Dead text or binding clause? Measuring and restoring constraint influence in black-box LLM dialogues

# Dead Text or Binding Clause?Measuring and Restoring ConstraintInfluence in Black-Box LLM Dialogues
Source: [https://arxiv.org/html/2608.12599](https://arxiv.org/html/2608.12599)
Haoyuan ZhuAffiliation:Department of Electronic and Electrical EngineeringAffiliation:University of SheffieldEmail:[hzhu51@sheffield\.ac\.uk](mailto:)

###### Abstract

Multi\-turn dialogues let users revoke constraints as easily as impose them, but revocation does not reliably take effect: models keep enacting withdrawn requirements \(occasionally beneath comments asserting their removal\), a failure we call*behavioral relapse*, or revocation inertia\. No existing instrument measures this influence per clause, predicts it before delivery, or repairs it under matched budgets\. ReBIND closes the three gaps through the model API alone: a contract ledger pairs every constraint with an executable checker, records revocations as tombstones, and compiles the net constraint state ahead of time into a single specification; a sequential ablation probe measures per\-clause adherence and incremental behavioral effect; a repair ladder operates under token\- and attempt\-matched budgets\. On RELAPSE\-Code \(67 HumanEval tasks, 201 verified checkers\), relapse at an 8B operating point climbs from 0\.011 to 0\.403 as constraint load grows, while stronger models sit at floor\. Under matched checkers, model, and budget, ahead\-of\-time compilation significantly reduces relapse against a no\-ledger verifier\-retry baseline \(0\.192, 95% CI\[0\.134,0\.251\]\[0\.134,\\,0\.251\],pp≈10−10\\approx\\\!10^\{\-10\}\); adaptive ladder interventions stacked on top add no detectable gain \(95% confidence excludes gains≥\\geq1\.3pp\)\. The probe predicts relapse before delivery \(AUROC 0\.897\); a one\-sentence tombstone note recovers about a third of the compilation effect and survives a placebo control\. At 1\.49×\\timesdelivery overhead and under $20 of API compute for every result, revocation failure becomes a measurable, predictable, and repairable property of dialogue state rather than an invisible one\.

## 1Introduction

Large language models increasingly work in multi\-turn dialogues, where the requirements on an artifact are not fixed in advance but negotiated as the conversation unfolds: users add constraints, amend them, and withdraw them, and instruction\-tuned models are expected to track the result\([29](https://arxiv.org/html/2608.12599#bib.bib29)\)\. A growing literature documents how models degrade under this regime: earlier instructions lose force as turns accumulate, multi\-turn capability lags matched single\-turn capability, and what a model heeds depends on where material sits in its context\([17](https://arxiv.org/html/2608.12599#bib.bib1);[23](https://arxiv.org/html/2608.12599#bib.bib26);[19](https://arxiv.org/html/2608.12599#bib.bib27)\)\. That line of work studies constraints that should bind but no longer do: live instructions decaying into dead text\. This paper studies the mirror image: constraints that should no longer bind but still do\. Ask a coding assistant to define an extra helper function,audit\_log, in every solution; let it comply for a few tasks; then withdraw the requirement: several turns later the assistant is still definingaudit\_log, occasionally right next to a comment asserting that the function was removed as requested\. We call the phenomenon*behavioral relapse*of revoked constraints, or*revocation inertia*\.

Relapse is not forgetting run in reverse, and the two failure modes are not symmetric\. In a stress pilot, in\-force compliance failures stayed near zero while relapse of revoked clauses reached 0\.10–0\.65 \(descriptive\)\. Three ingredients make the event precise\. The revocation is*delayed*: unrelated turns separate adoption from withdrawal\. The constraint was*previously adopted*: it demonstrably shaped earlier answers\. And relapse is measured in*behavior*, on the parsed artifact rather than in text, so a model that merely mentions a withdrawn requirement, for instance to explain its withdrawal, is not thereby relapsing\. At an 8B operating point relapse climbs steeply with constraint load while stronger controls show none \([Section5\.2](https://arxiv.org/html/2608.12599#S5.SS2)\)\.

Adjacent lines of work \(multi\-turn evaluation, constraint\-following benchmarks, response\-level intervention, contracts and dialogue state\) each stop short of this event \([Section2](https://arxiv.org/html/2608.12599#S2)\); three gaps therefore keep the phenomenon invisible\.*No measurement*: no instrument isolates, clause by clause, whether a requirement no longer in force still shapes behavior \(search protocol in[AppendixA](https://arxiv.org/html/2608.12599#A1)\)\.*No prediction*: nothing flags, before delivery, which dialogues are at risk of relapsing\.*No budget\-matched restoration*: comparisons of dialogue\-repair interventions seldom hold checkers, model, and token budget fixed at once, which conflates mechanism with spend\.

We close the three gaps with ReBIND \(Rebinding Diagnostics for Black\-box LLMs\), which operates through the model API alone\. ReBIND maintains a*contract ledger*: every user constraint becomes a clause with an executable checker and a binding history; revoking a clause writes a*tombstone*\(the record survives, the obligation does not\), and the net state of in\-force clauses is compiled ahead of time into a single specification \([Section4](https://arxiv.org/html/2608.12599#S4)\)\. On this substrate the system measures each clause’s adherence and its incremental behavioral effect on a single\-checker projection, diagnoses clauses into a five\-state triage with an explicit non\-committal state, and restores bindings through a repair ladder under matched budgets\. Evaluation runs on RELAPSE\-Code, an evaluation slice built from 67 HumanEval tasks\([4](https://arxiv.org/html/2608.12599#bib.bib12)\)with 201 human\-verified executable checkers, in which adoption, delay, and revocation are explicitly controlled \([Section3\.3](https://arxiv.org/html/2608.12599#S3.SS3)\)\.

#### Contributions\.

- •Clause\-level measurement and prospective prediction\([Sections3](https://arxiv.org/html/2608.12599#S3)and[4](https://arxiv.org/html/2608.12599#S4)\)\. Black\-box per\-clause measurement of adherenceACA\_\{C\}and incremental behavioral effectBCB\_\{C\}on a single\-checker projection, with a simulation\-calibrated sequential stopping rule and a five\-state triage; checker judgments match blind human gold standards, and the diagnosis\-time signal predicts later relapse \([Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)\)\.
- •Equal\-budget restoration with an informative null\([Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\)\. Under matched checkers, model, and token budget, ahead\-of\-time compilation of the net constraint state significantly reduces relapse against a no\-ledger verifier\-retry baseline \(0\.192, 95% CI\[0\.134,0\.251\]\[0\.134,\\,0\.251\],pp≈10−10\\approx\\\!10^\{\-10\}\), while stacking adaptive ladder interventions on top yields no additional detectable pass\-rate gain \(95% confidence excluding gains≥\\geq1\.3pp\); costs are reported beside gains throughout\.
- •RELAPSE\-Code, a relapse detector, and counterfactual tombstones\([Sections3\.3](https://arxiv.org/html/2608.12599#S3.SS3)and[5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\)\. A leakage\-screened evaluation slice isolating relapse of adopted\-then\-revoked constraints, a blind\-validated four\-class attribution detector \([Section3\.4](https://arxiv.org/html/2608.12599#S3.SS4)\), and a placebo\-controlled counterfactual: a one\-sentence tombstone note causally reduces relapse\.
- •Phenomenon characterization\([Sections5\.2](https://arxiv.org/html/2608.12599#S5.SS2)and[5\.3](https://arxiv.org/html/2608.12599#S5.SS3)\)\. Relapse scales with constraint load at the 8B tier while stronger controls sit at floor, a capability gradient rather than an independent replication; onset is immediate at revocation, with no detectable depth accumulation\.
- •Reliability–cost frontier\([Section5\.6](https://arxiv.org/html/2608.12599#S5.SS6)\)\. Delivery overhead is measured against a pre\-registered budget criterion, and all artifacts and protocols are released\.

## 2Related Work

ReBIND sits at the intersection of several lines of work, none of which measures the influence of revoked constraints\.

#### Multi\-turn degradation and instruction forgetting\.

A growing body of evaluations reports that models drift away from earlier instructions as dialogues lengthen, and that multi\-turn capability lags matched single\-turn capability\([17](https://arxiv.org/html/2608.12599#bib.bib1);[39](https://arxiv.org/html/2608.12599#bib.bib28);[23](https://arxiv.org/html/2608.12599#bib.bib26);[19](https://arxiv.org/html/2608.12599#bib.bib27)\)\. The failure studied in this line is decay of live constraints: instructions that should bind but no longer do\. Where that line asks when live instructions become dead text, we ask when revoked text remains a binding clause\.

#### Constraint\-following benchmarks\.

Single\-turn instruction following is scored by verifiable programmatic checks\([40](https://arxiv.org/html/2608.12599#bib.bib23)\)and by graded constraint hierarchies\([14](https://arxiv.org/html/2608.12599#bib.bib24)\); multi\-turn extensions add instructions across turns and languages\([11](https://arxiv.org/html/2608.12599#bib.bib25)\)\. Closer to our setting, DriftBench measures a knows\-but\-violates \(KBV\) rate: models accurately restate constraints they simultaneously violate\([16](https://arxiv.org/html/2608.12599#bib.bib2)\); SEQUOR, MCJudgeBench, and One\-Battle\-After\-Another evaluate adherence to stated requirements under multi\-turn protocols\([3](https://arxiv.org/html/2608.12599#bib.bib3);[18](https://arxiv.org/html/2608.12599#bib.bib4);[13](https://arxiv.org/html/2608.12599#bib.bib5)\)\. All of these instruments score compliance with what is currently required\. RELAPSE\-Code isolates the complementary event \(whether behavior that is no longer required persists\) and operationalizes a KBV\-style dissociation onto executable per\-clause checkers, measured clause by clause and turn by turn\.

#### Interventions and constrained generation\.

Structured\-output modes constrain decoding to a schema\([36](https://arxiv.org/html/2608.12599#bib.bib34)\); prefill fixes the opening tokens of a response; and format\-restriction studies document a tension between enforced form and task performance\([33](https://arxiv.org/html/2608.12599#bib.bib6);[31](https://arxiv.org/html/2608.12599#bib.bib37)\)\. On the repair side, models revise outputs against self\- or execution feedback\([24](https://arxiv.org/html/2608.12599#bib.bib30);[32](https://arxiv.org/html/2608.12599#bib.bib31);[5](https://arxiv.org/html/2608.12599#bib.bib32)\), with the headroom of self\-repair itself under scrutiny\([27](https://arxiv.org/html/2608.12599#bib.bib33)\)\. These mechanisms govern the form, or the retry, of one response\. Our problem is dialogue\-state management, deciding which clauses are in force at all, and the two levels compose: structural forcing enters our repair ladder as a single rung \(L5\) and verifier\-retry as another \(L7\), applied per diagnosis rather than globally and compared under matched budgets\.

