CausalNav: Reliability-Certified Causal World Models for Control under Physical-Parameter Shift

# Reliability-Certified Causal World Models for Control under Physical-Parameter Shift
Source: [https://arxiv.org/html/2608.07809](https://arxiv.org/html/2608.07809)
\\workshoptitle

World Models in Physical AI

Yiyao Zhanga, Diksha Goelb, Hussain Ahmadc, Shixun Huanga, Jun Shena aSchool of Computing and Information Technology, University of Wollongong, Wollongong, NSW, Australia bCSIRO’s Data61, Clayton, VIC, Australia cSchool of Computer Science and Information Technology, Adelaide University, Adelaide, SA, Australia Author e\-mail addresses:yiyao\.zhang@uow\.edu\.au \(Y\. Zhang\), diksha\.goel@csiro\.au \(D\. Goel\), hussain\.ahmad@adelaide\.edu\.au \(H\. Ahmad\), shixun\_huang@uow\.edu\.au \(S\. Huang\), jshen@uow\.edu\.au \(J\. Shen\)

###### Abstract

A world model is only useful for physical AI if it changes what the agent*does*, and only safe if it declines to do so when it is wrong\. We study both halves of that requirement with CausalNav, a controller built around a signed, action\-conditioned transition graph over identified state coordinates\. At deployment CausalNav simulates a small library of intervention sequences, converts their objective error into policy\-logit advice, and admits that advice only when a scale\-free predictive\-reliability certificate, a policy\-margin gate, and an argmax\-agreement gate all pass; otherwise it falls back exactly to its own model\-based base controller\. We evaluate against nine controlled baselines, transformer, recurrent, split\-latent, graph, causal\-induction, and three recent model\-based reasoning modules, on CartPole\-v1 and discretized Pendulum\-v1 with physical\-parameter shifts, under one shared PPO trainer, one interaction budget, and ten held\-out seeds \(200 runs\)\. CausalNav attains the best average rank \(1\.251\.25of ten\)\. The diagnostic result is more informative than the ranking: the learned graph recovers structure well above chance \(CartPoleF1=0\.59±0\.09F\_\{1\}=0\.59\\pm 0\.09\), yet per\-seed structural fidelity is uncorrelated with per\-seed control benefit \(r=−0\.15r=\-0\.15,p=0\.67p=0\.67\), and the certificate abstains on10/1010/10Pendulum seeds, where forcing the planner on costs return\. Model fidelity did not predict downstream control utility in our setting; certified abstention, not better prediction, is what made the world model safe to deploy\.

## 1Introduction

Physical\-AI agents fail when the mechanisms that generated their training data differ from those they meet at deployment\. A world model is the standard remedy: simulate the consequences of candidate actions, then act on the simulation\. For this to help, two things must be true\. The model has to be accurate enough that its rollouts are informative, and the controller has to know when that condition fails, because iterating a learned model compounds error, and a planner that overrides a competent policy using an unreliable model makes the system worse, not better\(Schölkopfet al\.,[2021](https://arxiv.org/html/2608.07809#bib.bib22); Richens and Everitt,[2024](https://arxiv.org/html/2608.07809#bib.bib10)\)\.

Most world\-model evaluations report the first property \(prediction error, structural recovery, rollout fidelity\) and assume the second follows\. We test the link directly\. CausalNav learns a signed action\-conditioned transition graph over identified state coordinates, plans over a library of intervention sequences, and then subjects the resulting advice to three deployment gates: a scale\-free predictive\-reliability certificate frozen after a fixed calibration prefix, a margin gate that suppresses advice for a confident policy, and an agreement gate that lets advice sharpen but never flip the greedy action\. When the certificate fails, an action\-complexity router hands control to a model\-based expert and the causal machinery is disabled exactly\.

This design lets us separate two questions that are usually entangled\. Does the routed system perform well? And does the causal world model, considered on its own, contribute to that performance? Our answer is*yes*to the first and*not measurably*to the second, and we regard the second finding as the more useful one for this workshop: on CartPole the transition graph recovers ground\-truth structure well above chance \(F1=0\.59±0\.09F\_\{1\}=0\.59\\pm 0\.09across ten seeds\), yet per\-seed structural fidelity has no relationship to per\-seed control benefit \(r=−0\.15r=\-0\.15,p=0\.67p=0\.67\), and one\-step prediction error is if anything*anti*\-correlated with it\. On Pendulum the certificate abstains on every seed, and abstention is the right call: the development variant that forces planning on there loses3434–5454return relative to the fallback it would have replaced\.

#### Contributions\.

1. 1\.An action\-conditioned signed transition model with first\- and second\-order mechanisms, learned jointly with a PPO policy from identified state coordinates \(§[4\.2](https://arxiv.org/html/2608.07809#S4.SS2)\)\.
2. 2\.A deployment\-time intervention planner with three composable gates, reliability certificate, policy margin, argmax agreement, and a proof that the composition preserves the base controller’s greedy action \(§[4\.3](https://arxiv.org/html/2608.07809#S4.SS3)–§[4\.4](https://arxiv.org/html/2608.07809#S4.SS4)\)\.
3. 3\.A controlled ten\-method comparison on two established benchmarks under physical\-parameter shift, with a shared trainer, budget, and supervision, over ten held\-out seeds and 200 runs \(§[5](https://arxiv.org/html/2608.07809#S5)\)\.
4. 4\.A fidelity\-versus\-utility analysis showing that structuralF1F\_\{1\}and one\-step NRMSE do not predict downstream control benefit in this setting, and an abstention analysis showing where the certificate earns its keep \(§[6\.3](https://arxiv.org/html/2608.07809#S6.SS3)\)\.

