\-qualityjudgementandtheseturnsareNOTdiscarded:theyaretheprimarysampleofthe

R7null\-truthanalysisandentertheR10detectabilityboundsandR11step\-weightedsecondary

outcomeinfull\.Excludedtrajectoriesarecountedandreportedperlengthbucket,alongside

thev3\.2exclusions,witheffectivenstatednexttoeveryrank\_fidelitynumber\.Registered

sensitivity\(R5b,notprimary\):rank\_fidelityrecomputedonthesubsetwith\>=4

nonzero\-A\_replayturns;primaryremainsallSpearman\-computabletrajectories\.Nothreshold

ortestspecaltered\.\*\*

\#\#\#3\.5structural\_bias\(Delta,perfamily\)\-\-\-replacesglobalmean\-Delta

Delta\_t=normalizedcredit\-normalizedA\_replay\(bothz\-scoredwithintrajectory\)\.Noglobalmean\-Deltaclaimismade\.Threeconfirmatorystructuraltests,specifiednow:

\-\*\*T1Deltaxturn\-position\*\*:per\-trajectorySpearman\(Delta\_t,t/T\);aggregate=medianacrosstrajectories,bootstrap95%CI\(10k\)\.SignificantifCIexcludes0\.

\-\*\*T2Deltaxaction\-type\*\*:ALFWorldactionsbinnedintofrozencategories\{goto,take,put,open/close,clean/heat/cool,toggle,examine/inventory/look\};Kruskal\-\-WallisstatisticonpooledDelta\_t,butthep\-valueisobtainedby\*\*trajectory\-levelclusterpermutation\*\*\(categorylabelsre\-permutedperwholetrajectory,10kpermutations\)\-\-\-pooledasymptoticpisinvalidbecauseturnswithinatrajectoryarenotindependent\.Ifsignificant,Dunnpost\-hocfordirection\(descriptive\)\.

\-\*\*T3Deltaxpolicy\-logprob\(a\_t\)\*\*\-\-\-\*namedpredictedbiasfortheimplicitfamily\*:per\-trajectorySpearman\(Delta\_t,meantokenlogpi\(a\_t\|s\_t\)underthepolicywithouts\_final\);aggregateasT1\.Directionalprediction,registerednow:\*\*positivefortheimplicitfamily\*\*\(fluent/high\-probabilityactionsreceiveinflatedcreditregardlessofcausaleffect\)\.Nodirectionalpredictionforthejudgefamily\.

\-\*\*Multiple\-comparisoncorrection\*\*:theconfirmatorysetis3testsx2families=6hypotheses;Holm\-\-Bonferroniatfamily\-wisealpha=0\.05\.Anythingoutsidethese6isexploratoryandlabeledassuch\.

\-\*\*sigma\_floorscope\(Edit3\)\*\*:T1\-\-T3runon\*\*allturns\*\*asprimary\-\-\-censoringby\|Delta\_t\|wouldselectonthedependentvariable’smagnitudeanddistortcorrelationstructure\.Thecensored\(\|Delta\_t\|\>2sigma\_floor\(t\)\)versionsarereportedassensitivityanalysesonly\.Thesigma\_floorgateappliesexclusivelytomagnitudeclaimsoftheform"Deltaatturntissignificantlynon\-zero\."

\#\#4\.Controls\(samebatchasintervention\-\-\-non\-negotiable\)

1\.\*\*Replicanoisefloor\*\*:factual\-actionreplays\(\>=3xat\*every\*intervenedturn,perS2/S3\.1\)doubleasthenoise\-floorinstrument\-\-\-sigma\_floor\(t\)=SDofoutcomeacrossfactualreplicasatturnt;pooledsigma\_floorreportedperlengthbucket\.Any\|Delta\_t\|entersS3\.5testsonlyif\|Delta\_t\|\>2sigma\_floor\(t\);censoredturnsarecountedandreported\.

\#\#\#4\.5Compute\-fallbacksubsampling\(pre\-registered;trigger\+schemefrozennow\)

\-\*\*Trigger\*\*:firedif,atday10,<60%ofscheduledturn\-interventionsarecomplete,ORprojectedtotalrolloutsexceed1\.3xthebudgetestimatedatharnesssign\-off\(estimatecommittedwiththeharness\)\.

\-\*\*Degradationladder,appliedstrictlyinorder,eachsteploggedinDECISIONS\.md\*\*:

1\.Turnstratification:trajectorieswithT<=12keepfullper\-turnreplay;forT\>12,interveneonceil\(T/2\)turnssampledstratifiedbypositiontercile,seed=1000\+trajectory\_id\.

2\.K:4\-\>3alternativeactions\(replicasneverdropbelow3;factualreplaysneverdropped\)\.

3\.n:50\-\>40trajectories,droppinghighestseedsfirst\(seeds49\-\>40\)\.

\-Nootherdegradationispermitted;ifstep3isinsufficient,escalateto\[AUTHOR\-1\]\(RuleH\),donotimprovise\.

2\.Randomcredit,within\-trajectoryshuffledcredit,uniformcredit\-\-\-scoredthroughtheidenticalrank\_fidelitypipeline\.

3\.Cross\-familyscorercontrols\(S2\)\-\-\-self\-preferencecheckforbothinstruments\.

4\.Truncated/timeouttrajectories:separatebucket,neverpooledintorankcorrelations\.

\#\#5\.Lengthbuckets\(frozen\)

Primarybucketingbyturncount:\*\*B1:<=10turns;B2:11\-\-20;B3:\>=21\.\*\*

Secondary\(reportingonly\):contexttokensatfinalturn,cutpoints3K/6K/12K\(comparabilitywithWho&WhenPro\)\.

AllS3metricsreportedperbucketperfamily\.Bucketclaimsrequire\>=8trajectoriesinbucket,else"insufficientn"isreported,notanumber\.

\#\#6\.Decisionrules\(frozenatsign\-off;perfamily,primary=pooled,interaction=S7\)

Letrho=medianwithin\-trajectorySpearmanforthefamily;CI=bootstrap95%CI\.

\|Verdict\|Rule\|

\|\-\-\-\|\-\-\-\|

\|\*\*H4\*\*\(creditisfine;motivationnumbersweretask\-mismatch\)\|rho\>=0\.6AND\*\*no\*\*S3\.5structuraltestsignificantforthefamilyafterHolmcorrection\|

\|\*\*H1\*\*\(rank\-preservedbutstructurallybiased;mechanismpaper\)\|rho\>=0\.6AND\>=1S3\.5structuraltestsignificantforthefamilyafterHolmcorrection\(T3\-positivefortheimplicitfamily=theregisteredpredictionconfirmed\)\|

\|\*\*H3\*\*\(placebocandidate;biggeststory\-\>immediatelyaddtrainingexperiment\)\|CI\(rho\)contains0ANDrho<=0\.2\|

\|\*\*H2\-partial\*\*\(partialfidelity;analysisbranch\)\|0\.2<rho<0\.6,orCIstraddles0\.2\-\-0\.6band\|

\|\*\*INFEASIBLE\*\*\|day\-7gate:end\-to\-endreplayof2trajectoriesnotworking\|

\*\*Verdictevaluationorder\(fixed,Edit2\)\*\*:Controlsgate\-\>INFEASIBLE\-\>H3\-\>H2\(CI\-straddletakesprecedence\)\-\>H1\-\>H4\.AwideCIalwaysoverridesapointestimate;afamilycannotreceiveH1/H4whileitsCIstraddlesthe0\.2\-\-0\.6band\.

Controlsgate:iftheshuffled\-creditcontrol’srhoCIoverlapsthefamily’srhoCI,thefamily’sverdictdefaultstoH3regardlessofpointestimate\.

Allpercentagesreportn;WilsonCIwhenn<50\(RuleS\)\.

\#\#7\.Pre\-registeredsecondaryanalyses\(namednow,notpost\-hoc\)

\-\*\*Cross\-familycomparison\*\*:paireddifferenceinper\-trajectorySpearman\(implicit\-judge\),bootstrapCI;"familyXtrackstruthbetter"claimedonlyifCIexcludes0\.

\-\*\*Familyxlengthinteraction\*\*:per\-bucketrhomedians;monotone\-degradationclaimrequiresorderedbucketmediansANDnon\-overlappingadjacentCIs\.

\-\*\*Self\-preference\*\*:same\-familyvscross\-familyscorerrhodifference,sameCIstandard\.

\#\#8\.Scope,timebox,escalation

\-Claimslockedto"replayablesingle\-agenttoolenvironments"\(RuleH/L\)\.Anytemptationtowiden\-\>STOPandflag\.

\-Timebox14daysfromsign\-off;day\-7INFEASIBLEgate;negativeresultisafulldeliverable\.

\-Check\-ins:day\-7gate,RuleHflags,day\-14verdictonly\.

\-Everyexperiment:ALL\_EXPERIMENTS\_RECORDentry\(\[ZH\]\[ZH\]/\[ZH\]\[ZH\]\[ZH\]/\[ZH\]\[ZH\]/\[ZH\]\[ZH\]\[ZH\]/\[ZH\]\[ZH\]\[ZH\]\[ZH\]/\[ZH\]\[ZH\]\[ZH\]\[ZH\]\+PREREG/PROVENANCE/CONTROLS/SIDE\-EFFECTS\)beforeanynumberiscited\.

\#\#9\.Sign\-offblock

\-\[x\]DECISIONA:judgemodel=\*\*Qwen2\.5\-72B\-Instruct\*\*\(GPT\-4\.1anchor,12trajectories,4/bucket,lowestseeds\)

\-\[x\]Thresholdsfrozen\*\*withedits\*\*:\(1\)T2p\-valuebytrajectory\-levelclusterpermutation,10k;\(2\)fixedverdictorderControls\-\>INFEASIBLE\-\>H3\-\>H2\-\>H1\-\>H4,wideCIoverridespointestimate;\(3\)T1\-\-T3primaryonallturns,sigma\_floorcensoring=sensitivityonly,gatescopedtomagnitudeclaims\.

\-\[x\]\[AUTHOR\-1\]sign\-off:\*\*2026\-07\-31,ratifiedinconversation\("\[ZH\]\[ZH\]\[ZH\]\[ZH\]\[ZH\]\[ZH\]\[ZH\]\[ZH\]\.\.\.withedits"\)\*\*\.ThresholdsnowIMMUTABLE\.Datacollectionunlocked\.

#### KS1\-XFAM \(the cross\-family replication\)\.

\#KS1CROSS\-FAMILYAMENDMENT\-\-\-Llama\-3\.1\-8B\-InstructasPOLICY

Status:\*\*SIGNED2026\-08\-07,tag‘ks1\-xfam\-v1\-signed‘\.\*\*Countersignedby\[AUTHOR\-1\]inthe

ideationpacketof2026\-08\-07withtheS0reframingandtheS0\.1implicit/judgedistinction\.

ExecutionauthorisedinthepipelineorderofS8,underthe$60ceilingandthe$40

post\-collectionprojectionstop\.

\#\#0\.WHYTHISISANAMENDMENTANDNOTARE\-RUN\-\-\-threesimultaneouschanges

KILLSHOT\_PREREG\.md\*\*S2line19\*\*freezesthepolicy:

\>‘\|Policy\|Qwen2\.5\-7B\-Instruct\(HFrevisionpinnedatharnesscommit\),vLLM,temp0\.7samplingforrollouts\|‘

\*\*Thisisadesign\-levelfinding,notbookkeeping\.\*\*Swappingthepolicychanges\*\*three

thingsatonce\*\*,becauseKS1’sdesigncouplesallthreetothesamecheckpoint:

1\.\*\*Themeasuredobject\*\*\-\-\-therolloutdistribution,i\.e\.thetrajectoriesthemselves\.

2\.\*\*Themeasuringinstrument\*\*\-\-\-S2line20definestheimplicit\-creditscoreras\*"Same

policycheckpoint\(faithfultoHCAPO\)"\*\.Therho\_tinstrumentis\*\*madeof\*\*thepolicy\.

3\.\*\*Theruler\*\*\-\-\-S2line25buildsreplaygroundtruthbyresamplingalternatives\*"from

samepolicysnapshot"\*\.

Soapolicyswapswapstheobject,theinstrumentandtheruler\*\*simultaneouslyand

inseparably\*\*\.Nodesigncandecomposethatatanyn:itisapropertyofKS1’sarchitecture,

notofthisamendment’sbudget\.Anyresultmustthereforebereportedas\*"under

Llama\-3\.1\-8Baspolicy\-scorer\-and\-ruler"\*,neveras\*"KS1withadifferentmodel"\*\.

\#\#\#S0\.1Thewhole\-systemframingappliestotheIMPLICITfamilyONLY

Thisdistinctionisload\-bearingandmustappearwherevereitherfamilyisdescribed\.

\*\*Fortheimplicitfamilythewhole\-systemframingisCORRECT,anditisafeature,nota

limitation\.\*\*HCAPO’sscorer\*\*is\*\*thepolicybydefinition,andreplaygroundtruthis

definedover\*\*thepolicy’sownactiondistribution\*\*\.Policy,scorerandruleraretherefore

\*\*oneobject\*\*,andT3isacoherentsystem\-levelclaimaboutthatobject:

\>\*"apolicy’sownimplicitcreditdoesnottrackitsowncausalgroundtruth\."\*

ReplicatingT3underasecondpolicyfamilytestsexactlythatclaim,withnothingheld

artificiallyfixedthatthetheorysaysshouldvary\.

\*\*ForthejudgefamilyitdoesNOTapply\.\*\*ThejudgeisQwen2\.5\-72B\-Instructand\*\*doesnot

changewhenthepolicychanges\*\*,soforthatfamilytheswapisa\*\*cleansingle\-variable

change\*\*:sameinstrument,differentmeasuredobject\.Thisiswhythe\(descriptive\)judge

column,underpoweredasitis,isinterpretableinawaytheimplicitcolumnisnot\.

\*\*THENARROWERCLAIMTHISDESIGNCANNOTSUPPORT,statedsoitisneverimplied:\*\*thatthe

\*\*scoringinstrumentisbadindependentlyofthepolicy\*\*\.Fortheimplicitfamilythat

statementisnotevenwell\-formed\-\-\-thereisnoinstrumentseparablefromthepolicyto

evaluate\.Forthejudgefamilythedesignlacksthepowertoassertit\(S4\)\.\*\*Nodocument

arisingfromthisamendmentmayclaimthatimplicitcreditscoringisintrinsically

unfaithful;onlythatapolicy’sownimplicitcreditdoesnottrackitsowncausaltruth,in

thesystemstested\.\*\*

\*\*KS1’sfrozenprereg,itsanalysispipeline,andVERDICT\.mdareUNTOUCHEDandremainthe

recordforQwen2\.5\-7B\.\*\*NothingheremayreviseorreinterpretaKS1confirmatorynumber\.

\#\#1\.SCOPE\-\-\-oneprimaryendpoint

\#\#\#PRIMARY\(thesoleregisteredendpoint\):\*\*T3\*\*

‘T3=per\-trajectorySpearman\(Delta\_t,meantokenlogpi\(a\_t\|s\_t\)underthepolicywithouts\_final\)‘,

aggregatedasT1\(KILLSHOT\_PREREGS3\.5line73\),withtheregisteredKS1directional

prediction:\*\*positivefortheimplicitfamily\*\*\.

\*\*WhyT3andonlyT3\*\*\(\[AUTHOR\-1\]’sruling,reasoningrecorded\):T3\*is\*themechanismclaim\-\-\-the

fluencyecho,thatfluenthigh\-probabilityactionsreceiveinflatedcreditregardlessofcausal

effect\.Itisthefindingmostinneedofcross\-familysupport,andperS4itis\*\*theonly

quantitythisncanactuallyresolve\*\*\(effect\+0\.752againstanMDEof0\.116\-\-0\.127,roughly

six\-foldheadroom\)\.

\#\#\#DESCRIPTIVE,SAMEBATCH,PRE\-LABELLEDUNDERPOWERED\(notendpoints,noverdict\)

Familyfidelityforbothinstruments\(rho\)andthemeasurabilitymaparecomputedfromthesame

trajectoriesatnoextracostandreported\*\*withtheirMDEsprintedbesideeverypoint

estimate\*\*,explicitlylabelled\*underpowered,descriptiveonly\*\.\*\*Theycannotsupportor

refuteanythingunderthisamendment\.\*\*Reportingthemisforcompletenessandforwhatevera

futurebetter\-poweredstudycanpool\.

\*\*NOTreplicatedandnottobeinferred:\*\*therestoftheS3\.5battery,theHolm\-corrected

confirmatoryfamily,theS6verdictorder,self\-preference,precision@pivotal,cross\-family

paireddifferences\.\*\*NoH1/H2/H3/H4verdictisissued\.\*\*

\#\#2\.THEDIFFvsKS1

\|Element\|KS1\(frozen\)\|Thisamendment\|Changed?\|

\|\-\-\-\|\-\-\-\|\-\-\-\|\-\-\-\|

\|Policy\|Qwen2\.5\-7B\-Instruct\|\*\*Llama\-3\.1\-8B\-Instruct\*\*\|\*\*YES\*\*\|

\|Implicitscorer\|samepolicycheckpoint\|\*\*=Llama\-3\.1\-8B\*\*\|\*\*YES,bycoupling\(S2L20\)\*\*\|

\|Replay\-truthpolicy\|samepolicysnapshot\|\*\*=Llama\-3\.1\-8B\*\*\|\*\*YES,bycoupling\(S2L25\)\*\*\|

\|Judge\|Qwen2\.5\-72B\-Instruct,w/o\-gold\|Qwen2\.5\-72B\-Instruct,w/o\-gold\|no\-\-\-\*\*heldfixeddeliberately\*\*\|

\|Judgeprompt\|frozenTARL\-derived\|unchanged\|no\|

\|Trajectories\|50collected/37effective\|\*\*~=25\-\-30collected\*\*\|\*\*YES\(scope\)\*\*\|

\|ReplayK\|K=4alts,\>=3rolloutseach,factualre\-executed\>=3x\|unchanged\|no\|

\|Temperature\|0\.7rollouts\|unchanged\|no\|

\|rho\_tdefinition\|HCAPOEqs6\-\-7\|unchanged\|no\|

\|T3statistic\|per\-trajSpearman\(Delta\_t,meantokenlogpi\)\|unchanged\|no\|

\|\*\*T3’sstatus\*\*\|oneoftheS3\.5battery\|\*\*SOLEPRIMARYENDPOINT\*\*\|\*\*YES\(v2narrowing\)\*\*\|

\|\*\*Familyfidelitystatus\*\*\|confirmatory\|\*\*descriptive,underpowered\*\*\|\*\*YES\(v2narrowing\)\*\*\|

\|sigma\_floorscope\|T1\-\-T3allturnsprimary\|unchanged\|no\|

\|Analysispipeline\|frozenKS1code\|\*\*runTHROUGHit,unmodified\*\*\|no\|

\*\*Thejudgeisheldfixedonpurpose\.\*\*Changingpolicy\*and\*judgetogetherwouldconfound

"survivesadifferentpolicyfamily"with"survivesadifferentjudge"\.Holdingthejudge

constantkeepsthe\(descriptive\)judgecolumninterpretable;theimplicitcolumnis

unavoidablyconfoundedwiththepolicyswap\*\*byconstruction\*\*\-\-\-seeS0\-\-\-andthatasymmetry

isrestatedwherevertheimplicitnumbersappear\.