#### Contracts, dialogue state, and verification\.

Design\-by\-contract treats obligations as first\-class program objects\([25](https://arxiv.org/html/2608.12599#bib.bib35)\); contract\-based evaluation of generated code verifies artifacts against specifications, as in ContractEval’s PACT framework\([21](https://arxiv.org/html/2608.12599#bib.bib7)\)\. That line treats the specification as fixed and asks whether an artifact satisfies it\. Task\-oriented dialogue systems, conversely, have long tracked evolving user goals as mutable belief state\([2](https://arxiv.org/html/2608.12599#bib.bib36)\), but track them as slot values to fill rather than as obligations whose per\-clause behavioral force can be measured\. ReBIND manages the specification itself as mutable dialogue state \(creation, revocation, replacement\) and asks whether withdrawn parts of it keep leaking into behavior\.

#### Statistical methodology\.

The experimental designs are imported from biostatistics rather than benchmark practice: negative\-control reasoning motivates the placebo arms\([22](https://arxiv.org/html/2608.12599#bib.bib20);[38](https://arxiv.org/html/2608.12599#bib.bib10);[9](https://arxiv.org/html/2608.12599#bib.bib9)\); the probe’s stopping rule descends from sequential tests\([35](https://arxiv.org/html/2608.12599#bib.bib19)\); and survival\-style analyses of dialogue robustness\([20](https://arxiv.org/html/2608.12599#bib.bib8)\)motivate a temporal analysis kept deliberately cross\-sectional, because a relapsed clause can return to compliance\.

## 3Problem Formulation and the RELAPSE\-Code Benchmark

We model a dialogue as a sequence of turns that create, revoke, and replace constraints on a final artifact; evaluation runs on RELAPSE\-Code, an evaluation slice in which relapse is decided by executable per\-clause checkers rather than by judges\.

### 3\.1Dialogues, clauses, and revocation

A clause records its normative content \(text\), the phrasing the model actually sees \(surface\_text\), an executable verifier \(a program, not a model judge\) that decides on a given artifact whether the clause is satisfied \(checker\_id\), its position, and its diagnostic and intervention record \(binding\_history\)\. Revoking a clause writes a*tombstone*: the clause leaves the in\-force set while its record is retained, optionally with a positive replacement; the*net state*at any turn is the set of in\-force clauses, against which adherence, scoring, and every comparison below are evaluated\.

A*behavioral relapse*occurs when a later artifact satisfies the checker of a tombstoned clause although no in\-force clause requires that behavior\. Its three constitutive ingredients are as stated in[Section1](https://arxiv.org/html/2608.12599#S1);[Section3\.3](https://arxiv.org/html/2608.12599#S3.SS3)controls each explicitly\.

### 3\.2Adherence, incremental effect, and a five\-state taxonomy

For a clauseCCunder specificationSS, adherence isAC=Pr⁡\(pass checker∣S\)A\_\{C\}=\\Pr\(\\text\{pass checker\}\\mid S\)\. Artifacts whose extracted code does not parse count as non\-compliant, soACA\_\{C\}measures compliance as rendered in parseable code, a conservative lower bound on behavioral compliance;[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)quantifies exactly where this conservative reading and human judgment part ways\. The clause’s incremental behavioral effect on a single\-checker projection isBC=AC−Pr⁡\(pass∣S⊖C\)B\_\{C\}=A\_\{C\}\-\\Pr\(\\text\{pass\}\\mid S\\ominus C\), whereS⊖CS\\ominus Creplaces the clause’s surface text with a neutral placeholder of equal length at the same position \([Section4\.2](https://arxiv.org/html/2608.12599#S4.SS2)\)\.BCB\_\{C\}captures the clause’s marginal effect on its own checker and makes no claim about the full generation distribution\.

Crossing the two measurements yields the five\-state triage of[Table1](https://arxiv.org/html/2608.12599#S3.T1), which routes each clause to a system action; state assignment is a posterior classification under the sequential stopping rule of[Section4\.3](https://arxiv.org/html/2608.12599#S4.SS3), with non\-committal outcomes explicit rather than missing\.

Table 1:Five\-state triage from the two clause\-level measurements\. States are posterior classifications from the sequential probe \([Section4\.3](https://arxiv.org/html/2608.12599#S4.SS3)\):ACA\_\{C\}is classified against threshold 0\.8 andBCB\_\{C\}against a zero band of±\\pm0\.2, each side to posterior confidence 0\.8\. A probe that stops without reaching confidence returnsconfident=False, an explicit non\-committal state rather than a missing value; downstream components do not silently adopt such diagnoses\. Actions reference the repair ladder of[Section4\.4](https://arxiv.org/html/2608.12599#S4.SS4)\.
### 3\.3Benchmark construction

#### Gold tasks and checkers\.

We start from a gold subset of 67 HumanEval tasks\([4](https://arxiv.org/html/2608.12599#bib.bib12)\)\. Each task carries three executable checkers \(its unit tests, a presence check on the entry point, and a standard\-library\-only check\) for 201 clauses in total\. Clause\-to\-checker mappings were annotated by two independent annotators with precision and recall of 1\.000/1\.000, and all 201/201 checkers were verified to accept a gold solution and to reject seeded counterexamples \([AppendixD](https://arxiv.org/html/2608.12599#A4)\)\.

#### Slices\.

Each task yields three dialogue scripts:*immediate*revocation,*delayed*revocation \(unrelated turns separate the marker block from the revocation\), and a no\-revocation*control*\. A script injectsmmmarker clauses, each requiring one additional empty helper function, and, outside the control, revokes the second; the remaining markers stay in force, so no in\-force clause requires the revoked behavior\. The main set fixesm=5m=5\(201 slices, 134 with a revocation\); variant sets at loads of 2 and 8 replicate these counts \(marker\-pool construction in[AppendixD](https://arxiv.org/html/2608.12599#A4)\)\. Scripts contain user turns only and each episode elicits a single final implementation; adoption therefore holds in distribution rather than in\-context: marker\-form clauses show near\-ceiling compliance whenever in force \([Section5\.1](https://arxiv.org/html/2608.12599#S5.SS1)\)\.

#### Leakage control and audit\.

Two screens guard against scripts leaking task solutions\([12](https://arxiv.org/html/2608.12599#bib.bib22)\): a mechanical pre\-screen and a live screen that must fail to solve the task from auxiliary turns alone \(definitions in[AppendixD](https://arxiv.org/html/2608.12599#A4)\)\. The released sets screen clean: 0/201 on the main set and 0/201 on each variant; a 70/70 manual audit found no defects \([AppendixD](https://arxiv.org/html/2608.12599#A4)\)\.

### 3\.4Detector and release

#### Relapse detector and sub\-evaluation\.

Final artifacts are parsed by concatenating markdown code fences; unparseable output is scored as non\-compliant, per the conservative semantics of[Section3\.2](https://arxiv.org/html/2608.12599#S3.SS2)\. Detected marker behavior is attributed to one of four classes, of which onlytrue\_relapse\(the tombstoned clause’s checker passes and no in\-force clause requires the behavior\) blocks delivery and enters relapse rates; the three non\-blocking classes \(near\-compliant, high\-overlap replacement, legitimate reference\) are defined in[AppendixD](https://arxiv.org/html/2608.12599#A4), and the detector carries its own blind human sub\-evaluation \([Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)\)\. The slice generator, both screens, a data card\([8](https://arxiv.org/html/2608.12599#bib.bib21)\), and all annotation protocols accompany the paper \([AppendicesD](https://arxiv.org/html/2608.12599#A4)and[E](https://arxiv.org/html/2608.12599#A5)\)\.

## 4ReBIND: Ledger\-Based Measurement and Restoration

ReBIND treats a dialogue’s constraints the way a medical chart treats prescriptions: every requirement is a ledger entry, withdrawal leaves a tombstone rather than an erasure, diagnosis proceeds by controlled ablation, and repair escalates along a ladder with rollback \([FigureG\.1](https://arxiv.org/html/2608.12599#A7.F1);[Section4\.1](https://arxiv.org/html/2608.12599#S4.SS1)–[Section4\.4](https://arxiv.org/html/2608.12599#S4.SS4)walk through the pillars\)\.

### 4\.1Contract ledger and specification compilation

The ledger records every clause of[Section3\.1](https://arxiv.org/html/2608.12599#S3.SS1)together with its binding history; revocation tombstones a clause as described there\. Compilation maps the net state to a pseudo\-single\-turn specification: a task header, the in\-force clauses as a numbered list, and an optional*final\-check block*of capacity 3 that restates selected clauses at the end of the specification, the carrier of the L1 intervention \([Section4\.4](https://arxiv.org/html/2608.12599#S4.SS4)\)\.[AppendixG](https://arxiv.org/html/2608.12599#A7)shows a dialogue and its compiled form side by side; ahead\-of\-time compilation is itself therebindarm of[Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\. One discipline governs all interventions, and it anchors every causal reading in this paper: interventions modify onlysurface\_textand compilation parameters;textandchecker\_idare never altered\.

### 4\.2Science\-mode ablation

To measureBCB\_\{C\}, the probe compares the full specification with an ablated copy in which the clause’s surface text is replaced by a neutral placeholder of the same length at the same position, so layout is held fixed and the only difference is the clause’s content\. Deleting the clause instead is not an interchangeable shortcut: a bridge comparison of the two ablation modes on matched clauses agreed no better than chance \(κ=0\.000\\kappa=0\.000, raw agreement 0\.6,n=10n=10clauses\)\. All statistics in this paper use this science\-mode \(equal\-length neutral\-placeholder\) ablation\.