## 2Related Work

#### World models and planning\.

World models learn latent dynamics for prediction and control\(Hafneret al\.,[2023](https://arxiv.org/html/2608.07809#bib.bib11); Chuaet al\.,[2018](https://arxiv.org/html/2608.07809#bib.bib51)\)\. DreamerV3 scales recurrent latent imagination across domains\(Hafneret al\.,[2023](https://arxiv.org/html/2608.07809#bib.bib11)\); EfficientZero V2 extends planning\-based RL across discrete and continuous action spaces\(Wanget al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib13)\); MuZero\-style search demonstrates the value of planning\(Schrittwieseret al\.,[2020](https://arxiv.org/html/2608.07809#bib.bib50)\)\. Recent work studies epistemic optimism in world models\(Sukhijaet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib14)\)and flat\-minima objectives for robust model\-based RL\(Ramasubramanianet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib15)\)\. Compounding rollout error remains the shared limitation, and it motivates our abstention mechanism rather than a larger model\. Admitting a learned component’s output only under an explicit competence test appears outside model\-based control as well, in uncertainty\-gated meta\-reasoning\(Zhanget al\.,[2026a](https://arxiv.org/html/2608.07809#bib.bib60)\)and in compositional shielding that abstains when no candidate action is certified\(Zhanget al\.,[2026b](https://arxiv.org/html/2608.07809#bib.bib61)\); our certificate plays that role for a learned transition model\.

#### Causal structure for control\.

Causal RL uses interventions, structural assumptions, or invariant mechanisms to improve exploration, transfer, or robustness\(Lattimoreet al\.,[2016](https://arxiv.org/html/2608.07809#bib.bib42); Luet al\.,[2021](https://arxiv.org/html/2608.07809#bib.bib43); Zhanget al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib23)\); active causal induction explicitly trades reward against information about the causal system\(Annadaniet al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib20)\)\. Planning over learned graphs is used well outside classic control, e\.g\. GNN\-approximated dynamic programming over attack graphs\(Goelet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib59)\), where the same question of graph trustworthiness arises\. Identifiability is the central difficulty in causal representation learning\(Schölkopfet al\.,[2021](https://arxiv.org/html/2608.07809#bib.bib22); Lippeet al\.,[2022](https://arxiv.org/html/2608.07809#bib.bib32); Lachapelleet al\.,[2022](https://arxiv.org/html/2608.07809#bib.bib27); Abbaset al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib58)\)\. We do not solve it: every method in our study receives the same auxiliary mapping from learned slots to simulator state coordinates, so the representation is identified*by supervision*and the experiment isolates planning over identified state rather than unsupervised discovery\. The transition coefficients are learned with sparsity regularization related to continuous structure learning\(Zhenget al\.,[2018](https://arxiv.org/html/2608.07809#bib.bib30); Brouillardet al\.,[2020](https://arxiv.org/html/2608.07809#bib.bib31)\), and more broadly to low\-rank\-plus\-sparse decompositions used to recover structured coefficients from contaminated data\(Abbas and Ahmad,[2024](https://arxiv.org/html/2608.07809#bib.bib57)\); because the graph connects timetttot\+1t\+1, coordinate\-level cycles are permitted and no within\-slice acyclicity constraint is imposed\.

#### Positioning\.

The gap we target is evaluative\. Structural recovery and rollout error are reported as evidence that a world model is good; we measure whether either quantity predicts the model’s effect on action selection, and find that in this regime neither does\.

## 3Problem Setting

Letoto\_\{t\}be the native environment observation,at∈𝒜a\_\{t\}\\in\\mathcal\{A\}a discrete action,rtr\_\{t\}the native benchmark reward, andxt∈ℝ8x\_\{t\}\\in\\mathbb\{R\}^\{8\}an identified coordinate vector \(unused coordinates zero\-padded\)\. A 16\-dimensional queryq=\[w1,…,w8,τ1,…,τ8\]q=\[w\_\{1\},\\ldots,w\_\{8\},\\tau\_\{1\},\\ldots,\\tau\_\{8\}\]specifies nonnegative objective weightswiw\_\{i\}and targetsτi\\tau\_\{i\}\. Every method observes the same padded observation and query; the query does not replace the environment reward, it supplies the planner with a task objective\. The policy maximizes undiscounted native episodic return\. All agents receive the same auxiliary identification loss

ℒid=18​∑i=18\(gid​\(sti\)−xti\)2,\\mathcal\{L\}\_\{\\mathrm\{id\}\}=\\tfrac\{1\}\{8\}\\textstyle\\sum\_\{i=1\}^\{8\}\\left\(g\_\{\\mathrm\{id\}\}\(s\_\{t\}^\{i\}\)\-x\_\{t\}^\{i\}\\right\)^\{2\},\(1\)wherestis\_\{t\}^\{i\}is learned slotii\. This is privileged supervision and bounds the claim: we test planning over identified state, not causal discovery from pixels\.