\#\#3\.CRITERION\-\-\-appliestoT3alone

\*\*T3replicatesiffBOTH:\*\*

1\.theT3pointestimatefalls\*\*withinKS1’soriginal95%CI\[0\.647,0\.793\]\*\*,AND

2\.the\*\*controlsgatefiresinthesamedirection\*\*\(shuffledcontroldoesnotreproducethe

T3effect\),asinKS1\.

ReferencevaluesfromVERDICT\.md,untouchedbythisamendment:

\|Quantity\|KS1point\|KS195%CI\|Statushere\|

\|\-\-\-\|\-\-\-\|\-\-\-\|\-\-\-\|

\|\*\*implicitT3\*\*\|\*\*\+0\.752\*\*\|\*\*\[0\.647,0\.793\]\*\*\|\*\*PRIMARY\*\*\|

\|implicitrho\|0\.0193\|\[\-0\.109,0\.081\]\|descriptive,underpowered\|

\|judgerho\|0\.1142\|\[0\.027,0\.168\]\|descriptive,underpowered\|

\|implicitshuffledcontrol\|\-\-\-\|\[0\.005,0\.114\]\|controlsgate\|

\|judgeshuffledcontrol\|\-\-\-\|\[\-0\.049,0\.117\]\|controlsgate\|

\#\#4\.MDEATTHISn\-\-\-andwhyitforcedthenarrowing

DerivedfromKS1’sownpublishedCIs\(half\-width\-\>SE\-\>impliedper\-trajectorySD\-\>SEatthe

newn\);80%power,two\-sidedalpha=0\.05:

\|Quantity\|impliedSD\|n=25:95%half\-width/MDE\|n=30:95%half\-width/MDE\|

\|\-\-\-\|\-\-\-\|\-\-\-\|\-\-\-\|

\|\*\*implicitT3\(PRIMARY\)\*\*\|0\.227\|0\.089/\*\*0\.127\*\*\|0\.081/\*\*0\.116\*\*\|

\|implicitrho\(descriptive\)\|0\.295\|0\.116/\*\*0\.165\*\*\|0\.106/\*\*0\.151\*\*\|

\|judgerho\(descriptive\)\|0\.219\|0\.086/\*\*0\.123\*\*\|0\.078/\*\*0\.112\*\*\|

\*\*Thearithmeticthatdrovetheruling:\*\*thejudge\-rhoMDE\(0\.112\-\-0\.123\)is\*\*aslargeasKS1’s

entirejudgepointestimate\(0\.114\)\*\*\.Atthisnthatcomparisoncannotdistinguish"theeffect

vanished"from"theeffectisexactlywhatKS1measured"\-\-\-bothlieinsideoneCI\.Registering

itasanendpointwouldmanufactureadecisionthedatacannotsupport\.\*\*T3clearsitsMDEby

roughlysix\-foldandisthereforetheonlydefensibleprimary\.\*\*

\*\*BINDINGINTERPRETATIONRULE\(retainedverbatimfromv1\):\*\*

\>\*\*FAILURETOFALLWITHINTHEORIGINALCIsISINCONCLUSIVE,NOTAREFUTATION\.\*\*

\>Amissisreportedas\*"notreplicatedatn~=25\-\-30,MDE=X,belowwhichthisdesigncannot

\>discriminate"\*\-\-\-neveras\*"KS1doesnotgeneralize"\*\.Onlya\*\*T3SIGNREVERSAL\*\*\(median

\>Spearmansignificantlynegative\)ispositiveevidenceagainsttheKS1mechanismclaim,

\>becauseT3istheonlyquantitythisnresolves\.Thisapplieswithevenmoreforcetothe

\>descriptiveoutputs,whichcannotbecalledafailuretoreplicateatall\.

\#\#5\.ABORTGATE\-\-\-retained;thelikeliestfailuremode

\*\*ONE\-DAYPARSER\-ADAPTATIONABORTGATE\.\*\*Theactionparserischeckpoint\-sensitive\-\-\-aknown,

twice\-realizedlandmine\(e17tag\-formatdrift;e30,thecanonicalizerthatsilentlyproduced

1\-\-3%agreement\)\.Llama\-3\.1’sactionformattingwilldifferfromQwen2\.5’s\.

\-\*\*Oneday\*\*toadapttheparserandreachanacceptableparserateonapilotbatch\.

\-\*\*Pre\-registeredpilotgate:\>=90%strict\-tagparserateon20pilottrajectories\.\*\*Below

that,\*\*ABORT\*\*andreporttheparserateasthefinding\-\-\-anunparseablepolicyisareal

andpublishablemeasurabilityresult,notafailedrun\.

\-Parserchangesare\*\*additiveonly\*\*:theQwenpathstaysbyte\-identical,verifiedby

re\-runningtheKS1smokeandmatchingitstrajectoryhash\.\*\*Aparsereditthatchangesany

KS1numberisanautomaticstop\.\*\*

\#\#6\.OPERATIONALPRECONDITIONS

\-\*\*‘HF\_TOKEN‘REQUIRED\*\*:‘meta\-llama/Llama\-3\.1\-8B\-Instruct‘isa\*\*gated\*\*repo\.Accessmust

begrantedonthetoken’saccount\*before\*therun;agated\-repo401atloadtimeisastage

failure,notaretry\.

\-\*\*R21contentgate\(ironrule7\)\*\*unchanged:sha256ofevery‘\*\.safetensors‘shardagainst

theHFblobfilename,onthepodthatwillrunit,path\-boundtotheambient‘HF\_HOME‘

\(e34\),reportwrittento‘runs/<run\>/checkpoint\_verification\*\.json‘\.

\-Disk:asecond8Bpolicyalongsidetheexistingcache;F6verify\-then\-freeapplies\.

\-Ironrules8\(supervised\-run\),9\(report=disk,\*\*includingthee40/e41three\-clause

read\-back:NULcount0,textfiletype,andacontentassertionagainstintended

structure\*\*\)and10\(F7conformancegates\)applythroughout\.

\#\#7\.BUDGETANDDISCIPLINE

GPUcost\*\*notyetestimated\*\*;nofigureisassertedhere\.Acostedplanaccompaniesthe

countersignaturerequest\.Negativeandinconclusiveoutcomesare\*\*fulldeliverables\*\*\.

ALL\_EXPERIMENTS\_RECORDentryperstageboundary\.Exploratorythroughout;touchesnoKS1orKS2

confirmatoryfamily\.

\-\-\-

\*\*SIGNED\.ExecutionauthorisedinS8pipelineorder\.TheabortgateofS5andthebudgetstop

ofS7bindabsolutely\.\*\*

\#\#8\.PIPELINEORDER\(\[AUTHOR\-1\],2026\-08\-07\)\-\-\-ceilingcutstheleastvaluableitemfirst

1\.\*\*Parserpilot\+abortgate\*\*\-\-\-\>=90%strictlabel\-parseon20pilottrajectories,oneday

max\.Threepriorincidents\(e17tagdrift,e30canonicalizer,theA3Bcanonicalizer\)sayto

expectadaptationwork\.\*\*Donotfightpastthegate\.\*\*

2\.\*\*Collection\*\*\(n=25\-\-30\)\.

3\.\*\*Replaygroundtruth\.\*\*

4\.\*\*Logprobdumps\*\*\(policy\+hindsight,selfscorer\)\.

5\.\*\*T3analysis\-\-\-THESOLEPRIMARYENDPOINT\.\*\*Therunhasdelivereditspurposeoncethis

lands\.

6\.\*\*Implicitfamilyfidelity\+measurabilitymap\*\*\-\-\-descriptive,underpowered,MDEbeside

everyestimate\.

7\.\*\*72Bjudgescoring\-\-\-LASTandOPTIONAL\.\*\*Itservesonlyapre\-labelledunderpowered

descriptiveoutput,andcosts~2GPU\-hplusa145GBstagingoperationthathascaused

repeatedincidents\.\*\*Ifthebudgetceilingorthecalendarisanywherenear,SKIPITand

recordthatitwasskippedBYDESIGN,notbyfailure\.\*\*

\*\*BUDGETSTOP:\*\*afterstep2,measuretherealizedrate,projectthetotalforsteps3\-\-6,and

posttheprojectionbeforecontinuing\.\*\*Iftheprojectionexceeds$40,STOPandqueuefor

\[AUTHOR\-1\]\.\*\*Overallceiling$60\.‘HF\_TOKEN‘required;ifauthfails,\*\*abortTask3,logit,and

continuethequeue\-\-\-donotstallthenight\.\*\*

#### KS2 \(the seven\-arm training experiment\)\.

\#KS2\_PREREG\-\-\-Training\-loopclosureoftheH3\(placebo\)verdict\(v1\.2\)

Status:PRESENTEDFORSIGN\-OFF\.Trainingblockeduntil\[AUTHOR\-1\]signs\(S10\)andtheanalysis

pipelineisfixture\-testedandtag\-frozen\(S8,CC\-5pattern\)\.Parent:KS1VERDICT\.md

\(double\-H3,Controlsgate;implicit:T3confirmed\)\.Governingkit:CLAUDE\.mdironrules,

R21content\-hashgate,RulesA\-\-S\.

\#\#1\.Question

KS1establishedthatbothper\-stepcreditfamiliesareplacebo\-levelat\*ranking\*causal

truth\.Thestandardrebuttal:"trainingmaynotconsumerankfidelity"\(group\-relative

aggregation,batcheffects\)\.KS2closestheloop:\*\*dothecreditfamiliesdifferfrom

eachother,fromnostep\-creditatall,andfromsign\-invertedcredit,inthetraining

outcometheywerebuilttoimprove?\*\*

\#\#2\.Trainingregime\(PlanA\-\-\-iteratedoffline\-scoringloop;frozen\)

Per\[AUTHOR\-1\]ruling\(Rule\-Afix\):NOTpureon\-policy\.Eachround:

1\.Currentpolicycollectsabatchoftrajectoriesonthefrozentrainingtasklist

\(temp0\.7,seeded\)\.

2\.Trainingpauses;allsevencreditsourcesarescoredOFFLINEoverthesamebatch\.

3\.EacharmappliesitsowncredittotheSAMEbaseupdaterule\(step\-weighted

group\-relativeadvantage,LoRAonQwen2\.5\-7B\-Instruct;optimizer/LR/stepsfrozenat

harnesssign\-off\);nextround\.

\-Rounds:\*\*3\*\*\.Batch:\*\*96\*\*trajectories/round/arm\-seed\.\(Reducedfromthev1draft’s

4x128\-\-\-BUDGET\-DRIVEN,frozennowviatheS9budgettable;anyfurtherchangeisamended

BEFOREanytraining,neverafter\.\)Round\-1collectionisSHAREDacrossarms\(identical

policy\+CRNstreamsmakethesevenround\-1batchesbyte\-identicalbyconstruction;

collectedonce,consumedsevenways\)\.

\-\*\*Registereddeviation\*\*:onestepremovedfromtheauditedpapers’on\-policysetting;

acceptedbecauseitmakesthesixarms’trainingdynamicsstrictlyisomorphic\-\-\-theonly

varyingfactoristhecreditsource\.Loggedhere,restatedinthepaper\.

\#\#3\.Arms\(seven;identicaleverythingexceptcreditsource\)

\|\#\|Arm\|Creditatroundr\|

\|\-\-\-\|\-\-\-\-\-\|\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\|

\|1\|outcome\-only\|group\-relativeoutcomeadvantage,noper\-stepweighting\|

\|2\|implicit\|HCAPOrho\_t\(Eqs\.6\-\-7,publishedconstants\)scoredbytheCURRENTpolicycheckpointontheround’sowntrajectories\|

\|3\|judge\|Qwen2\.5\-72Bjudge,frozenKS1prompt\(bloba1b59989\.\.\.\),w/o\-gold,scoredperround\-\-\-\*\*AWQint4permittedonlyifS7consistencygatepasses\*\*\|

\|4\|shuffled\|implicitinstrument\(HCAPOrho\_t\)runBYTHISARMonITSOWNcurrent\-roundbatch,thenpermutedwithintrajectory\(seeded\)\|

\|5\|inverted\|implicitinstrumentrunBYTHISARMonITSOWNcurrent\-roundbatch,thensign\-flippedaboutthetrajectorymean\|

\|6\|pivotal\-maskedtruth\|cheapreplayontheround’sowntrajectories,\*\*stratified50%ofturns\*\*\(position\-tercilestratified,seed=3000\+traj\_id;unsampledturnscarrycredit0\):K=2alternativesx2replicas\+factualx2,sign\(A\_replay\)only;credit=\+/\-1onsampledturnswithdefinednonzerosign,0elsewhere\|

\|7\|shuffled\-judge\|judgeinstrumentrunBYTHISARMonITSOWNcurrent\-roundbatch,thenpermutedwithintrajectory\(seeded\)\-\-\-judge’sOWNmarginal\(\{1,0,\-1\},tie\-heavy\),sotheC2controlmatchesthearmitcontrolsfor\|

\*\*Control\-armcreditsourcerule\(Rule\-Afix,v1\.2\):\*\*fromround2thearms’policies

divergeandeacharmcollectsitsownbatch,so"arm\-2/arm\-3values"donotexistona

controlarm’strajectories\.EachcontrolarmthereforeRUNSTHERELEVANTINSTRUMENTITSELF

onitsownbatch\(arms2/4/5\-\>implicitscoring;arms3/7\-\>judgescoring\)andappliesits

transformtothosescores\.Semantics:thecontrolmeasurestheeffectoftheinstrument’s

scoreDISTRIBUTIONwithitsinformationremoved,onthatarm’sowndata\.Atround1the

sharedCRNbatchmakesthisexactlyequivalenttotheearlierphrasing\.

Arm\-6replaybudgetisaREDUCED\-RESOLUTIONinstrument\(signonly\);thisisstatedwherever

arm\-6isdiscussedandneverconflatedwithKS1’sK=4x3estimator\.

\*\*Arm\-6degradationladder\(frozennow,appliedinorder,eachsteplogged\):\*\*

1\.Turnsampling50%\-\>33%\(samestratification,sameseedrule\)\.

2\.K=2x2\+factualx2\-\>K=2x1\+factualx1\(3rollouts/turn;halvesarm\-6cost\)\.

Nootherdegradationpermitted;beyondstep2\-\>escalateto\[AUTHOR\-1\]\.

\#\#4\.Paireddesign\(commonrandomnumbers;frozen\)

\-Seeds:S=\{0,1,2\}perarm;\*\*identicalacrossarms\*\*\-\-\-sametaskorder,sameenvseeds,

sameround\-rcollectionRNGstreams\(armenterstheseedderivationonlydownstreamof

collection\)\.Allarm\-vs\-armcomparisonsareseed\-paired\.

\-SDsourceforthepowercheck\(statedprecisely\):arm\-1’s3seedsyieldtheBETWEEN\-SEED

SD,whichisaproxyUPPERBOUNDonthepairedSD\(CRNpairingcanonlyshrinkit\),so

theS4powerprojectioncomputedfromitisconservativeinthesafedirection\.

\-Adaptiverule,FROZENNOW:afterarm\-1’s3seedscomplete,computetherealizedpairedSD;

ifprojectedpaired\-TOSTpowerat\+/\-3pp<80%,extendALLarmsto5seeds\(S\+=\{3,4\}\);

budgetpre\-approved\(\+~$35\)\.Nootheradaptationpermitted\.

\#\#5\.Evaluationprotocol\(frozen\)

\-Held\-outset:ALFWorldunseensplit,tasklistof\*\*128taskscommittedbeforeany

training\*\*;disjointfromthetraininglistandfromcollect\_v2\.

\-Perseedpertask:\*\*1episode\*\*,greedydecoding\(temp0\)\.\(v1had2episodes\-\-\-a

determinismbug:ALFWorld\+temp0makesthesecondepisodebyte\-identicaltothefirst,

son=256wouldbefictitiousandtheWilsonCIfalselynarrow\.Honestn=128;taskcount

isthevariancedriver\.\)

\-Metric:winrateover128episodes/seed,reportedwithnandWilson95%CI,perarmper

round\(learningcurve\)andatthefinalround\(primaryendpoint\)\.

\#\#6\.Confirmatoryanalysis\(frozen;pairedTOST\+Holm\)

Primaryendpoint:final\-roundwinratedifference,seed\-paired\.

\-\*\*Equivalencemargin\+/\-3pp\*\*\(\[AUTHOR\-1\]\-ratified;=halftheSpurious\-Rewardsrandom\-vs\-truth

gap\)\.PairedTOSTatalpha=0\.05\.

\-Confirmatorycomparisons\(Holmoverexactlythesesix\),eachwithitsREGISTEREDtesttype:

C1implicitvsshuffled\(rho\)\-\-\-pairedTOST\(equivalence\)

C2judgevs\*\*shuffled\-judge\(arm\-7\)\*\*\-\-\-pairedTOST\(equivalence\);controlmatchesthe

controlledarm’sownmarginaldistribution

C3implicitvsoutcome\-only\-\-\-pairedTOST\(equivalence\)

C4judgevsoutcome\-only\-\-\-pairedTOST\(equivalence\)

C5invertedvsimplicit\-\-\-one\-sidedpairedsuperiority,registereddirection:invertedWORSE

C6pivotal\-maskedvsoutcome\-only\-\-\-one\-sidedpairedsuperiority,registereddirection:maskedBETTER

TheS7\.4fixturetestmustplantallthreetruthtypes\(equivalent/directionally

non\-equivalent/inconclusive\)andthepipelinemustrecovereachunderthismixedfamily\.

\-Reportingrule:"equivalent"ONLYifTOSTsignificant;TOSTnon\-significantAND

difference\-testnon\-significant\-\>\*\*inconclusive\*\*\(never"nodifference"\)\.Power

calculationwithassumedSDinS9;validatedagainstarm\-1realizedSD\(S4\)\.

\-Verdictlines\(independent,nevermerged\):

V1placebo\-closure:C1\-\-C4allequivalent\-\>per\-stepcreditcontentisinertintraining\.

V2information\-without\-alignment:C5showsinvertedsignificantlyWORSE\-\>creditcarries

signalthatismisaligned,notabsent\.

V3methodbyproduct:C6showspivotal\-maskedsignificantlyBETTER\-\>sparsecausal

maskingbeatsdenseheuristiccredit\.

\#\#7\.Phase\-0gates\(beforeanytraining\)

1\.R21content\-hashverificationofeverycheckpointonthenewpod\(ironrule\)\.

2\.\*\*AWQconsistencygate\*\*:scoretheKS1anchorset\(11frozentrajectories,224turns\)

with72B\-AWQvsthestored72B\-bf16judgments;requireexact\-agreement\>=90%AND

kappa\>=0\.8\(i\.e\.,AWQ\-vs\-bf16mustagreefarbetterthanjudge\-vs\-anchor’skappa=0\.496,so

quantizationnoiseissmallrelativetojudge\-modelnoise\)\.Pass\-\>arm\-3usesAWQon

1xA100;fail\-\>judgescoringroundsrunon2xA100bf16\(\+~$20\),logged\.