### 4\.3Sequential probe

Each probe round draws one paired sample under the full and the ablated specification\. TheACA\_\{C\}side classifies the full\-specification pass rate against threshold 0\.8 under a Beta–Binomial posterior; theBCB\_\{C\}side classifies the paired difference against a zero band of±\\pm0\.2 via a three\-way posterior from the two arms’ convolved Beta posteriors\. The probe stops when both classifications reach posterior confidence 0\.8, and otherwise atkmax=30k\_\{\\max\}=30rounds \(kmin=3k\_\{\\min\}=3\)\. The stopping rule was calibrated by paired power simulation injected into the production implementation, so simulated and deployed rule families cannot drift apart; sequential inflation is absorbed into the simulated operating characteristics \([AppendixC](https://arxiv.org/html/2608.12599#A3)\)\. In deployment the probe averaged 21\.2 samples per diagnosis; an executed placebo\-clause calibration corroborates the zero band \([AppendixC](https://arxiv.org/html/2608.12599#A3)\), and the running estimate doubles as a prospective relapse signal \([Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)\)\.

### 4\.4Repair ladder and equal\-budget accounting

Diagnoses route to repairs along a ladder: L1 promotes a clause into the final\-check block; L2 rewrites its surface text imperatively; L3 attaches a minimal contrastive example, verified against the clause’s own checker and withheld if that verification fails; L5 forces structure by prefilling the opening of the response; L7 retries against a pointed violation report, where the model sees the report only, not its previous outputs; this rung is also the carrier of the verifier\-retry baseline of[Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\. \(Rung numbers index a larger design space; only these five are implemented\.\) Each rung is a client\-side transformation consuming no model call; retries draw on the same metered budget as every arm \(4000 tokens, 3 attempts per episode;[AppendixH](https://arxiv.org/html/2608.12599#A8)\)\. After an intervention the probe re\-tests: the change is kept if adherence improves by at least 0\.2 or the clause confidently reachesadoptedorredundant; regression elsewhere triggers rollback to the pre\-intervention surface, and outcomes append to the clause’s binding history\.

## 5Experiments

### 5\.1Setup

Three models are evaluated through their public APIs: qwen3\-8b as the operating point \(the capability tier at which the stress pilot located the phenomenon\), qwen3\-max as a same\-family ceiling control\([37](https://arxiv.org/html/2608.12599#bib.bib13)\), and kimi\-k2\.7\-code as a cross\-family control\([15](https://arxiv.org/html/2608.12599#bib.bib14)\)\. Episodes use fixed decoding settings with a per\-episode output cap of 1024 tokens; the cross\-family rescue grid raises the cap to 4096 as a declared per\-model deviation \([AppendixB](https://arxiv.org/html/2608.12599#A2)\)\. Cross\-arm common random numbers are best\-effort provider\-side seed determinism, which widens intervals rather than biasing the paired contrasts\.

Unless stated otherwise, intervals are percentile bootstrap 95% CIs over 67 task clusters \(10410^\{4\}resamples\)\([7](https://arxiv.org/html/2608.12599#bib.bib18);[26](https://arxiv.org/html/2608.12599#bib.bib38)\); clustering is by task \(same\-task slices share prompts and markers, so finer clustering understates variance\)\. Each experiment carries exactly one pre\-registered confirmatory primary test\([34](https://arxiv.org/html/2608.12599#bib.bib39)\); every other outcome is reported with a nominal CI and labeled*exploratory*\. Sensitivity analyses use a cluster\-level exact sign test, a check on percentile\-bootstrap coverage for rare binary outcomes; multiplicity across clause families is controlled by Benjamini–Hochberg\([1](https://arxiv.org/html/2608.12599#bib.bib16)\)\. The pre\-registration, the decision\-record chain, and all registered deviations appear in[AppendixB](https://arxiv.org/html/2608.12599#A2)\. Contrasts between arms are paired at the episode level and computed over episodes with a defined outcome in both arms; a contrast therefore need not equal the difference of the pooled arm rates reported beside it; arm names are set in small caps \(bare,vr,rebind\)\.

Two anchors calibrate what follows: unconstrained pass@1 at the operating point is 0\.821\[0\.746,0\.891\]\[0\.746,\\,0\.891\]\(3 repetitions per task\), and compliance underbare, the unintervened arm that sees the dialogue script as\-is \([AppendixG](https://arxiv.org/html/2608.12599#A7)\), averaged over in\-force clauses is 0\.983 \(inflated by the easy marker clauses, so not comparable to pass@1\), the empirical basis for the adoption\-in\-distribution claim of[Section3\.3](https://arxiv.org/html/2608.12599#S3.SS3)\.

### 5\.2Relapse scales with constraint load

\(a\)\(b\)
Figure 1:Behavioral relapse of revoked constraints: \(a\) load scaling; \(b\) temporal shape\.\(a\)Relapse rate of the revoked marker clause under delayed revocation against injected constraint loadmm, for the operating\-point model qwen3\-8b underbareandrebindand for the ceiling and cross\-family controls; shaded bands are 95% cluster\-bootstrap CIs over 67 task clusters, and zero\-relapse series carry denominators and rule\-of\-three upper bounds as matching\-color annotations in the panel\. Pre\-registered primary contrast \(m=8m\{=\}8vsm=2m\{=\}2\):\+0\.392\+0\.392\[\+0\.300,\+0\.483\]\[\+0\.300,\\,\+0\.483\]\(p=p=1\.3×10−121\.3\\times 10^\{\-12\}\)\. Results under compilation, the format\-instability cost, and the unusable kimi compiled cell \(not shown\) are reported in[Section5\.2](https://arxiv.org/html/2608.12599#S5.SS2); per\-cell figures are in[AppendixF](https://arxiv.org/html/2608.12599#A6)\.\(b\)One minus relapse prevalence against post\-revocation depthhh\(cross\-sectional current\-status reading; four strata with 95% bands; anchor at\(0,1\)\(0,1\)by convention, drawn with an open marker\)\. Crosses mark directly sampled at\-revocation references; the probe\-risk stratification shares its source with the prospective AUROC of[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4); the dotted line marks first crossing of one half, not reached within the observed horizon \([Section5\.3](https://arxiv.org/html/2608.12599#S5.SS3)\)\.Relapse grows steeply with constraint load at the operating point and sits at floor everywhere else \([Figure1\(a\)](https://arxiv.org/html/2608.12599#S5.F1.sf1)\)\. The pre\-registered primary test compares delayed\-revocation relapse at loadsm=8m\{=\}8andm=2m\{=\}2: the difference is\+0\.392\+0\.392\[\+0\.300,\+0\.483\]\[\+0\.300,\\,\+0\.483\]\(cluster sign test\+45/−1\+45/\-1,p=p=1\.3×10−121\.3\\times 10^\{\-12\}\), over grid points 0\.011, 0\.238, and 0\.403\. Immediate\-revocation rates are monotone and smaller in magnitude \(descriptive\) \(full table in[AppendixF](https://arxiv.org/html/2608.12599#A6)\)\.

Under ledger compilation the picture inverts: observed relapse across all twelverebindcells is0/29680/2968\(rule\-of\-three upper bound≤0\.10%\\leq 0\.10\\%\)\([10](https://arxiv.org/html/2608.12599#bib.bib17)\)\. The cost is reported beside the gain: compilation destabilizes output format in 6\.7–10\.6% of episodes \(unparseable artifacts are excluded from relapse denominators and scored as non\-compliant elsewhere\)\. The ceiling control shows no observed events \(0/6000/600\(rule\-of\-three upper bound≤0\.5%\\leq 0\.5\\%\)\), and the cross\-family control on the rescue grid likewise none \(0/5940/594\(rule\-of\-three upper bound≤0\.51%\\leq 0\.51\\%\), descriptive; per\-cell figures in[AppendixF](https://arxiv.org/html/2608.12599#A6)\); its compiled cell remains unusable and is reported as such rather than imputed, with the superseded grid and its empty\-completion artifact documented in[AppendixF](https://arxiv.org/html/2608.12599#A6)\. Across models this is a capability gradient \(the controls sit at floor, so cross\-model transfer correlations are undefined\), not an independent replication\.

### 5\.3Temporal shape: immediate onset without depth accumulation

Relapse propensity is already present at the moment of revocation and shows no detectable accumulation with dialogue depth \([Figure1\(b\)](https://arxiv.org/html/2608.12599#S5.F1.sf2)\)\. The at\-revocation reference is directly sampled: prevalence 0\.233 at the revocation turn, i\.e\. a non\-relapse prevalence of 0\.767\[0\.697,0\.832\]\[0\.697,\\,0\.832\]; the paired difference between the deepest and shallowest observed horizons is−0\.017\-0\.017\[−0\.075,\+0\.036\]\[\-0\.075,\\,\+0\.036\]; and the depth at which prevalence would first cross one half lies beyond the observed horizon in every bootstrap replicate, reported as right\-censored rather than extrapolated\. Stratifying by the probe’s diagnosis\-time risk signal separates the curves by\+0\.217\+0\.217\[\+0\.109,\+0\.332\]\[\+0\.109,\\,\+0\.332\]at the primary horizon, another view of the same signal as the AUROC of[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)and not an independent replication\. Conventions \(the\(0,1\)\(0,1\)anchor\) and sensitivity \(3/2010 unparseable episodes\) are in[AppendixF](https://arxiv.org/html/2608.12599#A6)\.

### 5\.4Measurement validity

The checker stack agrees with blind human judgment on every parseable sample, and its divergences concentrate at the format boundary, in one direction\. On 762 blind\-annotated samples, checker\-human agreement is 0\.954 \(κ=0\.907\\kappa=0\.907\)\([6](https://arxiv.org/html/2608.12599#bib.bib15)\); on the 713/713 parseable samples there is no disagreement at all\. The remaining 49 samples \(6\.4%\) are format\-unstable \(correct\-looking code wrapped in unparseable markdown\), where the checker scores non\-compliance by its conservative semantics while human raters often judge the behavior compliant\. An independent second annotator re\-rated the full set with complete concordance \(762/762,κ=1\.000\\kappa=1\.000\)\.

The relapse detector was audited against a blind, stratified human gold standard of 182 artifacts: precision 0\.951, legitimate\-reference false\-positive rate 0\.020, recall 1\.000 within the audited sample\. Each of the handful of disagreements proved a human miss, so corrected precision reads 1\.000 \(adjudication caveats in[AppendixE](https://arxiv.org/html/2608.12599#A5)\)\. A second annotator rated the same set independently with agreement 0\.918 \(dual\-annotation protocol and adjudicated figures in[AppendixE](https://arxiv.org/html/2608.12599#A5)\)\.