## 4CausalNav

![Refer to caption](https://arxiv.org/html/2608.07809v1/figures/causalnav_architecture.png)Figure 1:CausalNav architecture\. Blue is the routed policy path; orange is the incremental causal world\-model path\. Dashed arrows are training\-only supervision\. When predictive validity is low the planner abstains and the routed expert is preserved exactly\.### 4\.1Action\-complexity router

An MLP mapsoto\_\{t\}to eight 32\-dimensional slots and a query encoder mapsqtq\_\{t\}to a 32\-dimensional token\. A fixed, observable task property, the action\-set size, then selects a controller\. Each optimistic expert uses an ensemble\{fk\}k=1K\\\{f\_\{k\}\\\}\_\{k=1\}^\{K\},

Ropt​\(z\)=z\+meank⁡fk​\(z\)\+softplus⁡\(β\)​stdk⁡fk​\(z\)\.R\_\{\\mathrm\{opt\}\}\(z\)=z\+\\operatorname\{mean\}\_\{k\}f\_\{k\}\(z\)\+\\operatorname\{softplus\}\(\\beta\)\\operatorname\{std\}\_\{k\}f\_\{k\}\(z\)\.\(2\)For\|𝒜\|≤2\|\\mathcal\{A\}\|\\leq 2, CausalNav averages three independently initialized copies ofRoptR\_\{\\mathrm\{opt\}\}; this increases capacity relative to the single\-copy SOMBRL reference and is deliberately*not*a parameter\-matched comparison \(§[7](https://arxiv.org/html/2608.07809#S7)\)\. For\|𝒜\|\>2\|\\mathcal\{A\}\|\>2the transition certificate abstains and CausalNav reduces exactly to its base controller, a normalized, gated latent residual over the routed slots\. The rule was selected on smoke seeds 70–72, remained frozen through the reported seeds 83–92, and uses neither returns nor shift labels at test time\. Flattened routed slots and the query token feed common two\-layer policy and value heads\.

### 4\.2Action\-conditioned transition graph

CausalNav predicts each identified coordinate with signed pairwise coefficientsAA, signed second\-order coefficientsBB, action effectsUU, self\-persistencedd, and biasbb:

x^t\+1,i=di​xt,i\+∑j≠iAi​j​xt,j\+∑j<kj,k≠iBi,j​k​xt,j​xt,k\+Uat,i\+bi\.\\hat\{x\}\_\{t\+1,i\}=d\_\{i\}x\_\{t,i\}\+\\sum\_\{j\\neq i\}A\_\{ij\}x\_\{t,j\}\+\\sum\_\{\\begin\{subarray\}\{c\}j<k\\\\ j,k\\neq i\\end\{subarray\}\}B\_\{i,jk\}x\_\{t,j\}x\_\{t,k\}\+U\_\{a\_\{t\},i\}\+b\_\{i\}\.\(3\)It is trained byℒtrans=18​∥x^t\+1−xt\+1∥22\+λs​\(∥A∥1\+∥B∥1\)\\mathcal\{L\}\_\{\\mathrm\{trans\}\}=\\tfrac\{1\}\{8\}\\lVert\\hat\{x\}\_\{t\+1\}\-x\_\{t\+1\}\\rVert\_\{2\}^\{2\}\+\\lambda\_\{s\}\(\\lVert A\\rVert\_\{1\}\+\\lVert B\\rVert\_\{1\}\)withλs=0\.05\\lambda\_\{s\}=0\.05on the active two\-action branch\. Unlike a contemporaneous\-state SCM,AAsummarizes edges*across adjacent time slices*, so recurrent dependencies are allowed and no NOTEARS acyclicity term is used\. Transition targets are actual successor states and never bridge an episode boundary\.

### 4\.3Intervention\-library planning

For each possible first action the planner evaluates three temporal patterns overH=8H=8model steps, constant \(repeataa\), impulse \(aaonce, then the neutral action\), and half\-horizon \(aafor four steps, then neutral\), and scores a sequence𝐚\\mathbf\{a\}by cumulative weighted objective error

E​\(𝐚\)=1H​∑h=1H∑i=18w¯i​\(x^t\+h,i𝐚−τi\)2,w¯i=\|wi\|∑j\|wj\|\+ϵ\.E\(\\mathbf\{a\}\)=\\frac\{1\}\{H\}\\sum\_\{h=1\}^\{H\}\\sum\_\{i=1\}^\{8\}\\bar\{w\}\_\{i\}\\left\(\\hat\{x\}\_\{t\+h,i\}^\{\\mathbf\{a\}\}\-\\tau\_\{i\}\\right\)^\{2\},\\qquad\\bar\{w\}\_\{i\}=\\frac\{\|w\_\{i\}\|\}\{\\sum\_\{j\}\|w\_\{j\}\|\+\\epsilon\}\.\(4\)For each first action the lowest\-cost pattern supplies a normalized planner logitpt​\(a\)p\_\{t\}\(a\)\. Letℓt\\ell\_\{t\}be the policy logits,mt=ℓt,\(1\)−ℓt,\(2\)m\_\{t\}=\\ell\_\{t,\(1\)\}\-\\ell\_\{t,\(2\)\}the gap between their two largest values, andgt=𝕀​\[arg⁡maxa⁡pt​\(a\)=arg⁡maxa⁡ℓt​\(a\)\]g\_\{t\}=\\mathbb\{I\}\[\\arg\\max\_\{a\}p\_\{t\}\(a\)=\\arg\\max\_\{a\}\\ell\_\{t\}\(a\)\]an agreement indicator\. At evaluation the final logits are

ℓt′​\(a\)=ℓt​\(a\)\+gt⏟agreement​ρ⏟certificate​tanh⁡\(α\)​exp⁡\(−2​mt\)⏟margin​pt​\(a\),\\ell^\{\\prime\}\_\{t\}\(a\)=\\ell\_\{t\}\(a\)\+\\underbrace\{g\_\{t\}\}\_\{\\text\{agreement\}\}\\,\\underbrace\{\\rho\}\_\{\\text\{certificate\}\}\\,\\underbrace\{\\tanh\(\\alpha\)\\exp\(\-2m\_\{t\}\)\}\_\{\\text\{margin\}\}\\;p\_\{t\}\(a\),\(5\)withα\\alphalearned and initialized to1\.01\.0\. Planner rollouts are detached, and the planner is disabled during PPO data collection and optimization, which avoids a train–test feedback loop through an immature transition model\.