3\.\*\*R29decomposition\(pre\-training,exploratory,intothepaperregardlessofoutcome\)\*\*:

fromexistingcollect\_v2dumps\-\-\-incrementg\_t=logpi\_hind\-logpi\_policy;

reportcorr\(g\_t,A\_replay\)\(allcompleteturns\+pivotal\-only\),partial

corr\(rho\_t,A\_replay\|logpi\_policy\),andDeltaregressedon\(fluency,increment\)\.

Claimtemplateitfeeds:"outcome\-conditioningbuysnocausalinformation\."

4\.Analysispipelinefixturetest\(CC\-5\):syntheticrunswithplanted

equivalent/non\-equivalent/inconclusivetruths;pipelinemustrecoverallthree;

tag‘ks2\-analysis\-frozen‘BEFOREfirsttrainingbatchlands\.

\#\#8\.Records&discipline

\-ALL\_EXPERIMENTS\_RECORDentryperarm\-seed\-round,writtenateachround’sscoringpoint,

neverbatchedattheend\.

\-Oneconfigchangeperrun;configsarefiles;everyroundwritestrajectories,credit

files,updatelogs,evalJSON,gitSHA\.

\-Repropackageskeleton\(env,prompts,scoringscripts,analysis\)growsalongsideruns

\(RuleR\)\.

\-Monitorsauto\-advancethe18\+runs;humanappearsonlyatround\-boundaryscoringpoints

andtheS10gates\.

\#\#9\.Scope,budget,calendar

\-\*\*Scopelock\(frozenwording\)\*\*:allKS2conclusionsarelimitedtotheQwen2\.5model

family,ALFWorld,LoRAfine\-tuningatthefrozenscale,underthePlan\-Aiterated

offline\-scoringregime\.Nocross\-familyorcross\-environmentgeneralizationisclaimed\.

\-\*\*Budgettable\(perstage,atKS1measuredrates:1,700continuation\-rollouts/hand

~800trajectories/hatthe48\-workertieron1xA100\+16vCPU;112\-workertiermeasured

4,465/honthejudgepodisupsidemargin,notassumed\):\*\*

\|Stage\|Volume\|GPU\.h\|$\|

\|\-\-\-\|\-\-\-\|\-\-\-\|\-\-\-\|

\|Collection\(r1shared\+r2\-\-3x7armsx3seedsx96\)\|4,320traj\|5\.4\|$8\|

\|Arm\-6replay,defaulttier\(50%turnsx6rolloutsx3rx3s\)\|51,840rollouts\|30\.5\|$45\|

\|Judgescoring,arms3AND7\(2x17,280turns,AWQ@~1,000turns/h\)\|34,560turns\|34\.6\|$52\|

\|LoRAupdates\(allarms\)\|\-\-\-\|4\|$6\|

\|Eval\(7armsx3seedsx128tasksx1ep,greedy\)\|2,688eps\|3\.4\|$5\|

\|Overhead\(loads,gates,R29\)\|\-\-\-\|~3\|$4\|

\|\*\*Basetotal\*\*\|\|\*\*~81\*\*\|\*\*~$120\*\*\|

\|Adaptive5\-seedextension\(x5/3onseed\-scaledstages\)\|\|\|caprisesto$200\(rulebelow\)\|

\|Arm\-6ladderstep2\(ifinvoked\)\|\-25,920rollouts\|\-15\.2\|\-$23\|

\|AWQ\-failcontingency\(judgestageon2xA100bf16\)\|\|\|\+$20\|

AssumedpairedSDfortheS6powercalc:1\.5pp\(validatedperS4;between\-seedproxyisa

conservativeupperbound\)\.

\-\*\*Cap\-interactionrule\(frozennow\):\*\*iftheS4adaptive5\-seedrulefires,thebudget

caprisesautomaticallyto\*\*$200\*\*\(pre\-approvedby\[AUTHOR\-1\]\)andarm\-6REMAINSatits

defaulttier\-\-\-thedegradationladderdoesNOTco\-firewiththeseedextension\.

Instrumentresolutionisnevertradedagainststatisticalpower;theladderisa

triggeredfallbackforitsownS9conditionsonly\.

\-Arm\-6defaulttierCONFIRMEDat50%turnsx6rollouts\(\[AUTHOR\-1\]ruling\):C6isaone\-sided

superiorityclaim,andcoarsersignestimatesattenuatetheeffecttowardzero\-\-\-the

ladderisafallback,notthedefault\.

\-Calendar:sign\-\>podup\-\>S7gates\+R29\(day1\)\-\>trainingrounds\(days1\-\-3\)\-\>

eval\+analysis\+VERDICT\_KS2\(day3\-\-4\)\-\>numbersby2026\-08\-10\.ScienceWorldcheckpoint

2026\-08\-20per\[AUTHOR\-1\]ruling\(3\)\.

\#\#10\.Sign\-offblock

\-\[x\]PlanAratified\(registereddeviationfromon\-policyaccepted\)

\-\[x\]Arms1\-\-7asspecified;arm\-6reduced\-resolutioninstrument\+frozenladder;arm\-7

marginal\-matchedcontrolforC2

\-\[x\]Budgettablereviewed;rounds=3/batch=96acceptedasbudget\-drivenfreezes

\-\[x\]Evaln=128\(1greedyepisode/task\)accepted

\-\[x\]PairedCRNdesign\+frozenadaptive\-seedrule

\-\[x\]TOST\+/\-3pp,HolmoverC1\-\-C6,inconclusive\-reportingrule

\-\[x\]Phase\-0gatesincl\.AWQkappa\>=0\.8/exact\>=90%threshold

\-\[x\]\[AUTHOR\-1\]signature:\*\*\[AUTHOR\-1\],2026\-08\-02\*\*\-\-\-SIGNEDasv1\.2withthesix/sevenword\-levelfix\.Thresholds,arms,budgetrules,andgatesIMMUTABLEfromtagks2\-prereg\-v1\.2\-signed\.

\#\#Amendmentv1\.3\(2026\-08\-03,\[AUTHOR\-1\]rulingsR33/R34ontheE014budgetstop;signedBEFOREround1\-\-\-notrainingdataexistedatsigning\)

1\.\*\*Arm\-6ladderstep1INVOKED\*\*\(itsregisteredS9budgetconditionfired\-\-\-E014ledger\):

turnsampling50%\-\>33%\(want=ceil\(T/3\)\),sametercilestratification,samefrozenseed

rule\(3000\+traj\_id\),T<=12keep\-allunchanged\.LoggedperS3\("eachsteplogged"\)\.

2\.\*\*Arm\-6resolutionstatement\*\*:thealternative\-drawcapis20seededdraws/turn\.Turns

where2distinctadmissiblealternativesarenotfoundwithin20drawscarrycredit0\-\-\-

identicalinkindtoarm\-6’sexistingsemanticsforunsampled/undefinedturns\.This

restatesthereduced\-resolutioninstrument’sresolution;theestimator\(sign\(A\_replay\),

K=2x2\+factualx2onsampleddefinedturns\)isunchanged\.

3\.\*\*Evalschedule\(R34\)\*\*:primaryendpointUNCHANGED\-\-\-finalround,all7armsx3seeds,

128tasks,greedy,WilsonCI\.Per\-roundlearningcurvesdemotedtocrn\-seed\-0only

\(7evalsperroundforrounds1\-\-2\),labeledexploratory/descriptive\.

4\.Budget:operationalcap$160standalone/$220iftheS45\-seedrulefires\(R37\)\.LoRA

linerebasedtomeasured16\.8GPU\.h\(R35\)\.Batch96/rounds3untouched\(R36\)\.

\[AUTHOR\-1\]signature:\*\*\[AUTHOR\-1\],2026\-08\-03\*\*\-\-\-SIGNEDasv1\.3\.Allotherv1\.2freezesunchanged\.

\#\#Amendmentv1\.4\(2026\-08\-04,\[AUTHOR\-1\]rulingR41ontheE016policycollapse;signedBEFOREanyconfirmatorynumberexists\-\-\-ther1evalsunderv1\.3arediagnosticsofharnessfailure,quarantinedperR41c\)

S2updateruleREPLACEDforallsevenarmsidentically\(creditsourceremainstheonly

cross\-armdifference\):

1\.PPO\-styleper\-tokenratioclippingagainstthecollection\-timelogprobsstoredin

gen\_logprobs,eps=0\.2\.

2\.Advantagez\-normalizationperbatchbeforeweighting:A\_z=\(outcome\-batchmean\)/batchSD

\(sd=0\-\>degenerate\-batchruleunchanged\)\.Creditw\_tisappliedtoA\_zexactlyasbefore;

zero\-credit=\>zero\-gradientisPRESERVED\(normalizingtheproductwouldgiveunsampled/

undefinedturnsnonzerogradientandsilentlybreakarm\-6/\-3/\-7semantics\)\.Pre/poststats

recordedperD2\.

3\.Optimizerbudget:max1epoch\(unchanged\),lr5e\-5\(was1e\-4\)\.

4\.KLanchortotheround\-startpolicy,coefficient0\.05,estimatedontherealizedtokens

fromthesamestoredlogprobs;realizedKLloggedperupdate\.

R41b:post\-updategenerationsanitygate\(4greedyepisodes;assertno\>8\-tokenrepeatloops

andnonzeroaction\-extraction\)addedtothefixturesANDrunper\-armbeforeeveryeval\.

R41c:v1\.3\-ruleadapters/evalsquarantined,keptasthetraining\-fragilityevidencebase\.

R41e:C6isreadjointlywithper\-armeffective\-optimizer\-stepcounts;sparsity\-mediated

survivalisanamedconfound\.

Budget:re\-runinsideexistingledgerlines\.Calendar:verdicttarget8/7,hardline8/10\.

\[AUTHOR\-1\]signature:\*\*\[AUTHOR\-1\],2026\-08\-04\*\*\-\-\-SIGNEDasv1\.4\.Allotherfreezesunchanged\.

#### A3B \(checkpoint divergence\), with itsΔ\\Deltapre\-registration and amendments\.

\#A3B\_PREREG\-\-\-Doescreditsourcesystematicallyshapepolicybehaviour?

Status:PRE\-REGISTEREDBEFOREANYAGREEMENTNUMBERWASCOMPUTED\.Tag‘a3b\-prereg\-v1‘\.

Exploratorythroughout;touchesnoconfirmatoryfamily\.KS1/KS2/PC/PC2preregsandboth

verdictsremainIMMUTABLE\.

\#\#Thesentenceundertest

E026/B23recorded:\*\*"sevenbehaviourallydistinctpolicieswithnodetectableperformance

difference\."\*\*A3\-RLestablishedthateacharmdiffers\*frombase\*\(~50%greedyaction

agreement\)\.ItdidNOTestablishthatthearmsdiffer\*fromeachotherinanarm\-specific

way\*\.Ifcheckpointsdifferfromeachotherbyroughlythesameamountwhetherornotthey

shareacreditrule,then"sevenbehaviourallydistinctpolicies"overstatestheevidenceand

thesentencemustbeWITHDRAWN\.Thispreregdecidesthat,withthresholdsfixedinadvance\.

\#\#Metrics

\-\*\*Primary:\*\*pairwisegreedyactionagreementoveraFIXEDstatebank,on\*\*canonicalized\*\*

actions\.

\-\*\*Secondary\(string\):\*\*raw\-stringagreement,samepairs,samestates\.

\-\*\*Secondary\(continuous\):\*\*pairwisesymmetric\-KLandJensen\-\-Shannondivergencebetween

next\-action\-tokendistributions\(teacher\-forcedlogprobsfromthesameforwardpass\)\.

Rationale:withonly21checkpoints,permutationpowercomesfromcheckpointcount;a

continuousmetriccutsper\-pairnoiseandsidestepsparsersensitivityentirely\.

\#\#Pairclasses

\-\*\*A\*\*\-\-\-samearm,differentseeds\(n=7armsx3seed\-pairs=21pairs\)

\-\*\*B\*\*\-\-\-differentarms,sameseed\(n=3seedsx21arm\-pairs=63pairs\)

\-\*\*C\*\*\-\-\-differentarms,differentseeds\(n=126pairs\)

\#\#\#CRNasymmetry\-\-\-stateddeliberately,inadvance

UnderthefrozenCRNdesign,\*\*round\-1collectionwasSHAREDacrossarms\*\*\.Therefore:

\-\*\*Bpairssharetheentireround\-1batch\*\*\(anddifferonlyincreditrulethereafter\)\.

\-\*\*ApairsshareNOcollecteddataatall\*\*\-\-\-differentseedsmeansdifferentround\-1,

round\-2andround\-3batches\.Theyshare\*onlythecreditrule\*\.

Requiring‘mean\(A\)\>mean\(B\)‘thereforeaskswhether\*\*thecreditruleshapesbehaviourmore

thanasharedcollectionhistorydoes\*\*\.Thatisthestrongbar,anditischosendeliberately\.

AresultwhereB\>Ameansshareddatadominatescreditrule\-\-\-i\.e\.collectionrandomnessis

thelargerforce\-\-\-andtheclaimfailsregardlessoftheA\-Cgap\.

\#\#Primarystatistic

‘gap=mean\(A\)\-mean\(C\)‘

\#\#Null\-\-\-RESTRICTEDPERMUTATION\(replacesfreepermutation\)

Permute\*\*armlabelsWITHINeachseedindependently\*\*,10,000times,recomputing‘gap‘each

time\.Rationalerecordednow:freepermutationacrossall21checkpointscreatespseudo\-arms

containingtwocheckpointsfromthe\*same\*seed,whichshareround\-1dataandthereforeinflate

thenull,wastingpower\.Within\-seedpermutationpreservestheexactdesignstructure\(exactly

onecheckpointperseedperarm\)andisthecorrectexchangeabilitynull\.

\#\#FROZENDECISIONRULE

Thesentenceis\*\*SUPPORTED\*\*iff\*\*allthree\*\*hold:

1\.‘gap=mean\(A\)\-mean\(C\)\>=5pp‘,AND

2\.restricted\-permutation‘p<0\.05‘,AND

3\.‘mean\(A\)\>mean\(B\)‘\.

Otherwisethesentenceis\*\*WITHDRAWN\*\*andthenullisreportedplainly\.‘mean\(A\)‘and

‘mean\(B\)‘arereportedseparatelyineverycase\.If‘B\>=A‘,collectionrandomnessdominates

andtheclaimfailsregardlessofthegap\.

\#\#Structuralhypotheses\-\-\-FROZENBEFORESEEINGTHE21x21MATRIX

Twomutuallyexclusivepartitionsofthesevenarms:

\-\*\*H\_instrument:\*\*\{2,4,5\}rho\-family\.\{3,7\}judge\-family\.\{6\}\.\{1\}

\-\*\*H\_information:\*\*\{2,3,6\}informative\.\{4,7\}shuffled\.\{5\}inverted\.\{1\}none

\*\*Fixedcomparisoncriterion\(statednow\):\*\*foreachpartitioncompute

‘Delta=mean\(within\-grouppairwisesimilarity\)\-mean\(between\-grouppairwisesimilarity\)‘,

usingarm\-levelsimilarity\(themeanoverthatarm\-pair’sconstituentcheckpointpairs\)\.

Eachpartitiongetsits\*\*ownrestrictedpermutationtest\*\*\(samewithin\-seedscheme,10,000

draws\)yieldingitsownp\.ThepartitionwiththelargerDelta\*\*and\*\*thesmallerpisdeclared

thebetterexplanation;iftheydisagree,thatisreportedasindeterminateratherthan

resolvedposthoc\.

\*\*Readingfixedinadvance:\*\*if\*\*H\_instrument\*\*wins,therecordedinterpretationisthat

behaviourisshapedbythecreditsignal’s\*\*DISTRIBUTIONALSHAPE,notitsinformation

content\*\*\-\-\-consistentwithKS1’sfluency\-echofindingandR29’szero\-informationincrement\.

\*\*ApartitionwillNOTbechosenafterseeingthematrix\.\*\*

\#\#Exclusions

\*\*arm5/seed2isEXCLUDEDfromallprimaryanalysis\*\*\(87\.7%tag\-in\-actionformatcollapse,

E020\)\.Itisreportedseparatelyasadegeneratecase\.EveryA/B/Ccountaboveisreduced

accordingly,andtherealizedcountsarereported\.

\#\#Stages

\-\*\*Stage0\(operational\):\*\*verifyall21finalarm\-seedadaptersexistontheRETAINED

NETWORKVOLUME\(notcontainerdisk\),withcontenthashes\.Anythinglivingonlyonthepodis

copiedtothevolumeandre\-hashed\.Fullinventoryreported\.ThepodisNOTshutdownuntil

Stage2completes\.

\-\*\*Stage1\(zeroGPU\):\*\*turn1ofeachofthe128held\-outtasksisfacedbyeverycheckpoint

fromabyte\-identicalinitialobservation\.Extracteachcheckpoint’sturn\-1actionfromthe

storedfinal\-roundevaltrajectories,canonicalize,computeA/B/C\+restrictedpermutation

overthese128unbiasedstates\.\*\*Ceilingriskreportedexplicitly:\*\*thefractionofstates

whereALLcheckpointsagree\(turn\-1ALFWorldmaybenear\-triviallyconstrained\)\.

\-\*\*Stage2\(GPU,ONLYifStage1isatceiling/underpowered/ambiguous\):\*\*~500states

sampledfrom\*\*BASE\-model\*\*trajectoriesonheld\-outtasks\(baseistheneutralcommon

ancestor\-\-\-sampledfromnoarm’sownrollouts\),stratifiedbyturnposition\.\*\*Statebankand

itshashcommittedBEFOREscoring\.\*\*All21checkpointsscoredgreedy\(temp0\)onidentical

promptsusingthesametemplateasRLtraining;rawgenerationsANDnext\-action\-token

logprobsstored\.Everythingrecomputedonthisbank\.

\#\#Normalization\(parserischeckpoint\-sensitive\-\-\-cf\.the‘\[action\>‘/‘<action\>‘/‘\[action\]‘lesson\)

Canonicalizetoabareactionstring:stripCoT/‘<think\>‘spans,stripalltagvariants,

lowercase,collapsewhitespace,maptotheALFWorldadmissiblevocabularywherepossible\.

Report\(a\)canonicalagreement,\(b\)raw\-stringagreement,and\(c\)\*\*canonicalization\-failure

countPERCHECKPOINT\*\*\.Acheckpointwithahighfailurerateisaformat\-degradedoutlierand

mustbeFLAGGED,neversilentlyaveragedin\.

\#\#Alsoreported\(exploratory,cheap\)

\-A/B/Crestrictedto\*\*CONTESTED\*\*states\(thosewherenotallcheckpointsagree\),asa

sensitivityagainstceilingeffects\.

\-The21x21pairwiseagreementmatrix\+clustering/MDS\.

\-Whether\*\*arm1\*\*\(outcome\-only,nostepcredit\)sitsapartfromthestep\-creditarms\.