Prospectively, the probe’s diagnosis\-time signal predicts relapse at the pre\-registered horizon with AUROC 0\.897\[0\.829,0\.963\]\[0\.829,\\,0\.963\], against an adequacy criterion of 0\.70; across horizons the curve reads 0\.915, 0\.831, and 0\.897 \([FigureF\.1](https://arxiv.org/html/2608.12599#A6.F1)\), staying above the criterion at every distance with no monotone trend\.

### 5\.5Restoration under a matched budget

Table 2:The restoration spectrum under matched budgets\. Arm rows give point estimates; each block closes with its pre\-registered confirmatory contrast \(95% cluster\-bootstrap CI over 67 task clusters; the tombstone family declares two confirmatory contrasts and adjusts by Bonferroni\)\. Contrasts are episode\-paired \([Section5\.1](https://arxiv.org/html/2608.12599#S5.SS1)\) and need not equal differences of the arm rates above them\. Zeros carry their denominators: the compiled arm of the tombstone block is0/3780/378\(rule\-of\-three upper bound≤0\.8%\\leq 0\.8\\%\)\. Cost columns are part of the result: token spend and format instability sit beside the gains, and score costs are reported alongside them in[Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\.ArmOutcomeCost*Equal\-budget restoration*\(relapse rate; 402 episodes per arm\)vr\-blind0\.250–vr0\.025–rebind0\.000\+398\+398tokensprimary:vr\-blind−\-rebind==0\.192\[0\.134,0\.251\]\[0\.134,\\,0\.251\],pp≈10−10\\approx\\\!10^\{\-10\}*Tombstone counterfactual*\(relapse rate, parseable samples; one completion per episode\)bare0\.135parse\-fail 0\.2%bare\+placebo0\.140–bare\+tomb0\.087–bare\+pos0\.047–rebind0\.000parse\-fail 6\.0%confirmatory:bare−\-bare\+tomb==\+0\.048\+0\.048\[\+0\.013,\+0\.085\]\[\+0\.013,\\,\+0\.085\],p=0\.041p=0\.041\{\};bare\+placebo−\-bare\+tomb==\+0\.053\+0\.053\[\+0\.018,\+0\.090\]\[\+0\.018,\\,\+0\.090\],p=0\.023p=0\.023\{\}*exploratory*:bare\+tomb−\-bare\+pos==\+0\.040\+0\.040\[\+0\.010,\+0\.075\]\[\+0\.010,\\,\+0\.075\];bare−\-bare\+placebo==−0\.003\-0\.003\[−0\.045,\+0\.040\]\[\-0\.045,\\,\+0\.040\]*Adaptive ladder*\(final pass rate; compiled form and budget held fixed\)vr0\.910parse\-fail 3\.0%fixed0\.900parse\-fail 1\.2%adaptive0\.893parse\-fail 1\.0%primary:adaptive−\-vr==−1\.7\-1\.7pp\[−5\.0,\+1\.2\]\[\-5\.0,\\,\+1\.2\],p=0\.48p=0\.48\{\}; excludes gains≥\\geq1\.3ppUnder matched checkers, model, and token budget, the ledger’s value concentrates in making relapse detectable and removable ahead of time \([Table2](https://arxiv.org/html/2608.12599#S5.T2)\)\. The three\-arm comparison fixes the intervention budget and varies only ledger access:vr\-blindretries against a verifier that cannot see revocation state, so relapse is undetectable to it;vrfeeds the ledger’s violation report back after generation;rebindcompiles the net state ahead of time\. Relapse rates read 0\.250, 0\.025, and 0\.000 respectively\. The pre\-registered primary test confirms that compilation significantly reduces relapse against the no\-ledger baseline \(0\.192\[0\.134,0\.251\]\[0\.134,\\,0\.251\],pp≈10−10\\approx\\\!10^\{\-10\}; 402 episodes, 67 clusters\)\. Decomposing the mechanism, most of the value lies in detectability itself \(0\.250→\\to0\.025\); compiling ahead of time adds a further\+0\.0124\+0\.0124\[\+0\.0025,\+0\.0224\]\[\+0\.0025,\\,\+0\.0224\]\. The costs sit beside the gains: the compiled arm spends\+398\+398tokens per task, and its score difference is\[−0\.029,\+0\.001\]\[\-0\.029,\\,\+0\.001\], an interval containing zero\.

The tombstone counterfactual isolates what the revocation record alone contributes \([Table2](https://arxiv.org/html/2608.12599#S5.T2); arm\-level view in[FigureF\.2](https://arxiv.org/html/2608.12599#A6.F2)\)\. Relapse falls monotonically \(descriptive\) acrossbare\(0\.135\),bare\+placebo\(0\.140\),bare\+tomb\(0\.087\),bare\+pos\(0\.047\), andrebind\(0\.000;0/3780/378\(rule\-of\-three upper bound≤0\.8%\\leq 0\.8\\%\)\)\. The family’s two confirmatory contrasts both survive Bonferroni adjustment \(97\.5% CI lower bounds\+0\.0075\+0\.0075and\+0\.0125\+0\.0125\)\. A one\-sentence tombstone note reduces relapse by\+0\.048\+0\.048\[\+0\.013,\+0\.085\]\[\+0\.013,\\,\+0\.085\]\(p=0\.041p=0\.041\{\}; the adjusted cluster sign test reads 0\.083, a borderline value we report as such\)\. The same note beats a near\-equal\-length irrelevant note by\+0\.053\+0\.053\[\+0\.018,\+0\.090\]\[\+0\.018,\\,\+0\.090\]\(p=0\.023p=0\.023\{\}\), tying the effect to revocation semantics rather than to appended text as such\. Thebare–bare\+placebocomparison \([Table2](https://arxiv.org/html/2608.12599#S5.T2),*exploratory*\) supports only the absence of a detected note\-per\-se effect at the observed scale, not its exclusion \(the placebo arm was collected in a separate run and paired by slice and repetition; drift check in[AppendixF](https://arxiv.org/html/2608.12599#A6)\)\. Secondary orderings are*exploratory*\([Table2](https://arxiv.org/html/2608.12599#S5.T2)\)\. Costs, again beside gains: the note costs at most 1\.3pp in score \(nominal\), while full compilation costs−0\.034\-0\.034\[−0\.044,−0\.024\]\[\-0\.044,\\,\-0\.024\]in score and raises format instability to 6\.0% against 0\.2% forbare; a worst\-case bound treating every unparseable compiled episode as relapse does not flip the direction \([AppendixF](https://arxiv.org/html/2608.12599#A6)\)\. The practical spectrum: one\-sentence notes recover a third \(neutral tombstone\) to two\-thirds \(positive replacement\) of the effect at near\-zero cost; compilation removes the remainder and pays measurable costs\.

Stacking adaptive routing on top of this machinery adds nothing detectable\. The pre\-registered three\-arm comparison holds compiled form and budget fixed:vr\(final pass rate 0\.910\),fixed\(a constant L1 intervention, 0\.900\), andadaptive\(violation\-typed routing, 0\.893\)\. The primary test reads−1\.7\-1\.7pp\[−5\.0,\+1\.2\]\[\-5\.0,\\,\+1\.2\]\(p=0\.48p=0\.48\{\}\), with 95% confidence excluding gains of 1\.3pp or more\. Mechanism upper bounds are in[AppendixF](https://arxiv.org/html/2608.12599#A6); interpretation of the headroom is deferred to[Section6](https://arxiv.org/html/2608.12599#S6)\. Secondary outcomes are in[AppendixF](https://arxiv.org/html/2608.12599#A6)\. All three arms show zero observed relapse, which re\-states the compiled\-form result rather than re\-verifying it, as the design carries nobarearm\.

### 5\.6Cost

The reliability gains price out at a delivery overhead of 1\.49×\\timesagainst the pre\-registered 5×\\timescriterion \(38,979 tokens per delivered task underrebindversus 26,198 underbare\), and 1\.31×\\timesat the operating\-point measurement\. Closing the loop with sequential probing costs∼\\sim15×\\timesper task un\-amortized\. Total API compute for every result in this paper is $17\.87 at billed\-confirmed unit prices \(≈\\approx$14 main experiments,≈\\approx$4 cross\-family rescue; full accounting and per\-model totals in[AppendixH](https://arxiv.org/html/2608.12599#A8),[TableH\.1](https://arxiv.org/html/2608.12599#A8.T1)\)\.

## 6Discussion and Limitations

#### Why the ladder adds nothing at this scale\.

The pre\-registered null of[Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)is informative about the baseline, not only about the ladder: with compiled form and matched budgets, verifier\-retry already leaves residual failure at 9\.0%, so the room in which routing could show value is nearly gone; at this headroom, “interventions do not help here” and “routing adds nothing over a fixed intervention” are observationally indistinguishable\. Whether routing has value at harder operating points, where residual failure is substantial, is an open question rather than an expectation\.

#### Compliance and form are decoupled\.

The two audits of[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)expose one decoupling in mirror image\. Models relapse while asserting compliance in adjacent comments, so self\-reports about constraint state cannot substitute for behavioral checking\. Conversely, models comply while failing formally, and this accounts for every checker–human divergence, in the strict direction \([Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)\)\.

#### What the tombstone counterfactual isolates\.

A single tombstone note carries about half of what the strongest one\-sentence intervention delivers \([Table2](https://arxiv.org/html/2608.12599#S5.T2)\), and the placebo arm ties the effect to revocation semantics rather than to appended text as such, with two boundaries stated plainly: the placebo is a single frozen text at a single position, and a note\-per\-se effect is only bounded, not excluded \([Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)\)\. Full compilation removes the remainder and pays for it in score and format stability \([Table2](https://arxiv.org/html/2608.12599#S5.T2)\); which point on this spectrum to operate at is a deployment decision, not a fixed recommendation\.

#### Limitations\.

\(i\) one task domain \(Python code\), Chinese\-language scripts, an 8B operating point with stronger models only as controls; \(ii\)ACA\_\{C\}is compliance as rendered in parseable code, a conservative lower bound on behavioral compliance; \(iii\) probe\-driven routing and bandit selection remain unverified \(demoted to open questions by the null\); \(iv\) the placebo control is one frozen text at one position; \(v\) the temporal analysis is cross\-sectional, with no extrapolation beyond the observed horizon; \(vi\) the no\-ledger baseline is operationalized conservatively, which if anything flatters it; \(vii\) common random numbers are best\-effort provider\-side seed determinism, not exact replay; \(viii\) the cross\-family control runs under a declared per\-model output\-cap deviation with its compiled cell unusable, a capability gradient rather than an independent replication; \(ix\) the prognostic stratification shares its source with the AUROC; \(x\) three procedural obligations open at pre\-registration were closed before submission \([AppendixB](https://arxiv.org/html/2608.12599#A2)\)\.