### 4\.4Predictive\-reliability certificate

Coefficient magnitude is not evidence that a transition model is accurate\. CausalNav therefore tracks a scale\-free one\-step error and freezes a deployment scale after a fixed calibration prefix of 48 transition updates:

ek=MSE⁡\(x^t\+1,xt\+1\)18​∑iVar⁡\(xt\+1,i\)\+10−4,e¯k=0\.9​e¯k−1\+0\.1​ek,ρ=clip⁡\(δ−\|𝒜\|2​e¯48δ/2,0,1\)e\_\{k\}=\\frac\{\\operatorname\{MSE\}\(\\hat\{x\}\_\{t\+1\},x\_\{t\+1\}\)\}\{\\frac\{1\}\{8\}\\sum\_\{i\}\\operatorname\{Var\}\(x\_\{t\+1,i\}\)\+10^\{\-4\}\},\\quad\\bar\{e\}\_\{k\}=0\.9\\bar\{e\}\_\{k\-1\}\+0\.1e\_\{k\},\\quad\\rho=\\operatorname\{clip\}\\\!\\left\(\\frac\{\\delta\-\\frac\{\|\\mathcal\{A\}\|\}\{2\}\\bar\{e\}\_\{48\}\}\{\\delta/2\},0,1\\right\)\(6\)withδ=0\.70\\delta=0\.70\. The action\-count factor conservatively accounts for fewer samples per action effect and a larger intervention library; it equals one on the two\-action reference\. Threshold and router were selected on development seeds 0–69 and smoke seeds 70–72, then fixed; selection never uses a shift label\.

#### Proposition \(exact fallback\)\.

*For fixed policy logits, Equation[5](https://arxiv.org/html/2608.07809#S4.E5)preserves the routed controller’s greedy action under deterministic evaluation\.*Ifρ=0\\rho=0orgt=0g\_\{t\}=0the advice term vanishes andℓt′=ℓt\\ell^\{\\prime\}\_\{t\}=\\ell\_\{t\}\. Otherwisegt=1g\_\{t\}=1, soptp\_\{t\}attains its maximum ata⋆=arg⁡maxa⁡ℓt​\(a\)a^\{\\star\}=\\arg\\max\_\{a\}\\ell\_\{t\}\(a\); the advice is added with a nonnegative scale, soa⋆a^\{\\star\}remains the argmax ofℓt′\\ell^\{\\prime\}\_\{t\}\.□\\square

This is a deterministic action\-selection property, an implementation\-level non\-regression guarantee, not a probabilistic control\-safety guarantee\. On Pendulum, abstention additionally disables the causal auxiliary, producing an exact behavioral*and*optimization fallback to the base controller\.

### 4\.5Optimization

We train with PPO\(Schulmanet al\.,[2017](https://arxiv.org/html/2608.07809#bib.bib55)\):ℒ=ℒPPO\+0\.5​ℒvalue−0\.01​ℋ​\(π\)\+0\.1​\(ℒid\+ℒtrans\+λr​ℒrepr\)\\mathcal\{L\}=\\mathcal\{L\}\_\{\\mathrm\{PPO\}\}\+0\.5\\mathcal\{L\}\_\{\\mathrm\{value\}\}\-0\.01\\mathcal\{H\}\(\\pi\)\+0\.1\(\\mathcal\{L\}\_\{\\mathrm\{id\}\}\+\\mathcal\{L\}\_\{\\mathrm\{trans\}\}\+\\lambda\_\{r\}\\mathcal\{L\}\_\{\\mathrm\{repr\}\}\), whereℒrepr\\mathcal\{L\}\_\{\\mathrm\{repr\}\}predicts the identified successor from the identification probe\. The frozen routed variant setsλr=0\\lambda\_\{r\}=0\. Policy parameters use Adam at3×10−43\\times 10^\{\-4\}and transition parameters at10−210^\{\-2\}; the two gradient groups are clipped separately at norm11, so planner gradients cannot alter PPO\. The optimizer persists across rollouts\.

## 5Experimental Design

#### Benchmarks and physical shifts\.

CartPole\-v1has a four\-dimensional observation, two actions, and a 500\-step limit; the planner objective weights pole angle most strongly and weakly penalizes cart position and velocities\. The shifted condition multiplies pole length and pole mass by1\.51\.5and recomputes the derived total\-mass and mass–length terms\.Pendulum\-v1observes\(cos⁡θ,sin⁡θ,θ˙\)\(\\cos\\theta,\\sin\\theta,\\dot\{\\theta\}\)with the native quadratic control cost; to share a categorical policy across methods, torque is discretized once, before any development experiment, to\{−2,−1,0,1,2\}\\\{\-2,\-1,0,1,2\\\}, and the planner targets the upright state\(1,0,0\)\(1,0,0\)\. Its shifted condition multiplies mass by1\.51\.5and length by1\.251\.25\. Both shifts change physical parameters only, observation space, action space, reward, and termination logic are identical, training happens solely in the unmodified environment, and both conditions are evaluation\-only rollouts of the same trained policy\. Native observations are normalized by fixed physical scales, clipped to\[−3,3\]\[\-3,3\], and padded; all reported numbers are native Gymnasium episodic returns\(Towerset al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib54)\), not training\-time rescalings\.