\-\*\*arm6’smuchsmallerparametermovement\(\|\|lora\_B\|\|1\.37vs~4\.7fortheothers\)\*\*asan

explicitcaveatwhereverarm6appearsintheclustering\.

\-Behaviouraldistancevsperformancedistanceacrosspairs\(expectedunderpowered;labelled

exploratory\)\.

\#\#Rules

Thresholdsarefrozenaboveandwerefixedbeforeanyresultwasviewed\.\*\*AWITHDRAWNclaimis

afulldeliverable\*\*\-\-\-ifA~=C,thatisstatedplainlyandthesentenceisdroppedfromthe

paper\.ALL\_EXPERIMENTS\_RECORDentryperstageboundary\.Budget:Stage1free;Stage2<=$10,

overruns\-\>RuleH\.ntfyateachstageboundaryandatthefinalstop\.

Signed\(executionpre\-registration,exploratory\):\*\*2026\-08\-07\*\*,tag‘a3b\-prereg\-v1‘\.

\#A3B\-DeltaPREREG\(addendumtoA3B\_PREREG\.md\)\-\-\-mechanismchainfortheA3Bsignature

Status:PRE\-REGISTEREDBEFOREANYMATRIX,STATISTICORCORRESPONDENCEWASCOMPUTED\.

Tag‘a3b\-delta\-v1‘\.Exploratorythroughout\(theD4chain\);touchesNOconfirmatoryfamily\.

A3B\_PREREG\.md\(‘a3b\-prereg\-v1‘\),KILLSHOT\_PREREG\.md,KS2\_PREREG\.md,PC/PC2preregsandboth

VERDICTsareIMMUTABLEandUNMODIFIED\-\-\-thisisaseparateaddendumfile,notanedittoany

ofthem\(ironrule1\)\.

\*\*\[AUTHOR\-1\]’sratifiedA3Bwording\(E031\)remainsthesinglesourceoftruth,unchangedby

anythinghere:thediscretenullandthecontinuouspositiveareALWAYSstatedtogether\.\*\*

Nothinginthisaddendummaybeusedtorestate,strengthenorsoftenE031\.

ZeroGPU\.Everyinputisalreadyondisk:theA3BJSmatrix,theper\-armcreditfiles,the

roundlogs,andthetrainersource\.\*\*IfanystepturnsouttorequireGPU,itSTOPSandis

reportedasblockedratherthanstarted\.\*\*

\-\-\-

\#\#0\.PREMISE\-\-\-theStep\-0findingthischainisbuilton\(DECISIONSR43,E032\)

Thev1\.4per\-batchz\-normalizationappliesto\*\*A\_iALONE\*\*\(‘scripts/ks2\_train\_update\.py:107\-108‘\);

theproduct‘w\_t\.A\_i‘isformedafterwardsat‘:208‘andneverrescaled\.‘w\_t‘isnever

normalized\.Thedivisor‘\_sd‘isafunctionof\*\*outcomesalone\*\*andistherefore

\*\*credit\-rule\-blind\*\*\.

\*\*SELECTEDnarrative\(a\):\*\*creditmarginalSCALEsurvivesnormalization=\>armswithdifferent

creditscalesreceivesystematicallydifferent\*\*effectivestepsizes\*\*\.

\*\*EXCLUDEDnarrative\(b\):\*\*thearXiv:2509\.02534S6\.3noise\-amplificationroute\.Barredfrom

alldrafts\(R43\)\.Itdoesnotreappearinthisdocumentexceptasanexclusion\.

ThisaddendumTESTStheselectednarrative\.Anullisafulldeliverableandisreportedas

plainlyasapositive\.

\-\-\-

\#\#1\.THEBY\-CONSTRUCTIONSPLIT

Verifiedfromsource,‘scripts/ks2\_credit\.py‘:

\-‘:78\-82shuffle\_within‘\-\-\-permutescreditvalues\*\*withinatrajectory\*\*\(seeded\)\.

arm4=shuffle\_within\(arm2’srho\_t\);arm7=shuffle\_within\(arm3’sjudgescores\)\.

\-‘:85\-87invert\_about\_mean‘\-\-\-‘w\_t=2\.mean\_traj\(rho\)\-rho\_t‘\.arm5=invert\(arm2’srho\_t\)\.

Consequences,statednow:

\-Shufflingpreservestheper\-trajectory\*\*multiset\*\*ofcreditvaluesEXACTLY=\>mean,SD,

kurtosis,sum,andsumofabsolutevaluesareallidenticalbetweenarm2/arm4andarm3/arm7\.

\-Mirroringpreservesthe\*\*meanandSD\*\*exactly\(reflectionpreservesevencentralmoments;

oddonesflipsign\)butdoes\*\*NOT\*\*preservetheabsolute\-valuemarginal:\|2m\-v\|\!=\|v\|in

general\.

Therefore\*\*mean/SD/kurtosisofthecreditmarginalcannotdistinguisharmswithin\{2,4,5\}or

within\{3,7\}\*\*\.ClusteringonthemreproducesH\_instrumentBYCONSTRUCTIONandisnotevidence\.

\#\#\#GROUPA\-\-\-construction\-invariant\(completenessonly;NEVERcarriesthemediationclaim\)

Credit\-marginal\*\*mean,SD,kurtosis\*\*\.Reportedforcompletenessandlabelledas

non\-evidentialwhereveritappears\.

\#\#\#GROUPB\-\-\-construction\-variant\(theonlystatisticsthatcancarrytheclaim\)

Internalpriorityfrozennow:\*\*B\-PRIMARYoutranksB\-CORROBORATIVE\*\*,andwithinB\-PRIMARY,

ALLOCATIONistheonlysub\-partthatcandistinguisharms\*within\*afamily\.

\#\#\#\#B\-PRIMARY\(inputside\-\-\-whatthegradientwasactuallyfed\)

Computedfromtherealizedappliedweights:foreveryturnactuallytrainedon,thequantity

‘\|w\_t\.A\_i\|‘with‘A\_i‘\*\*post\-normalization\*\*\(thevaluethetrainerapplied\),andeachturn

carryingits\*\*responsetokencount\*\*asitsfrequencyweight\(‘:242‘averagesthesurrogate

overresponsetokens,sotokencountisthecorrectfrequency\)\.

\*\*B\-PRIMARY\-SCALE\-\-\-construction\-invariantWITHIN\{2,4,5\}andWITHIN\{3,7\};Group\-A\-like,and

labelledassuch\.\*\*Statistics:\*\*meanandtotalof\|w\_t\.A\_i\|\*\*\.

Theselectednarrativepredictsthisseparates\*\*ACROSS\*\*families\(rho\-familyvsjudge\-familyvs

arm6vsarm1\)but\*\*NOTWITHIN\*\*them\.Thatisadirect,falsifiableconsequenceofStep0and

isreportedassuch\.

\>\*\*PIPELINESELF\-CHECK,frozennow\(notafinding\-\-\-atestofmyowncode\)\.\*\*Because

\>‘shuffle\_within‘permuteswithinatrajectoryand‘A\_i‘isconstantwithinatrajectory,

\>‘Sum\_t\|w\_t\.A\_i\|=\|A\_i\|\.Sum\_t\|w\_t\|‘is\*\*EXACTLY\*\*preservedbyshuffling\.Soonanybatchshared

\>betweenthem,B\-PRIMARY\-SCALEtotalsmustbe\*\*exactlyequal\*\*forarm2vsarm4andforarm3

\>vsarm7\.Round1’scollectionwasSHAREDacrossallsevenarms,soatround1thisequalityis

\>exactandanydeviationindicatesaBUGINMYCOMPUTATION,notaresult\.Atrounds2\-3each

\>armcollecteditsownbatch,soequalityisexpectedonlyapproximately\.

\>\*\*arm5isexplicitlyNOTpredictedequaltoarm2\*\*:mirroringpreservesmeanandSDbutnot

\>theabsolute\-valuemarginal\.Recordingthisinadvancesothatanarm2\!=arm5scaledifference

\>isnotlatermisreadaseitherabugoradiscovery\.

\*\*B\-PRIMARY\-ALLOCATION\-\-\-construction\-variant;theONLYpartthatcandistinguisharmswithina

family\.\*\*Shufflingchanges\*which\*turnsreceivewhichweight,andturnsdifferintokencount,

sothisgenuinelydiffersbetweenarm2andarm4\.Statistics,alltoken\-count\-weightedover

‘\|w\_t\.A\_i\|‘:

\-token\-count\-weighted\*\*quantiles\*\*q10/q25/q50/q75/q90;

\-\*\*Ginicoefficient\*\*\(tokencountsasfrequencyweights\);

\-\*\*effectivesamplesize\*\*oftheweightdistribution,Kishform‘ESS=\(Sumw\)^2/Sumw^2‘,

reportedbothrawandnormalizedbythenumberofturns\.

\#\#\#\#B\-CORROBORATIVE\(trainingoutcomes\-\-\-maysupport,NEVERcarry\)

Per\-round\*\*gradient\-normtrajectory\*\*and\*\*policy\-entropytrajectory\*\*\(R38logs\)\.Explicitly

demoted:usingtrainingoutcomestoprove"inputformdrivesoutputdistribution"risks

circularity,sincebotharedownstreamofthesameupdates\.Reported,neverdecisive\.

\-\-\-

\#\#2\.POSITIVECONTROL\-\-\-theyardstickthatmakesaGroup\-Bnullinterpretable

Per\-arm\*\*creditnon\-zerocoverage/sparsity\*\*:thefractionofturnswith‘w\_t\!=0‘\.

Known,byconstruction,tospanawiderange\-\-\-arm1uniform‘w\_t=1\.0‘oneveryturn;arm6sparse

\(signofA\_replayonsampledturnsonly,0elsewhere\);\{2,4,5\}continuousandnear\-fully

non\-zero;\{3,7\}three\-valuedin\{\-1,0,1\}withmanyexactzeros\.\*\*Thisspreadislargeandknown

inadvance,soitisayardstickwithadequaterange\.\*\*

Thesamecorrespondenceprocedure\(S3\)isrunagainsttheJSmatrixforsparsity\.

\#\#\#FROZENREADINGRULE\-\-\-exactlyonebranchisdeclaredtohavefired

\-\*\*sparsitycorrespondsANDB\-PRIMARYcorresponds\*\*\-\>mediation\*\*SUPPORTED\*\*\.

\-\*\*sparsitycorrespondsANDB\-PRIMARYnull\*\*\-\>theGroup\-Bnullis\*\*MECHANISTIC\*\*:thedesign

demonstrablydetectsarealcorrespondencewhenoneexists,andthisoneisabsent\.

\-\*\*sparsitydoesNOTcorrespond\*\*\-\>n=21pairsis\*\*UNDERPOWEREDforANYcorrespondenceclaim\*\*;

A3Bstaysdescriptiveand\*\*nomediationconclusionisdrawnineitherdirection\*\*\.

\#\#\#FROZENREADINGRULEfortheB\-PRIMARYsplit\(thisaddendum’saddition\)

\-\*\*SCALEseparatesacrossfamiliesANDALLOCATIONcorrespondstoJS\*\*\-\>themediationchainis

supportedat\*\*bothlinks\*\*\.

\-\*\*SCALEseparatesacrossfamiliesBUTALLOCATIONisnull\*\*\-\>theeffectiscarriedby\*\*scale

alone\*\*;within\-familyJSsimilarityisthenexplained\*\*byconstruction\*\*,andthemechanism

claimis\*\*limitedtoacross\-familydifferences\*\*\.Thisisstatedplainly,notsoftened\.

\-\*\*SCALEdoesNOTseparateacrossfamilies\*\*\-\>theStep\-0selectednarrativeis\*\*contradicted

byitsownpredictedconsequence\*\*\.Reportthatand\*\*RE\-OPENthenarrativequestionrather

thanproceeding\*\*\-\-\-donotfallbacktotheexcludednarrative\(b\),whichremainsbarred;the

correctresponseistodeclarethemechanismquestionopen\.

\-\-\-

\#\#3\.CORRESPONDENCEMETHOD\(frozen\)

Distance\-matrixcorrespondenceagainstthe\*\*A3BJS\-divergencematrix\*\*,computedSEPARATELYfor

GroupA,B\-PRIMARY\-SCALE,B\-PRIMARY\-ALLOCATION,B\-CORROBORATIVE,andthesparsitycontrol\.

\-Arm\-levelJSdistance=meanJSoverthatarm\-pair’sconstituentcheckpointpairs=\>a7x7

matrix,\*\*21uniqueoff\-diagonalpairs\*\*\.

\-Featuredistancebetweenarms:‘\|f\_i\-f\_j\|‘forscalarfeatures;Euclideandistanceoverthe

standardizedvectorformulti\-componentfeatures\(thequantilevector\)\.

\-\*\*Statistic:\*\*Pearsoncorrelationbetweenthe21JSpair\-distancesandthe21feature

pair\-distances\(Mantelform\)\.

\-\*\*Null:\*\*theSAMEwithin\-seedrestrictedpermutationasA3B\-\-\-permutearmlabels\*\*withineach

seedindependently\*\*,10,000draws,recomputingthearm\-levelmatricesandthecorrelationeach

time\.Reporttheobservedstatistic,thenulldistribution\(mean,SD,quantiles\)andp\.

\-\*\*arm5/seed2excluded\*\*fromprimary,asinA3B\_PREREG\.arm2\|s1andarm7\|s1flagged\(D2\)\.

\*\*POWERLIMITATION,statedinadvanceandrepeatedbesideeverycorrespondenceresult:\*\*with7

armsthereareonly21uniquepairs,andtheyarenotindependent\(eacharmappearsin6pairs\)\.

Thepermutationnullrespectsthatdependency,butthedesigncanonlydetectLARGE

correspondences\.Anullcorrespondencethereforedoes\*\*not\*\*establishabsenceofmediation

unlessthesparsitypositivecontrolfired\-\-\-whichispreciselywhythecontrolispre\-registered\.

\-\-\-

\#\#4\.REGISTEREDDIRECTIONALPREDICTION\-\-\-accumulationacrossrounds

Between\-armseparationinGroupB\*\*accumulates\*\*:\*\*r1<r2<r3\*\*\.

Themonotonicityitselfistested,notmerelyfinal\-roundmagnitude\.

\-\*\*Statistic:\*\*meanbetween\-armseparationintheGroup\-Bfeatureateachround;Spearman

correlationwithroundindex\(1,2,3\),computedperseedandaveraged\.

\-\*\*Primarytest:\*\*monotonicitypermutationtest\-\-\-permuteroundlabelswithinseed,10,000

draws\.\*\*Alsoreported:\*\*Page’sLtrendtest\.

\-\*\*Powercaveatfrozennow:\*\*3roundsx3seedsisaveryshortseries;Page’sLon3

conditionshasminimalresolution\.Reportedwiththatlimitationattached\.

\*\*Whyr1isthecleanestbaseline\(recordedinadvance\):\*\*round1’scollectionwas\*\*SHARED

acrossallsevenarms\*\*,soeveryarmsawtheidenticalbatchandr1’sseparationarisesfrom

\*\*exactlyoneupdate’sworthofcreditdifference\*\*\.Amonotoner1<r2<r3patternistherefore

evidence\*\*independentofabsolutemagnitude\*\*\.

\-\-\-

\#\#5\.STATISTICCORRECTION\(frozen\)

Thepreviously\-contemplated"fractionofzero\-variance\(all\-fail/all\-succeed\)groups"is

\*\*ill\-definedatG=1\*\*:thebaselineisthemeanoverthewhole96\-trajectorybatch,andat~40%

winratenobatchisall\-fail,soitistrivially0foreveryarm\.\*\*Withdrawn\.\*\*Replacedby:

\-\*\*per\-batchSDofA\_i\*\*,and

\-\*\*fractionoftrajectorieswith\|A\_i\|belowathresholdfixedhere:0\.5post\-normalization\*\*

\(halfabatchSD\)and\*\*0\.1pre\-normalization\*\*\.

\*\*TwodegeneraciesrecordedNOW,beforecomputing,sotheyarenotlatermistakenforfindings:\*\*

1\.Outcomesarebinaryandthebaselineisthebatchmean,sowithinabatch‘A\_i‘takesexactly

\*\*two\*\*values,‘\(1\-p\)‘and‘\-p‘forwinratep\.Hencethe"fractionbelowthreshold"isa

deterministicfunctionofpandcarriesnoinformationbeyondthewinrate\.

2\.\*\*Post\-normalizationtheper\-batchSDofA\_iisexactly1\.0byconstruction\.\*\*Theper\-batch

SDisthereforereported\*\*PRE\-normalization\*\*\(‘=sqrt\(p\(1\-p\)\)‘\),whereitisinformative\.

\-\-\-

\#\#6\.WRITING\-SIDECONSTRAINT\(travelswiththedata\)

The\*\*StepOPSDcredit\-budget\-normalizationimplicationisSTRICTLYCONDITIONALonB\-PRIMARY

correspondenceholding\.\*\*IfB\-PRIMARYisnull,thatimplicationappearsin\*\*NOdocument\*\*\.

Recordedheresotheconditiontravelswiththeresultratherthanlivingonlyincorrespondence\.

\-\-\-

\#\#7\.RULES

AllthresholdsandreadingrulesabovearefrozenBEFOREanyresultwasviewed\.D4isexploratory

andlabelledthroughout\.\*\*AnullB\-PRIMARYcorrespondenceisafulldeliverableandisreported

asplainlyasapositiveone\.\*\*ALL\_EXPERIMENTS\_RECORDentryperstepatthestepboundary\.

Everystageclaimopenswithaverbatimdiskprobe\(F1/F4\)\.Commitsverifiedbyre\-reading

‘gitlog‘,neverbytrustingareturnvalue\(e38\)\.ntfyateachstageboundaryandatthefinal

stop\.

Signed\(executionpre\-registration,exploratory\):\*\*2026\-08\-07\*\*,tag‘a3b\-delta\-v1‘\.

\#A3B\-DeltaAMENDMENT1\(Addenda2\+3\)\-\-\-frozenbeforeanymatrixwascomputed

AmendsA3B\_DELTA\_PREREG\.md\(‘a3b\-delta\-v1‘\)\.Tag‘a3b\-delta\-v2‘\.Exploratory;zeroGPU\.

A3B\_PREREG\.md,KILLSHOT\_PREREG\.md,KS2\_PREREG\.md,PC/PC2preregsandbothVERDICTsremain

IMMUTABLEanduntouched\.E031remainsthesinglesourceoftruthfortheA3Bwording:the

discretenullandthecontinuouspositivearealwaysstatedtogether\.

Status:\*\*nothinghadbeencomputedwhenthiswasfrozen\*\*\-\-\-nomatrix,nostatistic,no

correspondence\.ThedefectinSAwascaughtbeforeanyrun\(e39\)\.