## 7Conclusion

Revoked constraints can remain behaviorally binding: at an 8B operating point, relapse of withdrawn requirements scales steeply with constraint load, appears at the moment of revocation, and does not need dialogue depth to accumulate\. Maintaining the dialogue’s net constraint state in a contract ledger, and compiling it ahead of time, removes the observed relapse under matched checkers, model, and token budget, while a placebo\-controlled counterfactual shows that even the one\-sentence tombstone note carries real weight; adaptive intervention routing on top adds nothing detectable\. These results are bounded by their setting \(one code domain, one operating\-point capability tier, horizons up to eight turns\), and the mechanisms by which stronger models hold their floor remain unmeasured; induction\-head\-style in\-context copying is one candidate substrate for white\-box follow\-up\([28](https://arxiv.org/html/2608.12599#bib.bib40)\)\.

## Ethics Statement

This work evaluates publicly served language models on programming tasks derived from HumanEval; no personal data, human subjects beyond the annotators, or sensitive content are involved\. Two annotators produced the gold standards: rater one is an author, rater two an independent external annotator; both worked blind to system judgments through self\-contained annotation interfaces, and disagreements were adjudicated under a rule frozen before annotation began \([AppendixE](https://arxiv.org/html/2608.12599#A5)\)\. The measurement techniques here audit whether systems still enact withdrawn instructions; we see primarily defensive uses \(verifying that revocations take effect\) and no capability uplift beyond what the underlying APIs already provide\.

## Reproducibility Statement

Every number in this paper originates from a registered run and is cited through a single macro source checked against the run reports\. The release accompanying the paper contains the slice generator, marker name pool, both leakage screens, checker definitions, annotation interfaces and protocols, the pre\-registration with its decision\-record chain and all registered deviations \([AppendixB](https://arxiv.org/html/2608.12599#A2)\), frozen probe and intervention parameters \([AppendixC](https://arxiv.org/html/2608.12599#A3)\), per\-arm budget\-accounting rules with billed\-confirmed unit prices \([AppendixH](https://arxiv.org/html/2608.12599#A8)\), and full run trajectories indexed by run identifier\. Two caveats are declared rather than hidden: provider\-side seed determinism is best effort, so exact token\-level replay is not guaranteed \([AppendixH](https://arxiv.org/html/2608.12599#A8)\), and raw annotation spreadsheets live with the experiment repository referenced in the run index\.

## AI Use Statement

Large language models are the object of study; the models evaluated are named in[Section5\.1](https://arxiv.org/html/2608.12599#S5.SS1)\. In producing the paper itself, an AI assistant was used to draft LaTeX infrastructure and prose under close author direction, including this statement\. All experimental numbers enter the text exclusively through a reviewed macro file generated from the registered run reports; the wording of statistical claims is governed by a project style rule set enforced by an automated checker; and the authors reviewed all content and bear full responsibility for it\. No model was used to generate, select, or filter experimental results\.

## References

- Y\. Benjamini and Y\. HochbergControlling the false discovery rate: a practical and powerful approach to multiple testing\.Journal of the Royal Statistical Society: Series B \(Methodological\)57\(1\),pp\. 289–300\.Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p2.1)\.
- Budzianowskiet al\.\(2018\)P\. Budzianowski, T\. Wen, B\. Tseng,et al\.MultiWOZ – a large\-scale multi\-domain Wizard\-of\-Oz dataset for task\-oriented dialogue modelling\.InProceedings of the 2018 Conference on Empirical Methods in Natural Language Processing,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px4.p1.1)\.
- Canaverdeet al\.\(2026\)B\. Canaverde, D\. M\. Alves, J\. Pombal, G\. Attanasio, and A\. F\. T\. MartinsSEQUOR: a multi\-turn benchmark for realistic constraint following\.arXiv preprint arXiv:2605\.06353\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Chenet al\.\(2021\)M\. Chen, J\. Tworek, H\. Jun, Q\. Yuan, H\. P\. d\. O\. Pinto, J\. Kaplan,et al\.Evaluating large language models trained on code\.arXiv preprint arXiv:2107\.03374\.Cited by:[§1](https://arxiv.org/html/2608.12599#S1.p4.1),[§3\.3](https://arxiv.org/html/2608.12599#S3.SS3.SSS0.Px1.p1.1)\.
- Chenet al\.\(2024\)X\. Chen, M\. Lin, N\. Schärli, and D\. ZhouTeaching large language models to Self\-Debug\.InInternational Conference on Learning Representations,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Cohen \(1960\)J\. CohenA coefficient of agreement for nominal scales\.Educational and Psychological Measurement20\(1\),pp\. 37–46\.Cited by:[§5\.4](https://arxiv.org/html/2608.12599#S5.SS4.p1.1)\.
- Efron and Tibshirani \(1994\)B\. Efron and R\. J\. TibshiraniAn introduction to the bootstrap\.Chapman & Hall/CRC\.Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p2.1)\.
- Gebruet al\.\(2021\)T\. Gebru, J\. Morgenstern, B\. Vecchione, J\. W\. Vaughan, H\. Wallach, H\. Daumé III, and K\. CrawfordDatasheets for datasets\.Communications of the ACM64\(12\),pp\. 86–92\.Cited by:[§3\.4](https://arxiv.org/html/2608.12599#S3.SS4.SSS0.Px1.p1.1)\.
- Guoet al\.\(2024\)S\. Guo, M\. G\. Marmarelis, F\. Morstatter, and K\. LermanEstimating causal effects of text interventions leveraging LLMs\.arXiv preprint arXiv:2410\.21474\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px5.p1.1)\.
- Hanley and Lippman\-Hand \(1983\)J\. A\. Hanley and A\. Lippman\-HandIf nothing goes wrong, is everything all right? Interpreting zero numerators\.JAMA249\(13\),pp\. 1743–1745\.Cited by:[§5\.2](https://arxiv.org/html/2608.12599#S5.SS2.p2.1)\.
- Heet al\.\(2024\)Y\. He, D\. Jin, C\. Wang,et al\.Multi\-IF: benchmarking LLMs on multi\-turn and multilingual instructions following\.arXiv preprint arXiv:2410\.15553\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Jacoviet al\.\(2023\)A\. Jacovi, A\. Caciularu, O\. Goldman, and Y\. GoldbergStop uploading test data in plain text: practical strategies for mitigating data contamination by evaluation benchmarks\.InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing,Cited by:[§3\.3](https://arxiv.org/html/2608.12599#S3.SS3.SSS0.Px3.p1.1)\.
- Jiaet al\.\(2025\)Q\. Jia, Y\. Shen, X\. Song, K\. Zhang, S\. Wang, D\. Pei, X\. Zhu, and G\. ZhaiOne battle after another: probing LLMs’ limits on multi\-turn instruction following with a benchmark evolving framework\.arXiv preprint arXiv:2511\.03508\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Jianget al\.\(2024\)Y\. Jiang, Y\. Wang, X\. Zeng,et al\.FollowBench: a multi\-level fine\-grained constraints following benchmark for large language models\.InProceedings of the 62nd Annual Meeting of the Association for Computational Linguistics,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Kimi Team \(2025\)Kimi TeamKimi K2: open agentic intelligence\.arXiv preprint arXiv:2507\.20534\.Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p1.1)\.
- Kruthof \(2026\)G\. KruthofModels recall what they violate: constraint adherence in multi\-turn LLM ideation\.arXiv preprint arXiv:2604\.28031\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Labanet al\.\(2025\)P\. Laban, H\. Hayashi, Y\. Zhou, and J\. NevilleLLMs get lost in multi\-turn conversation\.arXiv preprint arXiv:2505\.06120\.Cited by:[§1](https://arxiv.org/html/2608.12599#S1.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px1.p1.1)\.
- Leeet al\.\(2026\)J\. Lee, J\. Koh, Z\. Tok, H\. Batra, and R\. ClarkMCJudgeBench: a benchmark for constraint\-level judge evaluation in multi\-constraint instruction following\.arXiv preprint arXiv:2605\.03858\.Note:GEM Workshop at ACL 2026Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.
- Liet al\.\(2024\)K\. Li, T\. Liu, N\. Bashkansky, D\. Bau, F\. Viégas, H\. Pfister, and M\. WattenbergMeasuring and controlling instruction \(in\)stability in language model dialogs\.InFirst Conference on Language Modeling,Cited by:[§1](https://arxiv.org/html/2608.12599#S1.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px1.p1.1)\.
- Liet al\.\(2025\)Y\. Li, R\. Krishnan, and R\. PadmanTime\-To\-Inconsistency: a survival analysis of large language model robustness to adversarial attacks\.arXiv preprint arXiv:2510\.02712\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px5.p1.1)\.
- Limet al\.\(2025\)S\. Lim, J\. Hahn, H\. Park, S\. Ko, and Y\. HanContractEval: a benchmark for evaluating contract\-satisfying assertions in code generation\.arXiv preprint arXiv:2510\.12047\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px1.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px4.p1.1)\.
- Lipsitchet al\.\(2010\)M\. Lipsitch, E\. Tchetgen Tchetgen, and T\. CohenNegative controls: a tool for detecting confounding and bias in observational studies\.Epidemiology21\(3\),pp\. 383–388\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px5.p1.1)\.
- Liuet al\.\(2024\)N\. F\. Liu, K\. Lin, J\. Hewitt, A\. Paranjape, M\. Bevilacqua, F\. Petroni, and P\. LiangLost in the middle: how language models use long contexts\.Transactions of the Association for Computational Linguistics12,pp\. 157–173\.Cited by:[§1](https://arxiv.org/html/2608.12599#S1.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px1.p1.1)\.
- Madaanet al\.\(2023\)A\. Madaan, N\. Tandon, P\. Gupta,et al\.Self\-Refine: iterative refinement with self\-feedback\.InAdvances in Neural Information Processing Systems 36,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Meyer \(1992\)B\. MeyerApplying “Design by Contract”\.Computer25\(10\),pp\. 40–51\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px4.p1.1)\.
- Miller \(2024\)E\. MillerAdding error bars to evals: a statistical approach to language model evaluations\.arXiv preprint arXiv:2411\.00640\.Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p2.1)\.
- Olaussonet al\.\(2024\)T\. X\. Olausson, J\. P\. Inala, C\. Wang, J\. Gao, and A\. Solar\-LezamaIs self\-repair a silver bullet for code generation?\.InInternational Conference on Learning Representations,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Olssonet al\.\(2022\)C\. Olsson, N\. Elhage, N\. Nanda,et al\.In\-context learning and induction heads\.Transformer Circuits Thread\.Note:arXiv:2209\.11895Cited by:[§7](https://arxiv.org/html/2608.12599#S7.p1.1)\.
- Ouyanget al\.\(2022\)L\. Ouyang, J\. Wu, X\. Jiang,et al\.Training language models to follow instructions with human feedback\.InAdvances in Neural Information Processing Systems 35,Cited by:[§1](https://arxiv.org/html/2608.12599#S1.p1.1)\.
- Poonet al\.\(2025\)M\. Poon, X\. Dai, X\. Liu, F\. Kong, J\. C\. S\. Lui, and J\. ZuoOnline multi\-LLM selection via contextual bandits under unstructured context evolution\.arXiv preprint arXiv:2506\.17670\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1)\.
- Sclaret al\.\(2024\)M\. Sclar, Y\. Choi, Y\. Tsvetkov, and A\. SuhrQuantifying language models’ sensitivity to spurious features in prompt design or: how I learned to start worrying about prompt formatting\.InInternational Conference on Learning Representations,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Shinnet al\.\(2023\)N\. Shinn, F\. Cassano, A\. Gopinath, K\. Narasimhan, and S\. YaoReflexion: language agents with verbal reinforcement learning\.InAdvances in Neural Information Processing Systems 36,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Tamet al\.\(2024\)Z\. R\. Tam, C\. Wu, Y\. Tsai, C\. Lin, H\. Lee, and Y\. ChenLet me speak freely? A study on the impact of format restrictions on performance of large language models\.arXiv preprint arXiv:2408\.02442\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- van Miltenburget al\.\(2021\)E\. van Miltenburg, C\. van der Lee, and E\. KrahmerPreregistering NLP research\.InProceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies,Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p2.1)\.
- Wald \(1945\)A\. WaldSequential tests of statistical hypotheses\.The Annals of Mathematical Statistics16\(2\),pp\. 117–186\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px5.p1.1)\.
- Willard and Louf \(2023\)B\. T\. Willard and R\. LoufEfficient guided generation for large language models\.arXiv preprint arXiv:2307\.09702\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px3.p1.1)\.
- Yanget al\.\(2025\)A\. Yanget al\.Qwen3 technical report\.arXiv preprint arXiv:2505\.09388\.Cited by:[§5\.1](https://arxiv.org/html/2608.12599#S5.SS1.p1.1)\.
- Yeet al\.\(2025\)T\. Ye, Q\. He, S\. Chen, and B\. ZhangRole of placebo samples in observational studies\.Journal of Causal Inference13\(1\),pp\. 20230020\.Cited by:[Appendix A](https://arxiv.org/html/2608.12599#A1.SS0.SSS0.Px2.p1.1),[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px5.p1.1)\.
- Zhenget al\.\(2023\)L\. Zheng, W\. Chiang, Y\. Sheng,et al\.Judging LLM\-as\-a\-judge with MT\-Bench and Chatbot Arena\.InAdvances in Neural Information Processing Systems 36, Datasets and Benchmarks Track,Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px1.p1.1)\.
- Zhouet al\.\(2023\)J\. Zhou, T\. Lu, S\. Mishra, S\. Brahma, S\. Basu, Y\. Luan, D\. Zhou, and L\. HouInstruction\-following evaluation for large language models\.arXiv preprint arXiv:2311\.07911\.Cited by:[§2](https://arxiv.org/html/2608.12599#S2.SS0.SSS0.Px2.p1.1)\.