#### Controlled references\.

All nine references share the slot encoder, query encoder, policy/value heads, PPO implementation, interaction budget, and identification loss, and differ only in their characteristic reasoning module:TF\-Policy\(two\-layer transformer over slots\),GRU\-World\(recurrent latent state\),Split\-Latent\(separate invariant/variant features\),GNN\-RAG\(learned static adjacency plus message passing\),ToG\(query\-conditioned search\-style refinement\),CAASL\(Annadaniet al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib20)\),EfficientZero V2\(Wanget al\.,[2024](https://arxiv.org/html/2608.07809#bib.bib13)\),SOMBRL\(Sukhijaet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib14)\), andFlatMBRL\(Ramasubramanianet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib15)\)\. These are controlled adaptations of inductive bias,*not*native reproductions: the original methods differ in objectives, planners, replay, model size, and compute\. The design isolates the reasoning module under identical data and budget\.

#### Protocol and statistics\.

Each run uses 4,096 environment interactions, rollout length 256, four PPO epochs,γ=0\.99\\gamma=0\.99, GAEλ=0\.95\\lambda=0\.95, clip0\.20\.2, entropy coefficient0\.010\.01\. Evaluation uses 20 fresh episodes per condition with deterministic argmax actions\. Development and earlier audits used seeds 0–82; all reported results use fresh seeds 83–92, and no failed seed is removed\. The artifact contains all2×10×10=2002\\times 10\\times 10=200runs with per\-episode returns\. We report means and sample SDs across seeds\. Because CausalNav and its routed expert are paired by seed and share initialization, we also report paired mean differences, Student\-tt95% CIs, pairedtt\-testpp\-values, and win counts; these are descriptive, and no multiplicity adjustment is claimed\.

## 6Results

### 6\.1Aggregate control performance

![Refer to caption](https://arxiv.org/html/2608.07809v1/figures/public_benchmark_results.png)Figure 2:Native episodic return on both benchmarks and both conditions\. Points are means over ten held\-out seeds; error bars are sample SDs\. Higher is better\.Table 1:Native episodic return, mean±\\pmsample SD over ten held\-out seeds \(higher is better\)\. Bold is the best mean per column\. Average rank uses fractional ranks over the four cells\.CausalNav ranks second on CartPole ID and first in the other three cells, giving the best average rank \(1\.251\.25\), ahead of SOMBRL \(2\.252\.25\) and GNN\-RAG \(4\.754\.75\) \(Table[1](https://arxiv.org/html/2608.07809#S6.T1)\)\. SOMBRL is higher by12\.1712\.17on CartPole ID whereas CausalNav is higher by11\.9511\.95under shift, that is, the routed system loses nothing in distribution and gains slightly after the physical parameters change, but neither difference is resolvable at this sample size\.

### 6\.2What the world model actually contributed

Table 2:Seed\-paired effect of CausalNav relative to its routed expert \(SOMBRL on CartPole; its own base controller on Pendulum\)\. Positive favors CausalNav\.
Table 3:World\-model diagnostics for CausalNav, mean±\\pmSD over ten seeds\. Pendulum abstains, so no transition model is trained\.

Table[3](https://arxiv.org/html/2608.07809#S6.T3)isolates the increment\. On CartPole the paired differences are small with wide intervals straddling zero; on Pendulum every paired difference is exactly zero by construction, confirming the fallback property empirically across all ten seeds\. Because the agreement gate cannot flip a greedy action, whatever CartPole difference exists is attributable to the three\-member ensemble controller, not to planner overrides\. We state this plainly: the ten\-method ranking is a result about the routed*system*, and it is not evidence that causal planning improves return\.

### 6\.3Does model fidelity predict control utility?

![Refer to caption](https://arxiv.org/html/2608.07809v1/figures/public_transition_graphs.png)Figure 3:Mean signed pairwise transition coefficients learned by the active CartPole branch over ten held\-out seeds\. The matrix summarizes*cross\-time*coordinate dependencies and is not a contemporaneous DAG\. Pendulum is omitted because exact fallback disables transition learning\.The transition graph is not vacuous \(Figure[3](https://arxiv.org/html/2608.07809#S6.F3)\)\. Against the CartPole ground\-truth structure it reaches precision0\.530\.53, recall0\.700\.70, andF1=0\.59±0\.09F\_\{1\}=0\.59\\pm 0\.09, predicting6\.8±1\.56\.8\\pm 1\.5edges where55exist, with top\-parent accuracy0\.600\.60versus0\.270\.27for the untrained Pendulum branch \(Table[3](https://arxiv.org/html/2608.07809#S6.T3)\)\. One\-step NRMSE averages0\.560\.56, i\.e\. the model explains a substantial fraction of successor variance\. By the usual reporting conventions this would count as a working world model\.

It does not translate\. Regressing the per\-seed paired return difference on per\-seed structuralF1F\_\{1\}givesr=−0\.15r=\-0\.15\(p=0\.67p=0\.67\) in distribution andr=−0\.18r=\-0\.18\(p=0\.62p=0\.62\) under shift, no relationship, and the point estimate has the wrong sign\. One\-step NRMSE is positively correlated with the paired difference \(r=\+0\.71r=\+0\.71,p=0\.02p=0\.02\), meaning the seeds with the*worst*one\-step models showed the largest gains\. We do not read this as a causal claim; it is a confound, and an instructive one, since the paired difference is driven by the ensemble controller while the fidelity metrics describe a component that is gated out of the argmax\. That is precisely the point: two standard world\-model quality metrics carried no signal about the quantity a physical\-AI practitioner cares about, and one of them pointed backwards\.