\-\-\-

\#\#A\.e39RESOLVED\-\-\-allocationisaNEGATIVECONTROL,notamediatorcandidate

Thetoken\-countfrequencyweightingin‘a3b\-delta\-v1‘S1is\*\*WITHDRAWN\*\*\.‘ks2\_train\_update\.py:242‘

dividesby‘rmask\.sum\(\-1\)‘,sotokencountnormalizesOUT:everyturncontributesequally

regardlessoflengthandtheeffectiveper\-tokenweightis‘\|w\_t\.A\_i\|/ntok\_t‘\.Replacedbyfour

\*\*pairing\*\*statistics\(weight\-to\-CONTENT,theonlythingshufflingchanges\):

\-Spearman‘corr\(w\_t,turnindex\)‘withintrajectory,averagedovertrajectories

\-Spearman‘corr\(w\_t,ntok\_t\)‘

\-Spearman‘corr\(w\_t,per\-turnmeansampled\-tokenNLL\)‘

\-ratiooftoken\-weightedtounweightedmean‘\|w\.A\|‘\(scalarsummaryofw\-to\-lengthalignment\)

\*\*ROLECHANGE\(frozen\):\*\*allocationisnowa\*\*NEGATIVECONTROL\*\*\.Reasoningrecorded:A3B

alreadyshowstheJSmatrixclustersbyinstrumentfamily,and\*within\*afamilythearmsdiffer

ONLYinallocation\(shuffle/mirror\)\.Sowithin\-familyJSsimilarity\*\*IS\*\*thefindingthat

allocationdoesnotdrivebehaviour\.Theallocationstatisticsarereported\*\*expectingthemto

differsharplywithinfamilywhileJSdoesnot\*\*\-\-\-thatcontrastisitselftheresult,and\*\*no

correspondencetestisrunorneededtoestablishit\*\*\.

\*\*REQUIREDNUMBER\(frozen\):\*\*fromthe21x21matrix,thebetween\-armJSdistancesfor

\*\*arm2\-vs\-arm4\*\*and\*\*arm3\-vs\-arm7\*\*specifically,reportedbesidewithin\-arm\(0\.0198\)and

overallbetween\-arm\(0\.0520\)\.Ifwithin\-familybetween\-arm~=within\-arm,thenegative\-control

argumentholds\.

\*\*PAPERNOTE\(frozen\):\*\*‘corr\(w\_t,per\-turnmeansampled\-tokenNLL\)‘is\*\*KS1’sT3mirroredonto

thetraininginput\*\*\-\-\-arm2predictedhigh,arm4nearzero\.Itre\-quantifiesthefluency\-echo

findingonthequantitythegradientactuallyconsumed,independentlyofA3B\.

\-\-\-

\#\#B\.OPTIMIZERINVARIANCE\-\-\-thepure\-scalereadingisDOWNGRADED

AdamW’supdate‘lr\.m/\(sqrtv\+eps\)‘isinvarianttouniformrescalingoftheloss\(‘g\-\>cg‘=\>‘m\-\>cm‘,

‘v\-\>c^2v‘,‘m/sqrtv‘unchanged\)\.AuniformdifferenceincreditSCALEacrossarmsistherefore

\*\*largelyABSORBED\*\*anddoesnottranslateintoeffectivestepsize\.WhatsurvivesAdam:

1\.\*\*ZEROSTRUCTURE\*\*\-\-\-‘w=0‘contributesexactlyzerogradient\(trainer‘:105\-106‘,andthe

‘:135‘filterdropsthoseexamplesentirely\),soarmsdifferin\*\*EFFECTIVESAMPLESIZE\*\*;

2\.\*\*WITHIN\-BATCHRELATIVEWEIGHTING\*\*\-\-\-whichexamplesdominatethegradientdirection;Adam

doesnotnormalizeacrossexamples;

3\.the\*\*earlytransient\*\*,plus\*\*gradientclipping\*\*\.

\*\*Codefacts,verified\(Bactions1and2\):\*\*

‘‘‘

scripts/ks2\_train\_update\.py:252gn=torch\.nn\.utils\.clip\_grad\_norm\_\(

scripts/ks2\_train\_update\.py:253\(pforpinmodel\.parameters\(\)ifp\.requires\_grad\),

scripts/ks2\_train\_update\.py:254opt\_cfg\["grad\_clip\_norm"\]\)

configs/ks2\_training\_config\.jsonoptimizer:\{"name":"AdamW","lr":5e\-05,"betas":\[0\.9,0\.999\],

"grad\_clip\_norm":1\.0,"weight\_decay":0\.0,

"schedule":"constant"\}

‘‘‘

\-\*\*ClippingEXISTSatnorm1\.0\*\*,soscaleinvarianceis\*\*notperfect\*\*andBOTHroutesare

reported\.Empiricallyit\*\*bindsrarelyandonlylate\*\*:fractionofoptimizerstepswith

grad\-norm\>1\.0is\*\*0\.000atr1\*\*forarms1/2/6,risingto\*\*0\.055\(arm1\)and0\.096\(arm2\)

atr3\*\*,and\*\*0\.000forarm6ateveryround\*\*\.Sothescalerouteisavailablemainlytothe

densearmsinround3\.

\-\*\*weight\_decay=0\.0\*\*=\>AdamW’sdecoupled\-decaychannel\(whichisNOTscale\-invariant\)is

\*\*INERTinthisdesign\*\*\.Recordedasachannelthatexistsinprincipleandisswitchedoff

here\.

\*\*AMENDEDR43NARRATIVE\(supersedesthepure\-scalewording\):\*\*

\>\*\*creditzero\-structure\+within\-batchrelativeweighting\-\>effectivesamplesizeandgradient

\>direction\-\>policydistribution\.\*\*

Thepure\-scalereading\("differentcreditscale=\>differenteffectivestepsize"\)is

\*\*DOWNGRADED\*\*toapartialchanneloperativeonlywhereclippingbinds\.Reasonwrittenout:under

AdamWauniformrescaleofthelossleaves‘m/sqrtv‘unchanged\.The\*\*excluded\*\*narrative\(b\),the

arXiv:2509\.02534S6\.3noise\-amplificationroute,\*\*remainsexcluded\*\*\(R43\)andisnotrevivedby

thisamendment\.

\*\*arm6REFRAME\(frozen\):\*\*\|\|lora\_B\|\|1\.37vs~4\.7is~3\.4x,whileacoverage\-basedpredictionwould

giveroughly8\-\-14x\-\-\-a\*\*compressionconsistentwithAdamabsorbingmuchofthemagnitude

differencewhilezero\-structurestillcostsrealgradient\*\*\.Therefore:report\*\*predicted\-by\-

coverageORDERINGvsobserved\|\|DeltaW\|\|ORDERING\*\*\(Spearman\)\.\*\*NOfalsifiableratiopredictionis

stated\*\*,becauseunderAdamWnosimpleanalyticmapexists\.

\*\*Consequentamendmenttoa3b\-delta\-v1S2branch3\*\*\(Addendum\-2item4\):"SCALEdoesnotseparate

acrossfamilies"does\*\*NOT\*\*byitselfcontradicttheStep\-0narrative\-\-\-thenarrativepredicts

scaledifferencesPROPAGATE,notthatarmsmustdifferincreditscale\.The\*\*upstream\*\*quantity

\(per\-armmean‘\|w\_t\|‘andnon\-zerocoverageoftheRAWcredit\)isreportedFIRST\.Thenarrativeis

contradictedonlyifcreditscales\*\*genuinelydifferacrossarmsAND\*\*‘\|w\_t\.A\_i\|‘/‘\|\|DeltaW\|\|‘

\*\*failtotrackthem\*\*\.

\-\-\-

\#\#C\.DeltaW:MAGNITUDE\*\*AND\*\*DIRECTION,reportedseparately

Newmediatornode,measuredindependentlyfromthe21storedadapters\(zeroGPU\):

\-\*\*Magnitude:\*\*‘\|\|lora\_B\|\|‘andthefull‘\|\|DeltaW\|\|=\|\|B\.A\|\|‘Frobenius,\*\*pertargetmoduleand

aggregate\*\*\.

\-\*\*Direction:\*\*flatteneach‘DeltaW=B\.A‘;\*\*21x21pairwisecosinesimilarity\*\*;plus

\*\*principalangles/subspaceoverlap\*\*betweenLoRAsubspaces\.

Rationalerecorded:twoadaptersofequalnormcanpointinentirelydifferentdirections,and

"didthesamecreditrulepushthemodelthesameWAY"istheclosestparameter\-spaceanalogueof

theJSbehaviouralmeasure\.\*\*Magnitudeanddirectionareorthogonalandcandissociate;theyare

reportedseparatelyandnevermerged\.\*\*

\-The\*\*sameA/B/C\+within\-seedrestrictedpermutation\*\*analysisisrunonthe\*\*direction\*\*

matrix\.

\-\*\*PartialMantel\*\*ofJSon‘\|\|DeltaW\|\|‘distance,\*\*withdirectionasaSECONDcovariate\*\*\.Both

\*\*zero\-orderandpartial\*\*statisticsreportedwiththeirnulls\.

\-\*\*FROZENREADING:\*\*signaturevanishesaftercontrollingstepsize\-\>theeffectis

\*\*scale\-mediatedandH\_instrumentisreallyH\_scale\-\-\-stateitplainly\*\*;residualsignature

survives\-\>\*\*allocation/contentcontributesbeyondscale\*\*\.

\-\-\-

\#\#D\.STALEARTIFACT\-\-\-corrected,withthetwoquestionskeptseparate

‘runs/ks2/r1/r38\_d2\_round1\_stats\.json‘asserts‘"std\_normalized":false‘citing

‘ks2\_train\_update\.py:96‘\(a\*\*v1\.3\*\*line\)\.Under\*\*v1\.4\*\*theadvantage\*\*IS\*\*std\-normalized

\(A\_ialone,R43\)\.Twothingsarecorrected\*\*separatelyandmuststayseparate\*\*:

1\.\*\*Theannotationwasstale\-\-\-factual,fixed\.\*\*

2\.\*\*WhetherDarkRoom’smechanismsnowapplyisaSEPARATEquestion\*\*,arguedonitsmerits,not

inheritedfrom\(1\)\.Ourdivisoriscomputed\*\*fromoutcomesaloneandiscredit\-blind\*\*,andat

\*\*G=1therearenogroups\*\*fortheall\-fail\-grouppropositiontorangeover\.

\*\*"Theannotationwaswrong"mustNOTexpandinto"theconclusionreverses"withoutthat

argument\.\*\*FeedsV4\.

\-\-\-

\#\#E\.ENTROPY\-\-\-corroborativeonly;availabilityaccepted

Full\-distributionpolicyentropywas\*\*neverlogged\*\*and\*\*staysunrun\*\*\(wouldneedGPU\)\.The

\*\*R38sampled\-tokenNLLproxy\*\*isreconstructedfrom‘gen\_logprobs‘for\*\*r2/r3\*\*perarm;\*\*r1is

sharedcollectionandthereforearm\-independent\*\*\.LabelledexactlyasR38did:\*mean\-logprobof

sampledtokens,arealizedcross\-entropyproxy,NOTfull\-distributionentropy\.\*

\*\*B\-CORROBORATIVEstandingreminder\(frozen\):\*\*grad\-normandNLL\-proxytrajectoriesare

\*\*OUTCOMESoftraining,notinput\-sidequantities\*\*;theymaycorrelatewiththefinalpolicy

distributionbecausebothareproducedbythesameprocess\.Theyremain\*\*corroborative\*\*\.The

mediationclaimrestson\*\*‘\|w\_t\.A\_i\|‘and‘\|\|DeltaW\|\|‘\*\*\.

\-\-\-

Signed\(executionpre\-registrationamendment,exploratory\):\*\*2026\-08\-07\*\*,tag‘a3b\-delta\-v2‘\.

\#A3B\-DeltaADDENDUM3\(ideationpacket2026\-08\-07\)\-\-\-dose\-matchedcontrast

AmendsA3B\_DELTA\_PREREG\.md\(‘a3b\-delta\-v1‘\)andA3B\_DELTA\_AMENDMENT\.md\(‘a3b\-delta\-v2‘\)\.

Tag‘a3b\-delta\-v3‘\.Exploratory\.Written\*\*beforeanyTask\-1computationwasrun\*\*\.

E031anditsfivetravellingconditionsareunchangedandremainthesinglesourceoftruth;

\*\*clause\(e\)ismandatorywhenevertheJSclusteringiscited\.\*\*

\-\-\-

\#\#0\.POST\-HOCDISCLOSURE\-\-\-READTHISBEFOREANYNUMBERBELOW

\>\*\*THISISAPOST\-HOCEQUIVALENCEANALYSIS,NOTAPRE\-REGISTEREDCONFIRMATORYTEST\.\*\*

\>Thethreedose\-matcheddistances\(0\.0272/0\.0124/0\.0281\)andthewithin\-armfloor

\>\(0\.0198\)werereportedinE034andappearintheideationpacketthatcommissionedthis

\>task\.Theyweretherefore\*\*visiblebeforeanyequivalencemargincouldbechosen\*\*\.No

\>marginselectednowcanbecalledpre\-registered,andthisanalysismustneverbepresented

\>asone\.

\>

\>\*\*WHATREMAINSVALID:\*\*therestricted\-permutationp\-values\.Theirnullisgeneratedby

\>permutationwiththeobservedstatisticheldfixed,sotheircalibrationdoesnotdependon

\>whentheobservedvaluewasseen\.

\>

\>\*\*WHATISCOMPROMISED:\*\*thechoiceofequivalencemargin,andanypass/failverdictthat

\>restsonit\.

\>

\>\*\*MITIGATION:\*\*themarginisfixedbyarulestatable\*\*independentlyoftheobserved

\>dose\-matchedvalues\*\*\-\-\-seeS2\-\-\-andtheprimaryread\-outisthe\*\*continuousposition

\>measure\*\*ofS4,whichneedsnomarginatall\.

Thisdisclosureisreproducedverbatimineveryreportofthisresult\.

\-\-\-

\#\#1\.CORRECTION1\-\-\-arm5isNOTmagnitude\-multiset\-identical

Mirroring‘v\-\>2m\-v‘preservesthe\*\*sum,mean,SDandrange\*\*\(the‘Sum\|2m\-v\|=Sum\|v\|‘

identityestablishedinE033,validbecausenomirroredvaluegoesnegative:0/3563turns,

min0\.7917\)\.Itdoes\*\*NOT\*\*preservethemagnitude\*\*multiset\*\*\-\-\-thedistributionis

\*\*REFLECTED\*\*,so\*\*skewflipssign\*\*\.

Registeredstatements,tobeusedverbatim:

\-\*\*arm2<\-\>arm4andarm3<\-\>arm7\*\*:dose\-matched\*\*ANDmagnitude\-multiset\-identical\*\*\(a

permutationofthesamevalues\),\*\*allocationdestroyed\*\*\.

\-\*\*arm2<\-\>arm5\*\*:dose\-matched,\*\*first\-andsecond\-momentmatched\*\*,magnitudedistribution

\*\*REFLECTED\(skewinverted\)\*\*,andthecredit\-\-fluencycorrelation\*\*sign\-flipped\*\*

\(\-0\.2890\-\>\+0\.2911,E034\)\.

\*\*Thephrase"magnitude\-multiset\-identical"mustneverbeappliedtoarm5\*\*inanydocument\.

\-\-\-

\#\#2\.CORRECTION2\-\-\-theequivalencemargin,andtherulethatfixesit

\*\*MARGINRULE,statableindependentlyoftheobserveddose\-matcheddistances:\*\*

\>Theequivalencemarginisthe\*\*95thpercentileofthewithin\-armacross\-seedJSdistance

\>distribution\*\*\(pairclassA:samearm,differentseeds;n=19pairs,arm5\|s2excluded\)\.

\*\*RATIONALE:\*\*classAisthedesign’sownestimateof\*"howfaraparttwocheckpointsget

whenthecreditruleisheldconstantandonlytheseeddiffers"\*\-\-\-i\.e\.seednoise\.Its95th

percentileisthenaturalupperedgeofthatnoise\.Therulereferencesonlyclass\-Apairs,

whichare\*\*not\*\*thequantityundertest,sothemarginisnotchosenbylookingatthe

dose\-matchedvalues\.Itwas,however,chosen\*after\*theclass\-Adistributionwasitself

visible,whichiswhythepost\-hoclabelinS0stillappliesandisnotliftedbythisrule\.

\*\*EQUIVALENCEVERDICT:\*\*adose\-matchedpairis\*equivalentwithinthestatedmargin\*iffits

distance<=margin\.Reportedasabinaryalongside\-\-\-neverinplaceof\-\-\-S4’spositionmeasure\.

\-\-\-

\#\#3\.CORRECTION3\-\-\-CRNasymmetryrunstheOPPOSITEwayhereandiscontrolled

Round\-1collectionwas\*\*SHAREDacrossallsevenarms\*\*\.Therefore,fordose\-matchedpairs:

\-\*\*\(a\)SAME\-seedcross\-arm\*\*\(e\.g\.arm2/s0<\-\>arm4/s0\):\*\*sharestheround\-1batch\*\*,differs

incredit\.Extradatasharingcanpullsuchapairtowardthewithin\-armfloorforreasons

thathavenothingtodowithcreditcontentbeinginert\.

\-\*\*\(b\)CROSS\-seedcross\-arm\*\*\(e\.g\.arm2/s0<\-\>arm4/s1\):\*\*sharesnodata\*\*,differsin

credit\.Thismatchesthewithin\-armfloor’sowndata\-sharingstatus\(classApairsalso

sharenodata\),soitisthe\*\*cleancontrastandthePRIMARYquantity\*\*forthe

equivalenceframing\.

\*\*BOTHarecomputedandreported,andeveryreportednumberstateswhetheritis\(a\)or\(b\)\.

If\(a\)and\(b\)diverge,thatdivergenceisitselfaresultandisreportedasone\.\*\*

Notethedirectionofthebiasthiscontrols:inA3B’soriginalframingtheCRNasymmetrymade

‘mean\(A\)\>mean\(B\)‘a\*strong\*bar;hereitrunstheotherway,makingsame\-seedpairslook

\*artificiallyclose\*\.Sameasymmetry,oppositesign,becausethecomparisontargetchanged\.

\-\-\-

\#\#4\.CORRECTION4\-\-\-continuouspositionmeasure\(theprimaryread\-out\)

Foreachdose\-matchedpair:

\>\*\*position=\(d\_pair\-d\_within\)/\(d\_between\-d\_within\)\*\*

where‘d\_within‘=meanclass\-A\(within\-arm,across\-seed\)JSand‘d\_between‘=meanoverall

between\-armJS\.0%=indistinguishablefromseednoise;100%=atypicalbetween\-armpair\.

\*\*ReportedwithaCI\*\*\(bootstrapovertheconstituentcheckpointpairs,10,000resamples\)\.

Thisis\*\*moreinformativethanapass/fail\*\*and\*\*doesnotdependonthecompromised

margin\*\*,soitistheprimaryread\-out\.Computedvaluesarereported;noanticipatedvalueis

recordedhere,preciselybecausetheinputswerealreadyvisible\.