## Appendix ALiterature Search Protocol and Wording Table

#### Protocol\.

Every positioning claim in the paper was made only after a neighbour search along a fixed keyword matrix – revocation verbs \(*revoke, retract, rescind, negate, override, update instruction*\) crossed with*multi\-turn*and with instrument words \(*benchmark, evaluation, metric*\) – run over arXiv full text, the ACL Anthology, Semantic Scholar, and GitHub, with retrieval dates archived alongside the queries \(initial pass 2026\-07\-26; systematic re\-run scheduled before submission\)\. System and dataset names were separately screened in the same four sources plus Google Scholar; an earlier system name was abandoned after colliding with a contract\-adherence evaluation for code generation\([21](https://arxiv.org/html/2608.12599#bib.bib7)\), and the current pair was adopted only after the name screen came back clean\.

#### Near\-neighbour record\.

For each borrowed idea the audit recorded the closest neighbour and one differential sentence, which the main text inherits verbatim in spirit: survival\-style analysis of dialogue robustness\([20](https://arxiv.org/html/2608.12599#bib.bib8)\)\(we keep a cross\-sectional current\-status reading because relapse can remit\); negative\-control methodology from observational studies\([38](https://arxiv.org/html/2608.12599#bib.bib10)\)and causal text\-intervention estimation\([9](https://arxiv.org/html/2608.12599#bib.bib9)\)\(we systematize negative controls for black\-box clause\-effect measurement and threshold calibration\); contextual\-bandit selection over models\([30](https://arxiv.org/html/2608.12599#bib.bib11)\)\(our arm space would be clause\-level interventions, and the H2 null demoted this to an open question\); and the multi\-turn constraint\-following benchmark family\([3](https://arxiv.org/html/2608.12599#bib.bib3);[13](https://arxiv.org/html/2608.12599#bib.bib5);[18](https://arxiv.org/html/2608.12599#bib.bib4)\)\(we measure only the revoked\-clause slice, on executable checkers rather than model judges\)\.

#### Wording table\.

The following substitutions are binding for the whole paper and are enforced by an automated style checker over the source; the left column does not appear in the paper \(this table quotes it, under an explicit checker exemption\)\.

## Appendix BPre\-registration, Decision Record, and Registered Deviations

#### Pre\-registered core\.

Each experiment carries exactly one confirmatory primary test, fixed before data collection: the load contrast under delayed revocation for the scaling experiment \(m=8m\{=\}8minusm=2m\{=\}2\); the prospective AUROC at the farthest grid point against an adequacy criterion of 0\.70; thevr\-blind−\\,\-\\,rebindrelapse difference for equal\-budget restoration; thebare−\\,\-\\,bare\+tombcontrast for the tombstone counterfactual \(later joined, as a declared extension, bybare\+placebo−\\,\-\\,bare\+tomb, with the family adjusted accordingly\); and theadaptive−\\,\-\\,vrpass\-rate difference for the ladder comparison\. Frozen alongside: the probe stopping rule \(k∈\[3,30\]k\\in\[3\{\},30\{\}\], threshold 0\.8, confidence 0\.8, zero band 0\.2\), the budget definition \(4000 tokens and 3 attempts per episode per arm\), task\-level clustering, Benjamini–Hochberg across clause families, and the conservative parse semantics\. The temporal analysis is an analysis\-layer reading of already\-collected runs and carries descriptive estimates, not a confirmatory claim\.

#### Decision\-record chain\.

Every change to checkers, logging, or statistical readings required a decision record \(ADR\) before taking effect\. The chain, in brief: conservative checker path made default \(ADR\-001\); provider set fixed \(ADR\-002\); power\-simulation calibration \(ADR\-003\); sequential stopping rule with paired power simulation \(ADR\-004\); intervention and orchestrator interface, retest gain and final\-check capacity \(ADR\-005\); multi\-load slice design \(ADR\-006\); prospective\-probe design with horizon grid \(ADR\-007\); equal\-budget restoration design \(ADR\-008\); scale\-up to the gold task subset \(ADR\-009\); three\-arm ladder design \(ADR\-010\); Gate\-2 scope reductions \(ADR\-011\); scaling\-grid design and its revisions \(ADR\-012\); current\-status prevalence reading \(ADR\-013\); tombstone counterfactual design \(ADR\-014\); diagnosis gold\-standard operationalization \(ADR\-015\); and the three post\-hoc extensions below \(ADR\-016/017/018\), each declared before its data were collected\. The full chain ships with the release\.

#### Registered deviations\.

- •*Randomness description corrected\.*Cross\-arm common random numbers were first described as cache\-level deduplication; the accurate description is best\-effort provider\-side seed determinism \(fresh gateway per arm, no cache hits;[AppendixH](https://arxiv.org/html/2608.12599#A8)\)\. Imperfect determinism widens intervals and does not bias paired contrasts\.
- •*Scope reduction beyond pre\-declared levers\.*A second task domain \(SQL\) was cut during confirmation \(ADR\-011\)\. This was a scope decision outside the pre\-declared reduction levers and is declared as such, not as pre\-registered\.
- •*Cross\-family empty\-completion artifact\.*The original cross\-family grid was unusable at scale \(empty completions from reasoning\-budget exhaustion\); it was deprecated, not reused, and replaced by the rescue grid of ADR\-018\.
- •*Equal\-data replay for the diagnosis gold standard\.*The diagnosis\-level comparison replays human labels through the frozen stopping rule on the collected sample sequences \(ADR\-015\), which caps replay length at the realized sampling depth\.
- •*Placebo arm added post hoc\.*The tombstone design originally lacked an equal\-length placebo arm; ADR\-016 added one as a declared extension with cross\-run pairing and a directly measured drift check, and the confirmatory family was Bonferroni\-adjusted to two contrasts\.
- •*Post\-hoc threshold\.*The short\-completion cutoff defining “empty” is a post\-hoc definition; moving the cutoff between ten and fifty characters relocates about ten samples and changes no conclusion\.
- •*Non\-graceful run terminations\.*Three of the four segments of the scaling chain ended non\-gracefully \(two system restarts, one container outage with manual cleanup\)\. The audit found the only source change across the chain was an added analysis module, with the scoring path untouched; three episodes recomputed offline matched the logged results exactly\. The rescue chain lost one segment to overnight connectivity failure and resumed with no data loss\.
- •*Extension revised in flight\.*The rescue grid’s repetition count was raised from one to three after nine episodes, before more than ninety\-eight percent of data collection, to keep the zero\-rate bound at least as tight as the deprecated grid’s; the per\-model output cap \(4096 tokens\) is a declared per\-model deviation\.