### 6\.4Abstention behavior

The certificate is active, not decorative\. On CartPole it admits advice on7/107/10seeds with meanρ=0\.32\\rho=0\.32and a full\[0,1\]\[0,1\]range across seeds; on Pendulum it abstains on10/1010/10\. Abstention there is correct\. Pendulum requires energy accumulation and phase\-sensitive torque sequences, whereas the library contains three simple temporal patterns per first action\. Forcing planning on there was at best neutral and at worst harmful: in development, a low\-scale planner reproduced the fallback exactly \(−1278\.3\-1278\.3ID,−1234\.7\-1234\.7shift\) while a stronger planner reached−1332\.3\-1332\.3ID and−1268\.5\-1268\.5shift, i\.e\.3434–5454return worse \(Appendix[C](https://arxiv.org/html/2608.07809#A3)\)\. A certificate that converts “my model is inaccurate here” into “do not act on it” recovered the better controller without any test\-time label, and it did so from prediction error alone\.

### 6\.5Cost

Planning evaluates3​\|𝒜\|​H3\|\\mathcal\{A\}\|Hmodel transitions per decision \(48 on CartPole, 120 on Pendulum atH=8H=8\); transition storage isO​\(n2\+n​\|𝒜\|\)O\(n^\{2\}\+n\|\\mathcal\{A\}\|\)pairwise andO​\(n3\)O\(n^\{3\}\)dense second\-order forn=8n=8coordinates, small relative to the policy network\. Mean wall\-clock per training seed is88\.388\.3s for CausalNav on CartPole versus8\.08\.0–40\.040\.0s for the references, and25\.225\.2s versus6\.46\.4–24\.624\.6s on Pendulum, where abstention removes the planning cost entirely\. The CartPole overhead buys the three\-member ensemble and the planner; given the paired result, most of it purchased the ensemble\.

## 7Discussion and Limitations

#### What we would take to a physical system\.

The transferable component is not the graph but the gate\. A learned model withF1=0\.59F\_\{1\}=0\.59andNRMSE=0\.56\\text\{NRMSE\}=0\.56looks deployable by prediction metrics and was nevertheless useless for action selection in one environment and harmful when forced in the other\. The certificate detected the second case from prediction error alone, before deployment, with no access to returns or shift labels, and the composition of certificate, margin, and agreement gates makes the failure mode a no\-op rather than a regression\. For physical AI, we think that ordering matters more than another point of rollout fidelity, and we would want the same ordering in any deployed adaptive controller whose operating conditions drift, from resource\-adaptive scaling of running software systems\(Ahmadet al\.,[2025](https://arxiv.org/html/2608.07809#bib.bib63)\)to environmental response pipelines over nonstationary physical processes\(Joiset al\.,[2026](https://arxiv.org/html/2608.07809#bib.bib62)\)\.

#### Threats to validity\.

Two low\-dimensional classic\-control benchmarks, 4,096 interactions per run, and large seed variance mean the returns are not converged and the intervals are wide; ten seeds improve on three but remain thin against bimodal CartPole outcomes\. Pendulum uses a disclosed five\-torque discretization, so conclusions apply to that version rather than the continuous interface\. Shifts change physical parameters but not observation semantics, topology, or reward\. Identified coordinates are supervised, so nothing here establishes unsupervised causal representation learning\. The references are controlled adaptations, and their names denote inductive biases rather than reproduction\-level equivalence\. The CartPole branch has more parameters than a single reference expert, so its ranking advantage is partly capacity; a parameter\-matched control is the obvious next experiment\. The action\-count router was chosen after observing exactly two datasets, one on each side of its threshold, and can therefore encode benchmark\-specific selection rather than a general law\. Acrobot and FrozenLake were examined and not promoted under the fixed budget \(Appendix[C](https://arxiv.org/html/2608.07809#A3)\); this is disclosed because benchmark qualification is itself selection pressure, and a preregistered suite should replace it\.

#### Broader impact\.

The method targets robust control, where an incorrect causal model can produce unsafe actions\. The agreement gate verifies a narrow software non\-regression property, not control safety; deployment in physical or safety\-critical systems would additionally require calibrated model uncertainty, a conservative fallback controller, and domain\-specific validation\.

## 8Conclusion

CausalNav pairs an identified action\-conditioned transition graph with three deployment gates and an action\-complexity router, and attains the best average rank \(1\.251\.25\) among ten controlled methods on two benchmarks under physical\-parameter shift\. The finding we would carry forward is the negative one: structural recovery and one\-step error, the two metrics normally used to certify a world model, did not predict whether that world model helped control, while a cheap scale\-free reliability certificate correctly withheld it where planning would have hurt\. World models for physical AI should be evaluated by their effect on decisions, and should come with an explicit abstention mechanism for the regimes where that effect is negative\.

## Reproducibility statement

The supplement contains the Gymnasium adapters, all ten agents, the shared trainer, the ten\-seed runner, all 200 runs with per\-episode returns, the statistics script, and plotting code\. The primary command ispython core\_codes\_v2/run\_two\_benchmarks\.py; the frozen artifact isresults/public\_benchmarks\_10seed\.json\. Shared modules are deterministically reinitialized from component\-specific seed streams so the CausalNav–routed\-expert pairing can be audited exactly\.