\-\-\-

\#\#5\.CORRECTIONOFANEARLIERCLAIMOFMINE\-\-\-"atorbelowwithin\-arm"wasWRONG

E034andPROGRESSB27statethatthewithin\-familycross\-armdistancesare\*"atorBELOWthe

within\-armlevel\(0\.0198\)"\*\.\*\*Thatisfalseandtheerrorismine\.\*\*Twoofthethreeare

\*\*ABOVE\*\*it:

\|dose\-matchedpair\|JS\|vswithin\-armfloor0\.0198\|

\|\-\-\-\|\-\-\-\|\-\-\-\|

\|arm3<\-\>arm7\|0\.0124\|\*\*below\*\*\|

\|arm2<\-\>arm4\|0\.0272\|\*\*ABOVE\*\*\|

\|arm2<\-\>arm5\|0\.0281\|\*\*ABOVE\*\*\|

Thesupportableclaimis:\*\*"abovethewithin\-armfloor,butfarbelowtheoverall

between\-armlevel\(0\.0515\)"\*\*\.Theoriginalwordingoverstatedthenegativecontrol\.It

originatedinmyownreportandwaspassedthroughunchecked;bothsitesarecorrectedin

placewiththecorrectionnoted,andthecorrectedformiswhateverylaterdocumentuses\.

\-\-\-

\#\#6\.FROZENREADING\(withthepost\-hoclabelpermanentlyattached\)

\-\*\*Equivalentwithinthestatedmargin\*\*\-\>thetraining\-layersentenceissupported,andis

written\*\*only\*\*withtheS0post\-hocdisclosureattached\.

\-\*\*Notequivalent\*\*\-\>reportthedistancesplainlyas\*\*"aboveseednoisebutfarbelow

between\-arm"\*\*,givethecontinuouspositionmeasureofS4,and\*\*DONOTwritethe

sentence\.\*\*

\*\*POWER:\*\*thereareonly\*\*3dose\-matchedcontrasts\*\*availableintheentiredesign

\(arm2<\-\>arm4,arm3<\-\>arm7,arm2<\-\>arm5\)\.Thisisreportedbesideeveryverdict\.Withn=3contrasts

noequivalenceclaimcanbestrong,andtheanalysiscannotdistinguishsmallrealdifferences

fromnoise\.

\-\-\-

Signed\(exploratoryaddendum,writtenbeforeanyTask\-1computation\):\*\*2026\-08\-07\*\*,

tag‘a3b\-delta\-v3‘\.

\#A3B\-DeltaADDENDUM4\-\-\-ther1dose\-matchedcontrast

Amends‘a3b\-delta\-v1‘/‘\-v2‘/‘\-v3‘\.Tag‘a3b\-delta\-v4‘\.Exploratorythroughout\.

\*\*Writtenbeforeanyr1agreement,JSorpositionnumberwascomputed\.\*\*

E031anditsfivetravellingconditionsunchanged;clause\(e\)mandatorywherevertheJS

clusteringiscited\.

\#\#0\.POST\-HOCDISCLOSURE\-\-\-strongerherethaninTask1,andstatedfirst

\>\*\*THISISANEXPLORATORYANALYSISWHOSETHRESHOLDSWERESETKNOWINGTHEr3RESULT\.\*\*Ihave

\>alreadyseenther3dose\-matchednumbers\(\+27\.0%/\+17\.8%/\-23\.2%,E036\)andther3

\>perturbationstrengths\(E040\)\.Nothingcomputedunderthisaddendumcanbecalled

\>pre\-registeredintheconfirmatorysense,anditmustneverbepresentedassuch\.

\>

\>\*\*WHATREMAINSVALID:\*\*therestricted\-permutationp\-values\-\-\-theirnullisgeneratedby

\>permutationwiththeobservedstatisticheldfixed,socalibrationdoesnotdependonwhen

\>anythingwasseen\.The\*\*margin\-freepositionmeasure\*\*likewiseneedsnothreshold\.

\>

\>\*\*WHATISCOMPROMISED:\*\*anyequivalencemargin,andthechoiceof"materiallydiffer"in

\>thefrozenreadingofS4\.S4thereforefixesthatphrasenumerically\*\*now\*\*,beforethe

\>computation,ratherthanafter\.

\#\#1\.WHYr1ISTHECLEANERCONTRAST

Task1’sthreedose\-matchedcontrastswerecomputedon\*\*r3\*\*adapters\.Byr3eacharmhad

collecteditsownr2andr3batches,sothearmsdifferin\*\*trainingdata\*\*aswellascredit

rule\-\-\-aconfoundTask1couldnotremove\.

\*\*Round1collectionwasSHAREDacrossallsevenarms\*\*:thesame288trajectories\(96tasksx

3seeds\),thesamedose,exactly\*\*one\*\*update,and\*\*creditistheonlydifference\*\*\.

Confirmedondisk:everyr1updatelogrecords

‘store=/workspace/ks1/runs/ks2/r1/shared/s<seed\>/trajectories‘\.The21r1adaptersexistand

aresha256\-recorded\(Task5,‘runs/pc2/a3b\_intermediate\_adapter\_check\.json‘,42/42present\)\.

\#\#2\.PROTOCOL\-\-\-identicaltoA3BStage2ineveryrespectexceptthecheckpointround

\-\*\*Samestatebank\*\*,verifiedbyhashbeforescoring:

‘sha256=8ec0924492f276e55fc8412e0c0ac048c7e4082f75144516b0ac4009afe22a36‘

\(‘runs/pc2/a3b\_state\_bank\.jsonl‘,500states,base\-modelgreedyoverthefrozen128held\-out

tasks\)\.Thehashisre\-verifiedatruntimeandpastedintherecord\.

\-Greedy,temperature0,‘TOPK=20‘\(vLLM’scap;JSonthetop\-20support\),sameprompt

template,same‘parse\_action‘canonicalizationviatheharness’se17parser\.

\-\*\*arm5\|s2excluded\*\*fromprimary,asin‘a3b\-prereg\-v1‘\.

\-Metrics:canonicalactionagreement,JSdivergence,classA/B/C,restrictedwithin\-seed

permutationnull\(10,000draws\),andthe\*\*margin\-freepositionmeasure\*\*

‘\(d\_pair\-d\_within\)/\(d\_between\-d\_within\)‘withbootstrapCI\.

\-\*\*CROSS\-SEEDdose\-matchedpairsarePRIMARY\*\*\(theysharenodata,matchingthewithin\-arm

floor’sstatus\);same\-seedreportedbesidethem,per‘a3b\-delta\-v3‘S3\.

\#\#3\.COSTGATE,BEFORELAUNCH

Measuretheper\-checkpointscoringrateonthe\*\*first3adapters\*\*,projectthetotalfor21,

and\*\*posttheprojectionbeforethefullrun\*\*\.Expected1\-\-2GPU\-h\.\*\*Iftheprojection

exceeds3GPU\-h,STOPandreportinsteadofproceeding\.\*\*r2isaddedonlyifitistrivial

oncetheserverisalreadyup,andissubjecttothesamecombinedceiling\.

\#\#4\.FROZENREADING\-\-\-with"materiallydiffer"fixednumericallynow

\-\*\*Ifther1contrastsdiffermateriallyfromr3\*\*\-\>ther3numbersare\*\*confoundedby

collectiondivergence\*\*,and\*\*r1becomesthereportedquantity\*\*\.

\-\*\*Iftheyagree\*\*\-\>ther3resultis\*\*strengthened\*\*\.

\-\*\*Eitherway,BOTHarereported\.\*\*

\*\*"Materiallydiffer"isfixedhere,beforecomputing,as:anydose\-matchedcontrastwhose

positionmeasuremovesbymorethan15percentagepointsbetweenr1andr3,ORanycontrast

thatchangessign\.\*\*15ppischosenasroughlyhalftheobservedr3spreadbetweenthe

extremecontrasts\(\+27\.0%to\-23\.2%~=50pp\),soitisadifferencelargeenoughtochange

whichcontrastisthelargest\-\-\-notathresholdtunedtother1answer,whichisunseen\.

\#\#4b\.CONTINUATIONGATEFORTHECROSS\-FAMILYRUN\-\-\-FROZEN2026\-08\-08,BEFORETHENUMBEREXISTS

\*\*Frozenby\[AUTHOR\-1\]whileItem3wasstillrunningandbeforeanyvirgin\-turncompletionrateor

MDEhadbeencomputed\.Writtenintothisaddendumatthatmoment;thetimestampisthecommit\.\*\*

\>\*\*Thecross\-familyruncontinuesIFANDONLYIFtheprojectedMDEforT3’s

\>per\-trajectory\-Spearmanmedian\-\-\-atthemeasuredvirgin\-turncompletionrate,afterapplying

\>KS1’sv3\.2exclusion\(trajectoriesretaining\>=4completeturns\)\-\-\-is<=0\.50\.\*\*

\*\*RATIONALE,recordedwiththethreshold:\*\*KS1’sobservedT3ismedian\*\*\+0\.752,CI

\[0\.647,0\.793\]\*\*\.AnMDEabove0\.50meanswecouldnotdetectaneffectmeaningfullysmaller

thanKS1’sown\*\*lowerCIbound\*\*,soareplicationattemptcouldnotdistinguish\*"doesnot

replicate"\*from\*"underpowered"\*\.Inthatcaseoption\(a\)buysnothingandoption\(d\)isthe

honestcall\.

\-\*\*MDE<=0\.50\-\>RESUME\*\*thereplaytocompletion\(withinthesignedcross\-familyrun;the$40

gateissatisfiedbythere\-projectionof$11\.38\-\-$22\.84\),thenpipelinesteps4\-\-5:logprob

dumps,thenT3analysis\.\*\*T3isthesoleregisteredprimaryendpoint\-\-\-onceitlandstherun

hasdelivereditspurpose\.\*\*The72Bjudgestageis\*\*NOT\*\*run:itservesonlya

pre\-labelledunderpowereddescriptiveoutputandcostsa145GBstagingoperationwitha

historyofincidents\.Skipped\*\*bydesign\*\*,notbyfailure\.

\-\*\*MDE\>0\.50\-\>STOP\*\*Task3,releasetheGPU,recordtheprojectionanditsarithmetic,and

queueoption\(d\)withthenumbers\.\*\*Donotresume\.\*\*

\*\*Additionalhardstop,frozenwiththegate:\*\*ifthevirgin\-turncompletionrateturnsout

materiallyworsethantheratethisgatewasevaluatedon,\*\*STOPandreport\*\*\-\-\-donot

re\-projectmid\-runtokeepgoing\.

\#\#5\.WHATTHISCANNOTSETTLE

The\*\*strength\-vs\-structurehypothesis\*\*\(DOSE\_CONFOUND\.md\)gainspointshere\-\-\-threecontrasts

perround,withrealizedperturbationstrengthcomputed\*\*perroundpercontrast\*\*\.Goingfrom

3to6or9pointsweakensthe"anytwo\-factormodelfitsthreepointsexactly"objectionbut

does\*\*not\*\*removeit:thetransformsarethesamethreeateveryround,sotheaddedpoints

are\*\*notindependent\*\*drawsovertransformtypes\.Thehypothesisstaysahypothesis\.

Signed\(exploratoryaddendum,writtenbeforeanyr1numberwascomputed\):\*\*2026\-08\-08\*\*,

tag‘a3b\-delta\-v4‘\.

#### R\_ROUTE \(the confidence router\)\.

Chinese\-major source; byte\-exact in the supplementary pack\. Structure, for the reader: frozen under tag1814166…; registered as EXPLORATORY; the single main result is threshold multiplier1\.01\.0, with the six\-multiplier grid registered as sensitivity only; recall and both cost granularities are required to be reported together\.

#### PC3 \(the substrate\-repair method line\)\.

No standalone PC3 pre\-registration file exists in the writing pack — roots searched before this absence claim, per the STOP\-for\-absent rule:/mnt/project/\*\.md\(all 52 knowledge files\),/home/claude/paper/\*\*\. The registered criterion \(S6: same\-type divergence⇒\{\\Rightarrow\}no further configurations\) lives inside the PC3 verdict document, which is Chinese\-major and ships byte\-exact: Its boundary table is rendered in English in Section[K\.4](https://arxiv.org/html/2608.19760#A11.SS4)below\.

### K\.2The four frozen prompt files

The HCAPO template below is extracted verbatim from that paper’s own appendix \(Appendix C\.2\.1\), not reconstructed, and is reproduced here so that the scoring instrument is reproducible from this paper alone\. Two byte\-differing copies of it were previously carried — a working copy and the original\-from\-bundle copy — and that redundancy is now merged to the single copy shown\.

#### Judge prompt v1\.

Role:TaskExecutionEvaluationJudge

Yourcoreresponsibilityistothoroughlyandpreciselyevaluateamulti\-turnepisodeinwhichanagent

interactswithahouseholdenvironment\(ALFWorld\)throughtextactions\.Youmustcarefullyreadtheepisode

topinpointwheretheagent’sdecisionsleadtodeviationsfromsuccessfultaskcompletion\.

InformationProvidedforYourEvaluation

Youwillbegiventhreekeypiecesofinformationtoguideyourassessment:

1\.TaskInstruction:Thehouseholdtasktheagentmustaccomplish\(e\.g\.,"putacleanmuginthecoffeemachine"\)\.

2\.EpisodeTrajectory:Thedetailedrecordofthemulti\-turnepisode\.Eachturnshowstheagent’sactionandthe

environment’sobservationinresponse\.Eachturnisprecededbyalabellike\[TurnN\]\.Actionsaretextcommands

\(e\.g\.,"gotocountertop1","takemug1fromcountertop1","cleanmug1withsinkbasin1","openfridge1",

"heategg1withmicrowave1","putmug1in/oncoffeemachine1"\)\.

3\.FinalOutcome:Whethertheepisodeendedintasksuccessorfailure\.

EvaluationProcess

Deviationsfromsuccessfultaskcompletiontypicallyarisedueto:

\-Theagentfailingtogathersufficientinformationabouttheenvironment\(e\.g\.,notfindingtherequiredobject\)\.

\-Incorrectreasoningorunderstandingbytheagentbasedontheobservationsitreceived\.

\-Theagentexecutingactionsthatareinvalid,redundant,orthatmovethetaskawayfromcompletion\.

Payexceptionallycloseattentiontostate\-changingoperations\(take,put,open/close,clean,heat,cool,toggle\):

thesedirectlydeterminetasksuccessandarecriticalevaluationpointsandfrequentsourcesoferror\.Threekinds

oferrorarepossiblewithstate\-changingoperations:

\(1\)Theagentmightperformtheoperationonthewrongobjectoratthewronglocation\.

\(2\)Theagentperformsanunnecessarystate\-changingoperationthatshouldneverbeexecuted\.

\(3\)Theagentdidnotperformastate\-changingoperationthatthetaskrequires\.

Ifanyofthethreecasesaboveoccurs,youneedtocarefullyreadtheepisodeandidentifytheturnswherethe

agentdeviatesfromthepathtotaskcompletion\.

Foreachturnintheepisode\(identifiedbythe\[TurnN\]tag\),youshouldevaluatewhethertheagent’sactionin

thatturnistheprimarycauseofadeviationfromtaskcompletion\.Assignascoreforeachturn\.Youhavethree

kindsofscoretoassign:

\-Iftheturniscorrect,assignascoreof1\.

\-Iftheturnistheprimaryreasonforadeviation,assignascoreof\-1\.Thiscanonlybeassignedtoatmostoneof

theepisodeturnsifdeviationisfound\.

\-Iftheturnhasissue\(e\.g\.,aninadmissibleactionoraredundantactionthatwastessteps\),assignascoreof0\.

YourResponseFormat

Youmustfirstconductyourevaluationprocesswithina<think\></think\>block\.

Aftercompletingyourthinkingprocess,youmustoutputonlyasingleJSONobject\.Noothertext,commentary,or

explanationshouldbeincludedoutsideoftheJSONblock\.TheJSONobjectmustadherestrictlytothefollowingformat,

includingallturn’sscoresfromscore\_0uptoscore\_n\(wherenisthetotalnumberofturns\)\.

\{

"score\_0":<turn0’sscore\>,

"score\_1":<turn1’sscore\>,

//\.\.\.\(includeallturnsupto’n’\)

"score\_n":<turnn’sscore\>

\}

#### Judge rubric v1\.

Role note: the 5\-point rubric variant is the R39 exploratory rubric\-format prompt \(PC\_PREREG Step 3\); it was never used in any reported number and ships for provenance completeness only\.

Role:TaskExecutionEvaluationJudge

Yourcoreresponsibilityistothoroughlyandpreciselyevaluateamulti\-turnepisodeinwhichanagent

interactswithahouseholdenvironment\(ALFWorld\)throughtextactions\.Youmustcarefullyreadtheepisode

topinpointwheretheagent’sdecisionsleadtodeviationsfromsuccessfultaskcompletion\.

InformationProvidedforYourEvaluation

Youwillbegiventhreekeypiecesofinformationtoguideyourassessment:

1\.TaskInstruction:Thehouseholdtasktheagentmustaccomplish\(e\.g\.,"putacleanmuginthecoffeemachine"\)\.

2\.EpisodeTrajectory:Thedetailedrecordofthemulti\-turnepisode\.Eachturnshowstheagent’sactionandthe

environment’sobservationinresponse\.Eachturnisprecededbyalabellike\[TurnN\]\.Actionsaretextcommands

\(e\.g\.,"gotocountertop1","takemug1fromcountertop1","cleanmug1withsinkbasin1","openfridge1",

"heategg1withmicrowave1","putmug1in/oncoffeemachine1"\)\.

3\.FinalOutcome:Whethertheepisodeendedintasksuccessorfailure\.

EvaluationProcess

Deviationsfromsuccessfultaskcompletiontypicallyarisedueto:

\-Theagentfailingtogathersufficientinformationabouttheenvironment\(e\.g\.,notfindingtherequiredobject\)\.

\-Incorrectreasoningorunderstandingbytheagentbasedontheobservationsitreceived\.

\-Theagentexecutingactionsthatareinvalid,redundant,orthatmovethetaskawayfromcompletion\.

Payexceptionallycloseattentiontostate\-changingoperations\(take,put,open/close,clean,heat,cool,toggle\):

thesedirectlydeterminetasksuccessandarecriticalevaluationpointsandfrequentsourcesoferror\.Threekinds

oferrorarepossiblewithstate\-changingoperations:

\(1\)Theagentmightperformtheoperationonthewrongobjectoratthewronglocation\.

\(2\)Theagentperformsanunnecessarystate\-changingoperationthatshouldneverbeexecuted\.

\(3\)Theagentdidnotperformastate\-changingoperationthatthetaskrequires\.

Ifanyofthethreecasesaboveoccurs,youneedtocarefullyreadtheepisodeandidentifytheturnswherethe

agentdeviatesfromthepathtotaskcompletion\.

Foreachturnintheepisode\(identifiedbythe\[TurnN\]tag\),youshouldevaluatewhethertheagent’sactionin

thatturnistheprimarycauseofadeviationfromtaskcompletion\.Assignascoreforeachturn\.Youhaveafive\-pointrubrictoassign:

\-5=clearlyadvancesthetask\(anecessaryorefficientsteptowardcompletion\)\.

\-4=usefulbutnotnecessary\(reasonableprogress,mildlysuboptimalorderingoraminordetour\)\.