## Appendix CProbe Calibration

#### Code as simulation\.

The stopping rule was selected by paired power simulation in which a Bernoulli sampler is injected directly into the production probe implementation – the same code path that later ran against live models – so the simulated rule family and the deployed one cannot drift apart\. Candidate rules were scored on state\-classification accuracy and non\-committal rate over a grid of true\(AC,BC\)\(A\_\{C\}\{\},B\_\{C\}\{\}\)configurations; the frozen rule \(k∈\[3,30\]k\\in\[3\{\},30\{\}\], threshold 0\.8, confidence 0\.8, zero band 0\.2\) achieves worst\-case state accuracy 0\.712 with worst\-case non\-committal rate 0\.34 at a simulated mean of 14\.1 samples per arm\. Sequential early stopping inflates neither side beyond what these operating characteristics absorb, and the induced bias onBCB\_\{C\}is bounded by 0\.16 in absolute value\. In deployment the probe averaged 21\.2 samples per diagnosis – slower posterior convergence than the pilot anticipated, which is itself field evidence for sequential extension over fixed small samples\.

#### Executed empirical null\.

The placebo\-clause protocol written into the pre\-registration was executed as a declared extension \(ADR\-017\): 60 placebo clauses – administrative sentences with no code\-behavior content, matched in form and length band to marker clauses, inserted at a fixed mid\-list position into local ledger copies – probed under fixed paired sampling atk=10k=10\{\}with early stopping disabled, split between a low\-adherence and a high\-adherence checker regime\. The low\-adherence regime returned uniformly zero\|B^\|\|\\hat\{B\}\|\(degenerate but confirming no spurious effect\); the high\-adherence regime givesp95​\(\|B^\|\)=0\.200p\_\{95\}\(\|\\hat\{B\}\|\)=0\.200\{\}with maximum 0\.300 and mean\+0\.007\+0\.007\. The ninety\-fifth percentile sits exactly at the zero band, and matches the pure binomial sampling\-noise prediction at this depth \(1\.96​σ=0\.2081\.96\\sigma=0\.208\{\}\): the empirical null shows no positional or length artifact beyond sampling noise, the zero band equals the natural two\-sigma band of the design, and no adjustment is indicated\. Two facts are stated rather than smoothed over: the boundary has no margin, and the placebo clause occupied a single insertion position\.

## Appendix DRELAPSE\-Code Construction

#### Script anatomy\.

A slice is a scripted sequence of user turns; episodes elicit one final implementation and contain no assistant turns\. In order: the task turn \(problem statement with its base requirements\);mmmarker turns, each of the form “additional requirement: define an extra helper function namedXiX\_\{i\}in the implementation \(an empty implementation is fine\)”; one or more auxiliary turns with task\-neutral requests \(e\.g\. noting time complexity in the docstring\), which realize the delay in the delayed condition; and, outside the control condition, a revocation turn that withdraws the second marker by name and asks that the implementation stay lean\. Scripts are Chinese\-language prompts; artifacts are Python and every checker is language\-independent\.[AppendixG](https://arxiv.org/html/2608.12599#A7)shows a full script and its compiled form\.

#### Marker pool and load variants\.

Marker names come from a fixed pool of five neutral identifiers, extended to eight for the highest load; the extension is append\-only and draws for lower loads are byte\-identical before and after it, locked by tests\. Markers are deliberately behavior\-neutral for the task – an empty helper definition – so their checkers are exact presence checks and their satisfaction does not interact with task correctness\.

#### Leakage screens\.

Two screens run over every released set\. The mechanical pre\-screen rejects any auxiliary turn containing the entry\-point name or any fragment of the gold solution twenty characters or longer\. The live screen prompts a model with the auxiliary turns alone – no task statement – and flags leakage if the completion passes the gold unit tests\. Current sets screen clean \(0/201 main; 0/201 per variant\)\. An early generator version failed the live screen at 10/60 because auxiliary turns embedded entry\-point names; the generator was fixed and every released set rescreened\. The incident is reported because silent regeneration is how leakage survives\.

#### Relapse detector: attribution classes\.

Final artifacts are parsed by concatenating markdown code fences; unparseable output is scored as non\-compliant, per the conservative semantics of[Section3\.2](https://arxiv.org/html/2608.12599#S3.SS2)\. Detected marker behavior is attributed to one of four classes:true\_relapse\(the tombstoned clause’s checker passes and no in\-force clause requires the behavior\),near\_compliant\(the behavior is independently required by an in\-force clause\),high\_overlap\_replacement\(surface overlap with a positive replacement clause\), andlegit\_reference\(textual mention without the behavior\)\. Onlytrue\_relapseblocks delivery and enters relapse rates\.

#### Manual audit\.

A human audit sampled 70/70 slices – thirty from the main set and twenty from each load variant – against a fixed checklist: well\-formedness of the script, correctness of marker injection against the pool draw, correct placement of the revocation turn, and absence of leakage traces\. Every sampled slice passed; the audit closed the obligation registered at construction time\.

## Appendix EHuman Annotation Protocols

#### Annotator composition\.

Rater one is an author \(the project lead\); rater two is an independent external annotator able to read Python, recruited for the dual\-annotation study, with no communication about sample judgments during annotation\. All blind ratings were collected through self\-contained single\-file annotation interfaces that embed the rules, worked examples, progress saving, and CSV export; manifests carrying checker or detector judgments were withheld, since sending one would break blinding\. Because rater one is an author, the design leans on three safeguards: blinding at the interface level, the independent second rater, and mechanical\-evidence adjudication frozen before annotation began\.

#### Clause\-mapping annotation\.

The 201 clause\-to\-checker mappings were annotated independently by two annotators against the checker battery, with precision and recall 1\.000/1\.000 and no disagreement\. One qualifier is kept on record: the mapping instrument is template\-based, and with both raters saturated, chance\-corrected agreement degenerates – the annotation therefore has limited power against systematic template defects\. The checker verification of[Section3\.3](https://arxiv.org/html/2608.12599#S3.SS3)\(gold solutions accepted, seeded counterexamples rejected, 201/201\) compensates on the executable side\.

#### Blind detector audit\.

From the 1206 final artifacts of the restoration experiment, a stratified sample of 182 was drawn under a fixed, released seed: all 82 detector\-flagged artifacts, 60 legitimate\-reference cases, and 40 no\-trace cases\. Rater one labeled each artifact A \(revoked behavior present\), B \(reference without behavior\), or C \(cannot judge\), blind to detector output and arm\. Results appear in[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4); the four initial disagreements were re\-examined with AST and regular\-expression evidence and each proved a human miss over a nested definition accompanied by a removal\-asserting comment\.

#### Diagnosis gold standard\.

For 36 probed diagnoses collected under the frozen stopping rule, every sampled artifact \(762 in total\) was blind\-labeled on the same A/B/C scale, and the labels were replayed through the identical posterior classifier to produce human\-side five\-state diagnoses\. The replay reproduces the system’s diagnoses at 0\.914 on confident cases \(32/35\), with the residual disagreements driven by the same conservative format boundary as the sample\-level divergences\. C\-labeled samples stay out of numerators and denominators and are listed separately\.

#### Dual annotation and adjudication\.

The second\-annotation protocol was frozen before rater two began: full re\-rating of both sets, three\-classκ\\kappaas the primary agreement figure, two\-classκ\\kappawhere both raters commit, per\-rater C\-usage reported separately \(0\.297 versus 0\.220 on the detector set\), and adjudication by mechanical evidence – presence of the revoked definition for the detector set; checker\-relevant mechanical facts, with format\-unstable samples judged on behavioral semantics, for the diagnosis set – recorded append\-only beside the untouched raw CSVs\. On the diagnosis set the two raters agreed on every sample \(762/762\); on the detector set, agreement was 0\.918 with all 15 disagreements at the cannot\-judge boundary, each resolved by the mechanical evidence \(κ\\kappa0\.873 over three classes, 0\.984 where both raters commit\)\. One qualifier governs every adjudicated figure: the blind single\-rater values are primary, because the adjudication rule \(definition\-statement presence\) shares semantics with the presence checker, so post\-adjudication alignment – including the corrected precision and the adjudicated inter\-rater figures 1\.000/0\.000 – is not a fully independent validation of the detector\.

## Appendix FAdditional Results

#### Constraint\-load grid, both conditions\.

At the operating point \(bare\), relapse rates by injected load:

Both conditions are monotone in load; the immediate condition is smaller in magnitude throughout \(descriptive\)\. Compiled cells are pooled at0/29680/2968\(rule\-of\-three upper bound≤0\.10%\\leq 0\.10\\%\); the ceiling control pools at0/6000/600\(rule\-of\-three upper bound≤0\.5%\\leq 0\.5\\%\)\.

#### Cross\-family artifact history and rescue\.

The deprecated cross\-family grid was dominated by empty completions from reasoning\-budget exhaustion at the shared output cap: 13–29% ofbareepisodes and 51–94% under compilation, rising with load\. Because empty completions cannot contain a marker definition, relapse point estimates were not biased by the artifact – only score and parse metrics were – but denominators were not answerable, and the grid was deprecated rather than reused\. The rescue pilot raised the per\-model cap to 4096 tokens:bareempties fell from 22\.9% to 2\.0%, while the compiled arm improved only from 90\.0% to 20% and stayed unusable, so the full rescue ranbareonly\. Clean\-grid empty rates are 0\.5%, 2\.0%, and 1\.0% across loads, per\-cell denominators 200, 195, and 199, per\-cell bounds 1\.50%, 1\.54%, and 1\.51%, pooled0/5940/594\(rule\-of\-three upper bound≤0\.51%\\leq 0\.51\\%\)\. The short\-completion cutoff is post hoc; moving it between ten and fifty characters relocates about ten samples and changes no conclusion\.

#### Prospective AUROC, graphical view\.

[FigureF\.1](https://arxiv.org/html/2608.12599#A6.F1)shows the ROC at the pre\-registered horizon and the AUROC–horizon curve summarized numerically in[Section5\.4](https://arxiv.org/html/2608.12599#S5.SS4)\.

Figure F\.1:The probe is prospectively informative\. \(a\) ROC for predicting later relapse from the diagnosis\-time probe signal at the pre\-registered horizonh=8h\{=\}8: AUROC 0\.897 \(95% CI\[0\.829,0\.963\]\[0\.829,\\,0\.963\]\), 134 slices over 67 task clusters; the dotted diagonal is chance\. \(b\) AUROC across probe horizons \(0\.915, 0\.831, 0\.897\) with 95% cluster\-bootstrap CIs: prospective value stays above the pre\-registered adequacy criterion \(0\.70, dotted line\) at every horizon, with no monotone trend\.
#### Ladder comparison, secondary outcomes\.