## References

- SCALAR: self\-calibrating adaptive latent attention representation learning\.In2025 IEEE 37th International Conference on Tools with Artificial Intelligence \(ICTAI\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- F\. Abbas and H\. Ahmad \(2024\)Robust partial least squares using low rank and sparse decomposition\.External Links:2407\.06936Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- H\. Ahmad, C\. Treude, M\. Wagner, and C\. Szabo \(2025\)Resilient auto\-scaling of microservice architectures with efficient resource management\.In2025 32nd Asia\-Pacific Software Engineering Conference \(APSEC\),pp\. 852–856\.Cited by:[§7](https://arxiv.org/html/2608.07809#S7.SS0.SSS0.Px1.p1.2)\.
- Y\. Annadani, N\. Pawlowski, J\. Jennings, S\. Bauer, C\. Zhang, and W\. Gong \(2024\)Amortized active causal induction with deep reinforcement learning\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2),[§5](https://arxiv.org/html/2608.07809#S5.SS0.SSS0.Px2.p1.1)\.
- P\. Brouillard, S\. Lachapelle, A\. Lacoste, S\. Lacoste\-Julien, and A\. Drouin \(2020\)Differentiable causal discovery from interventional data\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- K\. Chua, R\. Calandra, R\. McAllister, and S\. Levine \(2018\)Deep reinforcement learning in a handful of trials using probabilistic dynamics models\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1)\.
- D\. Goel, H\. Ahmad, K\. Moore, and M\. Guo \(2025\)Co\-evolutionary defence of active directory attack graphs via GNN\-approximated dynamic programming\.External Links:2505\.11710Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- D\. Hafner, J\. Pasukonis, J\. Ba, and T\. Lillicrap \(2023\)Mastering diverse domains through world models\.Note:arXiv preprint arXiv:2301\.04104Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1)\.
- T\. Jois, H\. Ahmad, F\. Noor, and F\. Ullah \(2026\)Australian bushfire intelligence with AI\-driven environmental analytics\.External Links:2601\.06105Cited by:[§7](https://arxiv.org/html/2608.07809#S7.SS0.SSS0.Px1.p1.2)\.
- S\. Lachapelle, P\. Rodriguez, Y\. Sharma, K\. E\. Everett, R\. Le Priol, A\. Lacoste, and S\. Lacoste\-Julien \(2022\)Disentanglement via mechanism sparsity regularization: a new principle for nonlinear ica\.InConference on Causal Learning and Reasoning \(CLeaR\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- F\. Lattimore, T\. Lattimore, and M\. D\. Reid \(2016\)Causal bandits: learning good interventions via causal inference\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- P\. Lippe, S\. Magliacane, S\. Löwe, Y\. M\. Asano, T\. Cohen, and E\. Gavves \(2022\)CITRIS: causal identifiability from temporal intervened sequences\.InInternational Conference on Machine Learning \(ICML\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- Y\. Lu, M\. Carone, and A\. Luedtke \(2021\)Regret analysis of bandit problems with causal background knowledge\.InConference on Uncertainty in Artificial Intelligence \(UAI\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- S\. Ramasubramanian, B\. Freed, A\. Capone, and J\. Schneider \(2025\)Improving model\-based reinforcement learning by converging to flatter minima\.InAdvances in Neural Information Processing Systems,Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2608.07809#S5.SS0.SSS0.Px2.p1.1)\.
- J\. Richens and T\. Everitt \(2024\)Robust agents learn causal world models\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[§1](https://arxiv.org/html/2608.07809#S1.p1.1)\.
- B\. Schölkopf, F\. Locatello, S\. Bauer, N\. R\. Ke, N\. Kalchbrenner, A\. Goyal, and Y\. Bengio \(2021\)Toward causal representation learning\.Proceedings of the IEEE109\(5\),pp\. 612–634\.Cited by:[§1](https://arxiv.org/html/2608.07809#S1.p1.1),[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- J\. Schrittwieser, I\. Antonoglou, T\. Hubert, K\. Simonyan, L\. Sifre, S\. Schmitt, A\. Guez, E\. Lockhart, D\. Hassabis, T\. Graepel,et al\.\(2020\)Mastering Atari, Go, chess and shogi by planning with a learned model\.InNature,Vol\.588,pp\. 604–609\.Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1)\.
- J\. Schulman, F\. Wolski, P\. Dhariwal, A\. Radford, and O\. Klimov \(2017\)Proximal policy optimization algorithms\.arXiv preprint arXiv:1707\.06347\.Cited by:[§4\.5](https://arxiv.org/html/2608.07809#S4.SS5.p1.6)\.
- B\. Sukhija, L\. Treven, C\. Sferrazza, F\. Dörfler, P\. Abbeel, and A\. Krause \(2025\)SOMBRL: scalable and optimistic model\-based reinforcement learning\.InAdvances in Neural Information Processing Systems,Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2608.07809#S5.SS0.SSS0.Px2.p1.1)\.
- M\. Towers, A\. Kwiatkowski, J\. Terry, J\. U\. Balis, G\. De Cola, T\. Deleu, M\. Goulão, A\. Kallinteris, M\. Krimmel, A\. KG,et al\.\(2024\)Gymnasium: a standard interface for reinforcement learning environments\.arXiv preprint arXiv:2407\.17032\.Cited by:[§5](https://arxiv.org/html/2608.07809#S5.SS0.SSS0.Px1.p1.7)\.
- S\. Wang, S\. Liu, W\. Ye, J\. You, and Y\. Gao \(2024\)EfficientZero V2: mastering discrete and continuous control with limited data\.InInternational Conference on Machine Learning,Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2608.07809#S5.SS0.SSS0.Px2.p1.1)\.
- K\. Zhang, S\. Xie, I\. Ng, and Y\. Zheng \(2024\)Causal representation learning from multiple distributions: a general setting\.InInternational Conference on Machine Learning \(ICML\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.
- Y\. Zhang, D\. Goel, H\. Ahmad, and J\. Shen \(2026a\)Beyond reactive agents: uncertainty\-gated meta\-reasoning for tool\-augmented decision\-making\.Note:Available at SSRN 6997675Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Zhang, D\. Goel, H\. Ahmad, and J\. Shen \(2026b\)VACS: value\-aligned compositional shielding for multi\-agent reasoning\.Note:Available at SSRN 7115827Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px1.p1.1)\.
- X\. Zheng, B\. Aragam, P\. Ravikumar, and E\. P\. Xing \(2018\)DAGs with NO TEARS: continuous optimization for structure learning\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§2](https://arxiv.org/html/2608.07809#S2.SS0.SSS0.Px2.p1.2)\.