\-3=neutral\(information\-gatheringwithnoprogressandnocost,oranunavoidablestep\)\.

\-2=wasteful\(aredundantaction,oronethatcostsastepwithoutgatheringusefulinformation\)\.

\-1=harmful\(aninadmissibleaction,oronethatactivelymovesawayfromtaskcompletion\)\.

Assignexactlyoneintegerfrom1to5toeveryturn\.Unlikeacoarsethree\-levelscale,youSHOULDusethe

fullrange:reserve5and1forclearcasesanduse4/3/2toexpresstheordinarygradationsbetweenthem\.

Thereisnolimitonhowmanyturnsmayreceiveanyparticularscore\.

YourResponseFormat

Youmustfirstconductyourevaluationprocesswithina<think\></think\>block\.

Aftercompletingyourthinkingprocess,youmustoutputonlyasingleJSONobject\.Noothertext,commentary,or

explanationshouldbeincludedoutsideoftheJSONblock\.TheJSONobjectmustadherestrictlytothefollowingformat,

includingallturn’sscoresfromscore\_0uptoscore\_n\(wherenisthetotalnumberofturns;everyscoreisanintegerfrom1to5\)\.

\{

"score\_0":<turn0’sscore,aninteger1\-5\>,

"score\_1":<turn1’sscore\>,

//\.\.\.\(includeallturnsupto’n’\)

"score\_n":<turnn’sscore\>

\}

#### TARL judge prompt, original\.

\#Verbatimextraction:TARL\(arXiv:2509\.14480\),AppendixC"LLMJudgeSetupfor

\#Turn\-LevelEvaluation"\.Extracted2026\-07\-31viapdftotextfrom

\#https://arxiv\.org/pdf/2509\.14480\(seePROVENANCESb\)\.Linesbelowarethe

\#publishedjudgeprompt,unmodified\(pdftotextligatureartifactspreserved\)\.

Role:TaskExecutionEvaluationJudge

Yourcoreresponsibilityistothoroughlyandpreciselyevaluatemulti\-turnconversationsbetweenauserandan

agent\.Youmustcarefullyreadeachconversationtopinpointwheretheagent’sdecisionsleadtodeviationsfromthe

ground\-truthfunction\-calltrajectories\.

InformationProvidedforYourEvaluation

Youwillbegivenfourkeypiecesofinformationtoguideyourassessment:

1\.Policy:Thisdocumentoutlinesthestrictrulestheagentmustadheretowhenmakingtoolcalls\.Ifanagent’s

actionviolatesthispolicy,youmustimmediatelyhaltitscurrentactionandinstructittoreconsiderandcorrect

itsapproach\.

2\.TaskInstruction:Thisisthespecificinstructionprovidedtotheuser\.Theuser’srequestsandresponsesshould

alwaysalignwiththisinstruction\.Theagentdoesnothaveaccesstothisinstruction\.

3\.Ground\-TruthFunctionCallTrajectories:Thisservesasthedefinitivestandardforassessingtheaccuracyofthe

agent’stoolcalls\.

\-Theagentdoesn’tneedtofollowtheexactorderofthistrajectory\.

\-It’sacceptablefortheagenttocallinformation\-gatheringfunctions\(e\.g\.,get\_order\_details\)multipletimes,

buttheagent’swriteoperation\(modifying,exchanging,returning,orcancelingorders\)needstomatchexactly

withtheground\-truthfunctioncalls\.

4\.ConversationTrajectories:Thisprovidesthedetailedrecordofthemulti\-turnconversationbetweentheuserand

theagent\.Youwillusetheseconversationstoidentifyexecutedtoolsandevaluatethecorrectnessoftheagent’s

processingofresults\.Eachagent’sreasoningandactionwithinaturnwillbeprecededbyalabellike\[TurnN\]\.

EvaluationProcess

Deviationsfromthegroundtruthtypicallyarisedueto:

\-Theagentfailingtogathersufficientorcorrectinformation,eitherthroughfunctioncallsorbyaskingtheuser\.

\-Incorrectreasoningorunderstandingbytheagentbasedontheresultsoftoolexecution\.

\-Theagentnotfollowingpolicy,resultinginwrongexecutionoftools\.

Payexceptionallycloseattentiontooperationsinvolvingmodifying,exchanging,returning,orcancelingorders\.The

agent’scallingforthesefunctionshouldmatchexactlywiththeground\-truth\.Thesearecriticalevaluationpointsand

frequentsourcesoferror\.Threekindsoferrorarepossiblewithwriteoperation:

\(1\)Theagentmightcallthefunctionwithwrongargumentsthatdonotmatchwithground\-truth\.

\(2\)Theagentcallsunnecessarywriteoperationthatshouldneverbecalled\.

\(3\)Theagentdidnotcallthewriteoperationwhichislistedintheground\-truth\.

Ifanyofthethreecasesaboveoccurs,youneedtocarefullyreadtheconversationandidentifytheturnswherethe

agentdeviatesfromtheground\-truth\.

Foreachturnintheconversation\(identifiedbythe\[TurnN\]tag\),youshouldevaluatewhetheragent’sreasoningand

actioninthatturnistheprimarycauseofadeviationfromtheground\-truthfunctioncall\.Assignascoreforeach

turn\.Youhavethreekindsofscoretoassign:

\-Iftheturniscorrect,assignascoreof1\.

\-Iftheturnistheprimaryreasonforadeviation,assignascoreof\-1\.Thiscanonlybeassignedtoatmostoneof

theconversationturnsifdeviationisfound\.

\-Iftheturnhasissue\(e\.g\.,notfollowingthepolicyorfunctioncallformats\),assignascoreof0\.

YourResponseFormat

Youmustfirstconductyourevaluationprocesswithina<think\></think\>block\.

Aftercompletingyourthinkingprocess,youmustoutputonlyasingleJSONobject\.Noothertext,commentary,or

explanationshouldbeincludedoutsideoftheJSONblock\.TheJSONobjectmustadherestrictlytothefollowingformat,

includingallturn’sscoresfromscore\_0uptoscore\_n\(wherenisthetotalnumberofturns\)\.

\{

"score\_0":<turn0’sscore\>,

"score\_1":<turn1’sscore\>,

//\.\.\.\(includeallturnsupto’n’\)

"score\_n":<turnn’sscore\>

\}

#### HCAPO ALFWorld agent template — extracted verbatim from the paper’s appendix, not a reconstruction \(E6 labelling\)\.

\#Verbatimextraction:HCAPO\(arXiv:2603\.08754\),AppendixC\.2\.1"ALFWorldAgent

\#TrainingTemplate"\.Extracted2026\-07\-31viapdftotext\(seePROVENANCESe\)\.

\#PlaceholdersarePython\.format\(\)slots\.Historylength=2forALFWorld

\#\(AppendixC\.2text\)\.Line\-continuationarrowsfromthepaper’slistingremoved\.

YouareanexpertagentoperatingintheALFREDembodiedEnvironment\.

Yourtaskisto:\{task\_description\}\.

Priortothisstep,youhavealreadytaken\{step\_count\}step\(s\)\.Belowarethemostrecent\{history\_length\}observationsandthecorrespondingactionsyoutook:

\{action\_history\}

Youarenowatstep\{current\_step\}andyourcurrentobservationis:\{current\_observation\}\.

Youradmissibleactionsofthecurrentsituationare:\[\{admissible\_actions\}\]\.

Nowit’syourturntotakeanaction\.Youshouldfirstreasonstep\-by\-stepaboutthecurrentsituation\.ThisreasoningprocessMUSTbeenclosedwithin<think\></think\>tags\.Onceyou’vefinishedyourreasoning,youshouldchooseanadmissibleactionforcurrentstepandpresentitwithin<action\></action\>tags\.

### K\.3PC/PC2 diagnostics

The PC2 diagnostics’ registered layer is carried by theΔ\\Deltaaddenda above \(perturbation strength, position monotonicity, the 500\-state bank\); their measured outputs enter the paper as Tier\-1 ledger rows \(Section[7](https://arxiv.org/html/2608.19760#S7); Figure[2](https://arxiv.org/html/2608.19760#A10.F2)\); the raw record entries are part of the append\-only experiment record, cited under the Tier\-3 rule only inside Section[8](https://arxiv.org/html/2608.19760#S8)and Appendix[A](https://arxiv.org/html/2608.19760#A1), and released in full in the replay archive\.

### K\.4The PC3 boundary table \(English rendering, faithfulness\-checked\)

Rendered from the verdict’s own “what this ruling supports / does not support” section; the element\-by\-element faithfulness matrix is in the assembly record\.

#### Supports\.

\(1\) On the G=4\-corrected substrate, the v1\.4 stabiliser family \(including its learning\-rate and grad\-clip variants\) cannot stably train an outcome\-only relative\-advantage signal; the divergence lineage is “pre\-clip gradient escapes first, KL breaches after,” insensitive to both orthogonal knobs \(step size5×10−5→2×10−55\{\\times\}10^\{\-5\}\{\\to\}2\{\\times\}10^\{\-5\}; clip threshold1\.0→0\.21\.0\{\\to\}0\.2\)\. \(2\) The batch\-level precursor — a gradient spike one to two batches before the KL breach — is reproducible and has warning value \(the PC3\-e60 reporting line fired ahead of the breach all three times\)\.

#### Does not support \(misreading guard\)\.

\[X\]“outcome\-only is ineffective” — none of the three configurations reached evaluation; no held\-out effect value exists\.\[X\]“the G=4 correction is useless or harmful” — G=4 made the advantage signal genuinely stronger \(C0 verdict\); exposing the stabiliser is not causing the pathology, and under KS2’s weak G=1 signal the same stabiliser ran 63 updates without divergence, corroborating that the mismatch is the combination*strong signal×\\timesv1\.4*\.\[X\]“substrate necrosis” — each configuration trained and improved during its healthy phase \(C2 win rate touched 0\.604; loss declined stably; KL smooth\); the collapse is a tail event, not whole\-run failure\.\[X\]“missing or failed gradient clipping” — clipping was active at every step from harness construction \(C2 tightened to 0\.2 with clip\-fraction 1\.00\) and the divergence persisted; the lesion is directional, not magnitude\.

#### Namespace discipline\.

PC3\-prefixed numbers stay prefixed; incident ids \(lowercase e52–e58\) and experiment ids \(uppercase E052–E058\) are different series that collide numerically and are never resolved into one another\.

#### Supersession note \(ruled 2026\-08\-18\)\.

The §8 placement of the e52 instance mandated in the split text above was superseded by the page\-ladder compression; the mandate is retained verbatim, the supersession recorded here\. The split mandate is an editorial arrangement of the writing stage, not a registered criterion; §8’s omission is therefore recorded as a supersession, not a breach\. The instance’s factual content is carried in full by Appendix[A](https://arxiv.org/html/2608.19760#A1)\.

### K\.5The incident chain

#### The ruled main\-text/appendix split, verbatim\.

> MAIN TEXT: e58 \(the pack was only ever checked against its own manifest, never the repository — an IDENTITY failure\) together with the Finding\-6 prediction arc as the central worked example: the taxonomy predicted that the next failure would land on IDENTITY or DIAGNOSABILITY because those two defences had never met a known\-positive; it landed on IDENTITY, and the prediction was recorded before the diff was run\. Plus e52 \(a generator encoding a configuration failure as\[UNVERIFIED\], the project’s marker for a genuinely untraceable number — the DIAGNOSABILITY instance\)\. APPENDIX: everything else: the four\-dimension table and its worked examples, the meta\-requirement, e53–e57, the chat\-layer channel \(4 relayed\-assertion instances \+ 1 unsourced reasoning error\), the PROVENANCE v1 swallowed\-appends sub\-case, and the incident\-supplied\-validation limitation\. Why this split: the main text carries the one thing a reviewer cannot get from a list of incidents — a taxonomy that made a falsifiable prediction and was confirmed by its own next failure — plus the single cleanest instance \(e52\)\. DIAGNOSABILITY remains an outstanding, live prediction and should be stated as such in the main text, not quietly dropped\.

#### Identifier note \(e52\)\.

The id e52 in this ruling text refers to the generator incident that encoded a configuration failure as\[UNVERIFIED\]— the DIAGNOSABILITY instance; in the frozen incident chain \(Appendix[A](https://arxiv.org/html/2608.19760#A1)\), e52 denotes the heartbeat NUL\-corruption incident \(persistence\); the numeric collision is historical and retained under the verbatim policy\.

#### Worked example \(e57\): an unvalidated verifier is worse than none — it manufactures confidence\.

grep \-c $’\\0’ FILEas a NUL counter: a NUL cannot be passed togrepas a pattern at all —execveargv entries are NUL\-terminated — so the argument collapses to a zero\-length pattern matching every line\. On a known\-negative three\-line file with no NULs, the true count is 0 and the check reports 3\. A missing check leaves a known hole; a broken check reports a clean result over the same hole, and that clean result is then cited\.

#### Identifier note\.

The id e57 in this worked example refers to the unvalidated NUL\-counter verifier instance; in the frozen incident chain \(Appendix[A](https://arxiv.org/html/2608.19760#A1)\), e57 denotes the nominal\-versus\-delivered\-dose incident; the numeric collision is historical and retained under the verbatim policy\.

#### e53–e57, full narratives\.

Retrieved from the governance decision record \(DECISIONS\.md:1519\-\-1721, held on the collection host; the errata log’s E5 names it as their source\) and shipped verbatim\. The source is Chinese\-major, so it takes rendering tier \(ii\): the byte\-exact file ships in the supplementary pack asK5\_verbatim/01\_e53\-e57\_incident\_narratives\.md, sha2563d08f01d3b83884fda64824db1a8c3faa2a66783386a82a3c26a3d904842bffe, 18,333 B, and is authoritative; the structured account of what each incident did to the record is given in English in Appendix[A](https://arxiv.org/html/2608.19760#A1)\(“The week the taxonomy was tested”\), labelled as a rendering\.

#### R\-3: why no∥Δ​W∥\\lVert\\Delta W\\rVert\-matched comparison was run \(verbatim\)\.

The ruling behind Section[6](https://arxiv.org/html/2608.19760#S6)’s cancellation sentence, English\-major, rendering tier \(i\); sha256c79df07b090869e7a8719316f9a0433d4bdab46a5353926413d238e7fa1e82e2, 3,269 B\.

\#RETRIEVAL2\-\-R\-3ruling:thethreerealreasonsforNOTrunningthematched\-\|\|dW\|\|comparison\(VERBATIM\)

\#SOURCE:pod/workspace/ks1/DECISIONS\.md,entry\(R46\)item\(1\)

\#SOURCEsha256:57ed00135455073ffeafb28bbdda02b609df64e27d18999dfb7153625697034e

\#LINES:1369\-1394

\#Retrieved2026\-08\-17\.Verbatim\-\-noedits\.

\-\-\-\-\-BEGINVERBATIM\-\-\-\-\-

\(R46\)\[2026\-08\-08,\[AUTHOR\-1\]FINALPACKET\-\-ratifiedcorrections\]

\(1\)\*\*\|\|dW\|\|\-MATCHEDCONFIRMATION:PERMANENTLYCANCELLED\.\*\*Addedtothe

permanently\-barredlistbesidethe5\-seedextension,CoT\-preserving

distillationandR40\.Thethreereasons,INTHERULEDORDER\-\-science

first,resourceslast,sotheanswerholdsifareviewerasks:

\(i\)THEPARTIALCORRELATIONALREADYANSWERSTHEQUESTION\.The

instrument\-familysignaturevanishesentirelywhen\|\|dW\|\|is

controlled\(\+0\.078,p=0\.774\)whilethepositivecontrolfires

\(\+0\.912,p=0\.0001\)\.Amatcheddesignwouldre\-answeraquestion

alreadyanswered\.

\(ii\)THEDESIGNHASANINHERENTFLAW\.\|\|dW\|\|overlapacrossarmsexists

onlyACROSSROUNDS\-\-adensearm’sr1againstasparsearm’sr3\-\-

socalipermatchingNECESSARILYintroducesaroundconfound,and

roundcovarieswithtrainingvolume\.Thematchedcomparisoncould

notbecleanevenifrun\.

\(iii\)COST\($25\-30,~3GPU\-h\)againstacalendarinwhichwritinghas

notstarted\.

CORRECTIONTOTHEINSTRUCTION,statedratherthansilentlycompliedwith:

\[AUTHOR\-1\]askedthat"theE040\-basedreason"beremovedfromtherecord\.

\*\*NOSUCHREASONEXISTS\.\*\*B28’srecordedreasonhasalwaysbeenthe

partial\-correlationadequacyplusthecalendar\(PROGRESSB28,"WHYNOT

NOW"\),andFINAL\_STATEsection3citesE033’spartialcorrelation\.E040

\(shuffle\-controlstrengthisformat\-dependent\)isnowheregivenasa

reasonfororagainstthematcheddesign\-\-and\[AUTHOR\-1\]isrightthatit

wouldbeorthogonalifitwere\.Nothingwasremovedbecausenothingwas

there;thethreeruledreasonsabovenowreplacethetwo\-reasonversion\.

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

\#CROSS\-REFERENCEinALL\_EXPERIMENTS\_RECORD\.md\(sha256eea4fcb1eabbe1f596dd97c85fb9df41583b7fd74951d32c1fbbdb6ce11b1bc8\),lines1176\-1178\.

\#NOTE:AERcarriesonlytheSUPERSEDEDpointer\(’specifiedandUNRUN,PROGRESSB28,\[AUTHOR\-1\]ruling2026\-08\-07’\)\.

\#ThethreeruledreasonsexistONLYinDECISIONSR46\(1\)above\.Nocompetingthree\-reasontextfoundinAER\.

\-\-\-\-\-BEGINVERBATIM\-\-\-\-\-

\>\>\>robusttodroppingarm6\(r=\+0\.9250,p=0\.0004\)andarm6\+arm1\(r=\+0\.9274,p=0\.0013\)\.The

\>\>\>partial\-correlationdesigncannotupgradethistoamatchedcomparison;the\|\|dW\|\|\-matched

\>\>\>confirmationthatwouldisspecifiedandUNRUN\(PROGRESSB28,\[AUTHOR\-1\]ruling2026\-08\-07\)\.

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

#### The S3\-gate withheld\-then\-released ruling, with its silent diff \(verbatim\)\.

The decision\-record entry behind Section[8](https://arxiv.org/html/2608.19760#S8)’s gate paragraph and its two releases; English\-major, rendering tier \(i\); sha256f537e7d1f098af48c60857bd3d3602ab9645fedf9bf7d6f14be53d3cc30377ed, 11,522 B\.

\#RETRIEVAL3\-\-DECISIONSmainentry:S3\-gatewithheld\-\>releasedruling\(VERBATIM\)\+silentdiff

\#SOURCE:pod/workspace/ks1/DECISIONS\.md,entry"\(REDOcap\-tripsalvageruling\)\[2026\-08\-11,\[AUTHOR\-1\]\]"

\#SOURCEsha256:57ed00135455073ffeafb28bbdda02b609df64e27d18999dfb7153625697034e

\#LINES:2205\-2232

\#Retrieved2026\-08\-17\.ArchivalcopyperG17\.Verbatim\-\-noedits\.