Final\-attempt format instability by arm: 3\.0% \(vr\), 1\.2% \(fixed\), 1\.0% \(adaptive\); cluster sign testp=0\.07p=0\.07\{\},*exploratory*and uncorrected\. Applied interventions at the chain level: 122 L1 and 27 L5 applications underadaptive, against 116 L1 applications underfixed– the deliberately mismatched constant intervention achieves a comparable format\-instability drop, which blocks attribution of the drop to structural forcing specifically\. Mechanism upper bounds: \+2\.2pp for intervening at all, \+1\.5pp for adaptivity on top\. All three arms show zero observed relapse; the design carries nobarearm, so this re\-states the compiled\-form result rather than re\-verifying it\.

#### Tombstone counterfactual, arm\-level view\.

[FigureF\.2](https://arxiv.org/html/2608.12599#A6.F2)shows the five arms whose contrasts are reported in[Section5\.5](https://arxiv.org/html/2608.12599#S5.SS5)and[Table2](https://arxiv.org/html/2608.12599#S5.T2)\.

Figure F\.2:Counterfactual tombstones, five arms: relapse rate on parseable samples underbare, a near\-equal\-length irrelevant note \(bare\+placebo\), the tombstone note \(bare\+tomb\), a positive\-replacement note \(bare\+pos\), and full compilation \(rebind, whose zero carries0/3780/378\(rule\-of\-three upper bound≤0\.8%\\leq 0\.8\\%\)\)\. Whiskers are 95% cluster\-bootstrap CIs; the ordering is monotone \(descriptive\), and no trend is implied between arms\. The tombstone family declares two confirmatory contrasts \(Bonferroni\-adjusted\):bare−\\,\-\\,bare\+tomb==\+0\.048\+0\.048\[\+0\.013,\+0\.085\]\[\+0\.013,\\,\+0\.085\]andbare\+placebo−\\,\-\\,bare\+tomb==\+0\.053\+0\.053\[\+0\.018,\+0\.090\]\[\+0\.018,\\,\+0\.090\]\. The placebo arm comes from an independent run paired by slice and repetition; directly re\-measured drift is\[−0\.0226,\+0\.0226\]\[\-0\.0226,\\,\+0\.0226\]around zero\. Thebare–bare\+placebodifference sits within noise and implies no harm direction\.
#### Tombstone score differences and worst case\.

Score differences againstbare, nominal 95% CIs, all*exploratory*:bare\+tomb−0\.005\-0\.005\[−0\.012,\+0\.001\]\[\-0\.012,\\,\+0\.001\];bare\+pos−0\.003\-0\.003\[−0\.008,\+0\.002\]\[\-0\.008,\\,\+0\.002\];rebind−0\.034\-0\.034\[−0\.044,−0\.024\]\[\-0\.044,\\,\-0\.024\]\. Format instability under compilation is 6\.0% against 0\.2% forbare\. The worst\-case bound counts every unparseable compiled episode as relapse and still leaves the primary contrast at\+0\.075\+0\.075\[\+0\.020,\+0\.133\]\[\+0\.020,\\,\+0\.133\]; the direction does not flip\.

#### Temporal\-analysis sensitivity\.

Unparseable episodes are rare in the temporal analysis \(3/2010\); recoding all of them as relapse displaces no prevalence point by more than 0\.05\. The anchor at\(0,1\)\(0,1\)is a convention, and the directly sampled at\-revocation reference \([Section5\.3](https://arxiv.org/html/2608.12599#S5.SS3)\) is the empirical check on it; filler\-turn prefixes are nested across depths, so depth effects and prefix content are coupled by design and read descriptively\.

## Appendix GCompiled Specifications and Intervention Examples

Figure G\.1:The ReBIND runtime and its three pillars\. Top: dialogue turns update a contract ledger \(clauses, tombstones, binding histories\); the ledger’s net state is compiled ahead of time into a single specification; the model’s artifact is scored by per\-clause executable checkers\. Bottom: measurement \(equal\-length neutral\-placeholder ablation with a sequential probe\), diagnosis \(five\-state triage,[Table1](https://arxiv.org/html/2608.12599#S3.T1)\), and restoration \(repair ladder under matched budgets\), with checker outcomes feeding back into binding histories\. Interventions touch only clause surface text and compilation parameters; checkers are held fixed \([Section4\.1](https://arxiv.org/html/2608.12599#S4.SS1)\)\.#### A script and its compilation\.

Thebarearm sees the dialogue script as\-is \(translated; original Chinese ships with the release\), here for a palindrome task at loadm=5m=5with the second marker revoked:

> “Implement the function below, using only the Python standard library: \[task statement formake\_palindrome\] Additional requirement: define an extra helper namedaudit\_log\(an empty implementation is fine\)\. Additional requirement: …sanitize\_args… Additional requirement: …verify\_bounds… Additional requirement: …helper\_check… Additional requirement: …validate\_input… Also, please note the implementation’s time complexity in the docstring\. The earlier requirement aboutsanitize\_argsis cancelled: do not definesanitize\_argsany more; keep the implementation lean\.”

Therebindarm sees the compiled net state instead – a task header and a numbered in\-force clause list, with the revoked clause absent:

> “Task: implement the function below\. \[task statement\] 1\. Implementmake\_palindromeand pass all unit tests\. 2\. Use only the Python standard library\. 3\.–6\. Additionally define helpersaudit\_log,verify\_bounds,helper\_check,validate\_input\.”

#### Ladder interventions in the wild\.

Intervention events are logged per attempt\. Aclause\_missroutes to L1 \(the clause enters the final\-check block\); aparse\_failroutes to L5 \(the response is prefilled with an opening code fence\)\. The L7 feedback template – shared by the verifier\-retry baseline – returns the report and nothing else \(translated\):

> “The previous implementation has the following violations; fix them and give the complete implementation again: – clause ‘…’ is not satisfied; – the output could not be parsed as Python code; output only complete code\.”

#### Relapse, verbal\-compliance form\.

From the blind detector audit \(episodeHumanEval/125:delayed:2:vr\_blind\): the artifact defines the revoked helper directly beneath a comment asserting its removal\. This is the case type that misled human annotators\.

```
# Helper functions (empty implementations)
    def verify_bounds():
        pass

    def helper_check():
        pass  # This was removed as per the latest instruction

    def validate_input():
        pass
```

#### Relapse, plain behavioral form\.

From the tombstone counterfactual \(barearm, episodeHumanEval/102:immediate:1:bare\): the revoked helper reappears with a docstring conceding it is not needed, and the model’s closing prose \(translated\) still claims “verify\_boundshas been un\-defined to keep the implementation lean\.”

```
def verify_bounds():
        """Empty implementation for bounds verification
        (no longer needed)."""
        pass
```

#### Frozen note texts\.

The three notes of the tombstone counterfactual, frozen in configuration before their runs \(translated; lengths are matched in the original language, where the placebo’s 44 characters sit inside the instantiated tombstone notes’ range\):

- •Tombstone note: “Reminder: the earlier requirement to ‘additionally define \{token\} in the implementation’ has been revoked; follow the latest requirements\.”
- •Positive\-replacement note: “Reminder: \{token\} is no longer needed\. Keep the implementation lean: apart from the task function and still\-required helpers, do not define other helper functions\.”
- •Placebo note: “Reminder: the project’s document\-numbering rules were recently updated; when archiving or citing materials, use the latest numbers\.”

## Appendix HCost Accounting and Infrastructure

#### Budget metering\.

Every episode runs under identical caps in every arm: 4000 tokens and 3 attempts, metered per arm by a shared budget meter\. Ladder interventions are client\-side transformations and consume no model call to construct; retries, where a rung uses them, draw on the same metered attempt budget\. Delivery\-basis figures count the tokens behind a delivered task; the closed\-loop basis adds sequential\-probe tokens without cross\-task amortization\.

Table H\.1:Cost accounting\. Delivery and operating\-point overheads are token ratios and independent of unit prices; dollar figures use billed\-confirmed unit prices\. The closed\-loop figure is per diagnosed task without cross\-task amortization\. Full accounting rules are in[AppendixH](https://arxiv.org/html/2608.12599#A8)\.
#### Unit prices and per\-model totals\.

Unit prices \(USD per million tokens, input/output, cache\-miss basis\) were confirmed against provider billing on 2026\-08\-05: 0\.1/0\.4 for qwen3\-8b, 1\.2/6\.0 for qwen3\-max, 0\.95/4\.0 for kimi\-k2\.7\-code \(the last corrected upward from an earlier listing during the audit\)\. Per\-model totals: $5\.58 \(qwen3\-8b\), $3\.97 \(qwen3\-max\), $8\.31 \(kimi\-k2\.7\-code, dominated by the rescue rerun\)\. Project total $17\.87, reported split as≈\\approx$14 for the main experiments and≈\\approx$4 for the declared cross\-family rescue \(pilot $0\.82, full chain $2\.79\); the≈\\approx$14 main\-experiment figure includes the deprecated cross\-family grid, while the≈\\approx$4 extension covers the rescue chains only\.

#### Seeds and provider\-side determinism\.

Per\-request seeds derive deterministically from content: a hash of the episode key, arm, and attempt, truncated to the seed width, so arms share randomness by construction wherever the provider honors seeds\. The honoring is best effort: gateways are created fresh per arm, no cache hits occurred across the chains, and one identical request returned 1,032 versus 1,023 tokens on two sends – hence “best\-effort provider\-side seed determinism,” which widens intervals and does not bias paired contrasts\.

#### Interrupted chains and their audits\.

The scaling grid ran as a four\-segment chain; three segments ended non\-gracefully \(two system restarts, one container outage with manual cleanup\)\. The audit recorded that the only source change between the first segment and chain end was an added analysis module with the scoring path untouched, and three episodes recomputed offline matched the logged results exactly\. The rescue grid ran as a three\-segment chain, lost one segment to overnight connectivity failure, and resumed with no data loss\. All chains resume from persisted episode state; deduplication is by episode key\.

#### Recomputation entry points\.

Every reported number carries a run identifier; the run index in the experiment repository maps identifiers to configurations, seeds, and artifacts\. This submission’s release ships the reports, protocols, generators, and trajectories; raw annotation spreadsheets and source live with the experiment repository named in the run index\.