\-\-\-\-\-BEGINVERBATIM\(DECISIONSmainentry\)\-\-\-\-\-

\(REDOcap\-tripsalvageruling\)\[2026\-08\-11,\[AUTHOR\-1\]\]

\(1\)Branch\(b\)AUTHORIZED:PARTIAL\-COVERAGEanalysisoftheredoreplayset,

zeroGPU,frozencallersonly\.Everynewvaluecarriesthe

PARTIAL\-COVERAGElabelanditsn\(statedasn=x/27perthetaskbrief,

withthe28\-filestorecountco\-statedasbefore\)\.

\(2\)ADDITIONALDISCLOSUREOBLIGATION:REDO\_REPORT\.mdgainsa

missingness\-nonrandomnesssection\-\-distributionofthe142missing

turnsovertrajectorylength;per\-bucket\(B1/B2/B3,frozen

analysis/fidelity\.pyBUCKETS\)coveragerates;anybucketwith

significantlyimbalancedcoveragehasitsbucket\-levelnumbersmarked

"insufficientcoverage"\.

\(3\)TAIL142TURNS:NOTre\-run,pertheE043precedent\-\-thedeterministic

bad\-alternativebacklogconvertsat~1%\(E042:retry\-backlog101turns

\-\>1complete,1\.0%\),sore\-attemptingspendsGPUwithoutaddingn\.

Recordedhereasthereasonofrecord\.

\(4\)tmp\+renameFORsummary\.jsonWRITES:enteredasaTO\-DOrequiring

signature;implementedonlyifaREDO\-classreplayiseverrestarted\.

\(Thenon\-atomicwritecostonesummarythisrun:task024/t049,

REDO\_MANIFEST\.json\.\)

\(5\)20/27THRESHOLDSEMANTICMISMATCH,recordedhonestly:theovernight

taskbrief’s"\>=20/27completetrajectories"salvagecriterionis

TRAJECTORY\-levelwhilethefrozenpipeline’sinclusionrule

\(amendmentv3\.2,\>=4completeturns\)isTURN\-level;thetworeadings

flipthebranchat88\.3%turncoverage/15\-of\-28fullcoverage\.The

thresholdwasatask\-briefinvention,notpreregcontent;precedent

followsE043\(registeredanalysisat1,129/1,225=92\.1%coverage\)\.

Theunattendedsessionwithheldanalysisperthestrictletterand

escalated;thisrulingresolvesitperE043\.

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

=====================================================================

SILENTDIFFvsREDO\_STATUS\.md/REDO\_REPORT\.md:4\-6/ALL\_EXPERIMENTS\_RECORD\.md:2399\-2400

REDO\_STATUS\.mdsha256cf98e58e07bcc128df42af97cb784f0edbcac9a09a1912b288f7528290c4b3ec

REDO\_REPORT\.mdsha256e3a71bc1a50a95a6165cdc564072536042bfcdfbf8e901d8140418c72af53715

AERsha256eea4fcb1eabbe1f596dd97c85fb9df41583b7fd74951d32c1fbbdb6ce11b1bc8

=====================================================================

\#\#A\.RELEASECONDITIONS\-\-onedivergencetoreport,oneconditionsatisfiedonlyinletter

A1\.PARTIAL\-COVERAGElabelling\+n\+28\-storeco\-statement\(rulingitem1\):CONSISTENT\.

REDO\_REPORT:3\-8carriestheblanketPARTIAL\-COVERAGEheader,per\-rown,andboththe

task\-brief"27"andthe28\-filestorecount\.Nodivergence\.

\(Formnote,non\-substantive:therulingspecifiesnas"n=x/27";thereportstates

turn\-levelnasx/1082orx/792forthemaprates,wherea/27denominatorisnot

defined\.Trajectory\-levelrowsdousen=27/"of28"\.\)

A2\.Missingness\-nonrandomnessdisclosure\(rulingitem2\):SATISFIEDINLETTER,BUTTHE

MANDATEDFLAGCANNOTBIND\.Therulingrequired"anybucketwithsignificantly

imbalancedcoverage"tobemarked"insufficientcoverage"butdidnotdefinethetest\.

REDO\_REPORT:62\-65definesitatreporttime\(bucketmarkedwhenits95%WilsonCI

excludestheoverallrate\),appliesit,andreportsNOBUCKETTRIPS\-\-whileitself

statingthatB3’sCI"containstheoverallratebyconstruction"becauseB3dominates

theuniverse\.Sotheruling\-mandatedflagisstructurallyincapableoffiringforthe

onlybucketwithmissingdata\.Thereportdisclosesthis;thepapershouldnotcite

"nobucketflagged"asevidenceofbalancedcoverage\.

Coverageasexecuted:B111/11=1\.000,B217/17=1\.000,B30\.881,overall0\.883;

all142missing\+1unparseableturnsfallexclusivelyinB3\(13trajectories,each

length\>=44turns\),i\.e\.missingnessISnon\-randombythereport’sownaccount\.

A3\.Tail142turnsnotre\-run\(rulingitem3\):CONSISTENT\.REDO\_REPORT:94\-95\.

A4\.tmp\+renameto\-donotimplemented\(rulingitem4\):CONSISTENT\.REDO\_REPORT:95\-96\.

\#\#B\.THETWOPILLARS\-\-ONESUBSTANTIVEDIVERGENCE

Thetwopillarssupportingrelease\(REDO\_STATUS:38\-42,DECISIONSitem5\):

Pillar1\-\-E043PRECEDENT:theregisteredoriginalanalysisranat1,129/1,225=92\.1%

coverage,so88\.3%is"materiallythesameregime"\.

Pillar2\-\-FROZENv3\.2INCLUSIONRULE:amendmentv3\.2\(\>=4completeturnsper

trajectory\)"wouldretainALL28trajectoriesatthiscoverage"\.

Pillar1:CONSISTENTacrossDECISIONS:2230\-2232,REDO\_STATUS:40\-41,REDO\_REPORT:94\.

Pillar2:\*\*DIVERGENT\-\-REPORTTOIDEATION\.\*\*

REDO\_STATUS:38\-41\(verbatim\):"theFROZENpipeline’sowninclusionrule\(amendment

v3\.2:\>=4completeturnspertrajectory\)wouldretain\*\*all28\*\*trajectoriesatthis

coverage"\.

REDO\_REPORT:27\(verbatim,executedrun\):"n\_eff=21\(v3\.2excl2,v3\.3excl5,of28\)"\.

Whenthefrozenrulewasactuallyrun,v3\.2EXCLUDED2OF28\-\-itretained26,not28\.

Thepillaraswordedinthewithholdingreportiscontradictedbytheexecuted

analysisitwasusedtoauthorize\.

MAGNITUDE/DOESITFLIPTHEBRANCH:no\.26\>=20undereitherthetrajectory\-levelor

turn\-levelreading,sothereleasedecisionstandsonthestatedfacts\.Butthe

sentence"wouldretainall28"mustNOTbequotedinthepaperaswritten\.

\#\#C\.DATEORDER\-\-CONSISTENT,butthereleaseisTWO\-STAGEandmustbedescribedassuch

2026\-08\-11,unattendedwindow:REDO\_STATUSwritten;S3gatereadas15/20\-\>ANALYSIS

WITHHELD;escalated\.\(REDO\_STATUS:1,:30\-51\)

2026\-08\-11,\[AUTHOR\-1\]:"\(REDOcap\-tripsalvageruling\)"\-\-branch\(b\)

AUTHORIZED;PARTIAL\-COVERAGEanalysisreleased\.

\(DECISIONS:2205\-2232\)

2026\-08\-11,post\-ruling:REDO\_REPORTwritten,citingthatruling\.

\(REDO\_REPORT:4\-6\)AtthispointREDO\_REPORT:92\-94still

records"theUNDERREVIEWannotationsremaininplace"\.

2026\-08\-11,F1\-arccloseout:item\(4\)"RELEASEoftheUNDERREVIEWclusterperR8’s

sequence\-\-executedinthissessionAFTER\(5\)passed"\.

\(DECISIONS:2251\-2254\)

AER:2399\-2400recordsthesameorder\("afterthecaptrip,bythe2026\-08\-11\[AUTHOR\-1\]

salvageruling\(branch\(b\),PARTIAL\-COVERAGE\)"\)andaddsthepriorauthorizationofthe

re\-replayitselfbySTAGE2\_VERDICT\.json\-\-adifferentscope,notacompetingaccount\.

NODATE\-ORDERDIVERGENCE\.Theonethingtostatepreciselyinthepaper:"withheld\-\>

released"isTWOreleasesonthesameday\-\-\(i\)theanalysisisreleasedbythesalvage

ruling,while\(ii\)theUNDERREVIEWannotationsontheclaimtextarereleasedonly

laterbytheF1\-arccloseoutitem\(4\)\.Asingle"withheldthenreleased"sentence

conflatesthem\.

Consequenceworthcarrying:DECISIONS"\(F1blockaddendum\)\[2026\-08\-10\]"\-\-"gen\_numbers\.py

runsPROHIBITEDwhiletheUNDERREVIEWannotationshold\.\.\.;prohibitionliftswiththe

review"\(DECISIONS:2182\-2184\)\.Theprohibitionliftsatstage\(ii\),notatstage\(i\)\.

\#\#SUPPORTINGVERBATIM

\-\-\-\-\-BEGINVERBATIM\(REDO\_STATUS\.md:30\-51\)\-\-\-\-\-

\#\#Whyanalysisiswithheld\(theS3branchdecision,statedhonestly\)

S3:"if\>=20/27trajectoriesarecomplete,runthefrozenanalysisonthecomplete

subset\[\.\.\.\]If<20/27,noanalysis\."Underthereadinginwhichatrajectoryis

"complete"wheneveryexpectedturnhasasummary\-\-theonlyreadingunderwhichthe

20\-of\-27thresholdandthen=<x\>/27labelcohere\-\-thecountis\*\*15<20\-\>analysis

withheld\*\*\.

Forthemorningruling,theotherreadingisstatedratherthanburied:theFROZEN

pipeline’sowninclusionrule\(amendmentv3\.2:\>=4completeturnspertrajectory\)would

retain\*\*all28\*\*trajectoriesatthiscoverage,andtheORIGINALXFAM\-v1analysisran

at1,129/1,225\(92\.1%\)coverage\-\-88\.3%hereismateriallythesameregime\.Underthat

readingtheanalysisispermissibleandonecommandaway:

‘‘‘

/venv\_gpu/bin/pythonruns/xfam\_ext/redo/analyze\_redo\.py\#zeroGPU,frozencallersonly

‘‘‘

Thechoicebetweenreadingsflipsthebranch,thewindowwasunattended,and"stopping

isalwaysthecorrectunattendeddefault"\-\-soitstopshere\.\*\*\[RECOMMENDATION,

labeledassuch:runitunderPARTIAL\-COVERAGElabeling;theE043precedentandthe

frozenv3\.2rulebothsupportanalyzabilityatthiscoverage\.\[AUTHOR\-1\]decides\.\]\*\*

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

\-\-\-\-\-BEGINVERBATIM\(REDO\_REPORT\.md:4\-6\)\-\-\-\-\-

1,082/1,225parseable=88\.3%;gate:‘REDO\_MANIFEST\.json‘\)\.Authorizedbythe

2026\-08\-11\[AUTHOR\-1\]ruling\(DECISIONS"\(REDOcap\-tripsalvageruling\)"\),executedwith

frozencallersonly\(‘analyze\_redo\.py‘;onegluequarantine\-renamecommittedwithits

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

\-\-\-\-\-BEGINVERBATIM\(REDO\_REPORT\.md:27,pillar\-2divergence\)\-\-\-\-\-

\|fidelitywithin\-trajSpearman\(P1pilotquantity\)\|\-0\.0800\[\-0\.2086,\+0\.1424\]n\_eff=18\|\*\*\-0\.0431\[\-0\.1245,\-0\.0164\]\*\*n\_eff=21\(v3\.2excl2,v3\.3excl5,of28\)\|CInowexcludes0onthenegativeside\-\-butseeverdictrow\|‘runs/xfam\_ext/mde/xfam\_ext\_mde\.json‘\(pilotblock\)\|‘redo\_family\_analysis\.json‘\-\>‘analysis\.aggregate\.spearman‘\|

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

\-\-\-\-\-BEGINVERBATIM\(REDO\_REPORT\.md:55\-70,missingness\)\-\-\-\-\-

\#\#Missingnessnon\-randomness\(ruling\-mandateddisclosure\)\-\-‘redo\_missingness\.json‘

\-The142missing\+1unparseableturnsareconcentrated\*\*exclusivelyinB3\(long\)

trajectories\*\*:13partially\-coveredtrajectories,everyoneoflength\>=44turns

\(listintheJSON\);B1\(11/11\)andB2\(17/17\)are100%covered\.

\-Per\-bucketcoverage\(frozen‘analysis/fidelity\.py‘BUCKETS\):B1\*\*1\.000\*\*

\[0\.741,1\.000\];B2\*\*1\.000\*\*\[0\.816,1\.000\];B3\*\*0\.881\*\*\[0\.861,0\.898\];overall

0\.883\.Flagcriterion\(stated,thenapplied\):abucketismarked\*insufficient

coverage\*whenits95%WilsonCIexcludestheoverallrate\-\-\*\*nobuckettripsit\*\*

\(B3dominatestheuniverse,soitsCIcontainstheoverallratebyconstruction;

thatstructuralfactisitselfpartofthisdisclosure\)\.

\-Mechanism:thecaptripcutoffthee27\-classtailbacklog,whichlivesinlong

trajectories’hardturns\.Missingturnsarethereforeplausibly\*harder\-than\-average\*

B3turns;theper\-bucketB3numbersinheritthatcaveateventhoughtheflag

criteriondoesnotfire\.Statedfortherecord;nocorrectionapplied\(noneis

registered\)\.

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

\-\-\-\-\-BEGINVERBATIM\(ALL\_EXPERIMENTS\_RECORD\.md:2399\-2400\)\-\-\-\-\-

\[10\.6,14\.7\]outsidethefrozen5ppband\)and,afterthecaptrip,bythe2026\-08\-11

\[AUTHOR\-1\]salvageruling\(branch\(b\),PARTIAL\-COVERAGE\)\.

\-\-\-\-\-ENDVERBATIM\-\-\-\-\-

#### New incident \(i\): the STOP\-for\-absent rule’s recurrence, one batch after it was written\.

The retrieval record of the G17 excerpt documents it in the retriever’s own words: two reports in the same session asserted the ruling text was “not on this machine” while it sat in an unenumerated root; the rule is tightened — the root list must be written out before the absence claim, not reconstructed afterwards\. Source: \(retrieval\-record header, English; ruling body Chinese\-major, byte\-exact in the supplementary pack\)\.

#### New incident \(ii\): the relock comparator’s own v1 failure\.

The mandatory lock\-target re\-verification after the CLAIMS change FAILED on its first run — on storage\-format artifacts \(blockquote prefixes, original\-linebreak markers, curly quotes\), the checker’s defect and not the file’s; kept on the record per the comparator lesson\. The full log ships in this delivery \(logs/claims\_relock\_log\.md\) and its v1\-failure paragraph is retained inside it verbatim\.

#### New incident \(iii\): the float\-saturation law\.

Recorded as a taxonomy entry in Appendix[A](https://arxiv.org/html/2608.19760#A1)\(“A length check against a float\-saturated flow”\), approved verbatim; the three\-stage forensic record \(word\-diff, ragged\-bottom exclusion, downstream deletion probe\) is in the compression report of this delivery\.

## Appendix LConcurrent work, reconciled

Three concurrent papers touch this paper’s objects\. The main text carries one\-sentence positions \(§§1–3, 6\); the full reconciliations are recorded here\.

#### CARL \(multi\-hop search\)\.

CARL reports that entropy separates critical from non\-critical states at the distribution level \(Cliff’sδ=0\.42\\delta=0\.42,n=294n=294, Brunner–Munzel\), in multi\-hop search, with criticality estimated from resampled continuations\. Their criticality signal does not enter training through a classification threshold\. It enters as an action\-density term — expansion count per unit entropy at a state — with the update set restricted to states that have more than one child; the operating point at which their method works is therefore an emergent property of the rollout budget, not a stated rule whose recall was measured\. We record the absence explicitly, because it is the substance of the difference: the paper reports no precision, recall, F1, or AUC for criticality identification, and no threshold, quantile, or top\-kkselection rule\. Two independent passes over the v3 text were made, over the sections named in the provenance record; the absence is a finding of those passes, not an inference from silence in a summary\. Nothing in our data speaks to multi\-hop search, and nothing in theirs measures a router’s recall; the designs answer different questions\. We reconcile against v3 \(2026\-05\); the bibliography entry carries the v1 date\. The revision, not the first posting, is what “concurrent” refers to here\.

#### CAR \(formalization\)\.

CAR formalizes per\-step causal effect measurement as do\-operations with re\-execution and validates the estimator on synthetic SCMs with planted effects — ground truth known by construction\. That validation and this audit are complementary ends of one chain: it establishes that the estimator recovers planted effects where truth is known; we deploy the instrument on a live environment where truth is not planted, to grade signals already in training use\. The premise their construction states — that executed re\-intervention is the right ground truth for step credit — is the premise this audit tests signals against\. Their own scope statement is explicit: real tools with side effects are, in their words, “out of scope” \(§7\)\. The delta is therefore theirs to state and ours to inherit: validation under planted effects on the one side, deployment in a live tool environment on the other\.

#### CSO\.

The phrase “policy reachability” appears in CSO’s abstract\([Li et al\. 2026a](https://arxiv.org/html/2608.19760#bib.bib2)\); the method section describes the requirement differently, as branches that remain within the policy’s capability\. We quote the abstract and say so, rather than attributing to their method a term their method does not use\. What neither section reports is the verification rate\. The rate is not a detail: it is the fraction of nominated steps whose counterfactual the policy actually supports, the quantity our measurability map measures at scale \(undefined at 13\.1% of intervened turns for Qwen, 26\.8% for Llama; §[3](https://arxiv.org/html/2608.19760#S3)\)\. Our audit is, among other things, that unreported number\.

#### C3\.

C3 describes a “first method\-agnostic auditing tool” for multi\-agent credit\. Its fidelity criterion is Spearman correlation against its own replay advantages — the tool grades credit against a quantity the same tool computes — audited on MAPPO/MAGRPO policies\. The criterion is internally coherent but self\-referential: it certifies agreement with the tool’s own ground\-truth estimate\. The object here is different: signals already in LLM\-agent training use, graded against an external, executed causal ground truth that consults none of them \(§[2](https://arxiv.org/html/2608.19760#S2)\)\. The two priority claims do not collide because the objects differ\.

### L\.1Source integrity

All sixteen source files above ship byte\-exact insupplementary/withSHA256SUMS\.txt; the per\-item sha256 values in the comments of this appendix’sLaTeXsource are the same values\. Verbatim means verbatim: the transliteration applies to the PDF rendering only, and the release pack is the authority\.