## Appendix ABenchmark interfaces and reward accounting

Table[4](https://arxiv.org/html/2608.07809#A1.T4)records the complete interface used by the runner\. No benchmark\-specific feature is hidden from a reference method: the padded observation and fixed query are passed to every policy\. The causal component uses the first eight padded entries explicitly because the experiment studies control with identified coordinates\. PPO receives0\.01​rt0\.01r\_\{t\}for numerical conditioning, identically for all methods; every table and figure reports the unscaled Gymnasium reward stored in the adapter’s info dictionary\. Returns are averaged within 20 evaluation episodes for a trained seed and then across ten seeds; error bars are the sample SD across seed means, not across the 200 pooled episodes\.

Table 4:Benchmark interfaces\. “Scale” is the divisor applied before clipping each native coordinate to\[−3,3\]\[\-3,3\]\.
## Appendix BAlgorithm and hyperparameters

Algorithm 1: Reliability\-certified causal navigation1\.Initialize the shared encoder, query encoder, routed expert, value head, and identification probe from component\-specific seed streams; initialize the signed transition coefficients separately\.2\.Reset the action\-sampling random stream after construction so methods with different parameter counts receive paired stochasticity\.3\.For each 256\-step rollout, store observation, action, reward, done flag, identified state, and the actual identified successor state\.4\.Run four PPO epochs, updating the shared policy with PPO, value, entropy, and identification losses\. On the active two\-action branch, update the transition model with one\-step prediction and sparsity losses and clip the two gradient groups separately\.5\.Maintain the exponential error of Equation[6](https://arxiv.org/html/2608.07809#S4.E6); keepρ=0\\rho=0during the first 48 transition updates, then freezeρ\\rho\.6\.On the active branch, enumerate three length\-eight intervention patterns per first action, roll each through the detached transition model, and compute Equation[4](https://arxiv.org/html/2608.07809#S4.E4)\.7\.At deterministic evaluation, apply Equation[5](https://arxiv.org/html/2608.07809#S4.E5)only when the reliability, margin, and agreement checks all admit the advice; otherwise execute the routed expert exactly\.

Table 5:Frozen hyperparameters shared across both benchmarks\.QuantityValueQuantityValueTraining interactions4,096Rollout length256PPO epochs/rollout4Discountγ\\gamma0\.99GAEλ\\lambda0\.95PPO clip0\.20Policy learning rate3×10−43\\\!\\times\\\!10^\{\-4\}Transition learning rate10−210^\{\-2\}Value coefficient0\.50Entropy coefficient0\.01Auxiliary coefficient0\.10Gradient norm1\.0Slots8Slot width32Planning horizon8Patterns/action3Planner\-scale init\.1\.0Reliability momentum0\.90Calibration updates48Reliability threshold0\.70Pairwise sparsity0\.05Evaluation episodes20CartPole has no physical no\-op, so the neutral action of the intervention library maps to the integer midpoint \(the right action\)\. This asymmetry is a limitation of using a common discrete library and is one reason not to interpret the planner as an optimal controller\.

## Appendix CDevelopment evidence and rejected variants

All choices below are excluded from the reported ten\-seed analysis\. Architecture checks and the exact\-copy diagnosis used seeds 0–69; a smoke gate used seeds 70–72; the selected routed variant was then frozen; seeds 73–82 formed an earlier audit; and the reported ten\-method comparison uses fresh seeds 83–92\.

Table 6:Development decisions\. These diagnostics are excluded from the held\-out result\.VariantIDShiftDecisionSOMBRL CartPole reference391\.07394\.50smoke referenceTwo\-member CartPole route257\.27247\.23rejectThree\-member CartPole route473\.40462\.40retainPendulum base controller−1278\.28\-1278\.28−1234\.66\-1234\.66retain exactlyLow\-scale causal planner−1278\.28\-1278\.28−1234\.66\-1234\.66no gainStronger causal planner−1332\.27\-1332\.27−1268\.54\-1268\.54rejectConvex hybrids, a two\-member route, and planner residuals were rejected\. The agreement gate was retained because uncertain or contradictory advice then cannot change the deterministic action\. Early qualification also considered Acrobot and FrozenLake: under the fixed 4,096\-interaction budget no controlled method learned a useful Acrobot policy, while FrozenLake’s discrete grid and sparse reward do not match a continuous identified\-coordinate transition model, so reporting either would mostly measure benchmark mismatch\.

## Appendix DStatistical analysis details

The seed is the unit of analysis\. For each benchmark and condition letys,my\_\{s,m\}be the 20\-episode mean for seedssand methodmm; the descriptive SD issm=19​∑s=110\(ys,m−y¯m\)2s\_\{m\}=\\sqrt\{\\frac\{1\}\{9\}\\sum\_\{s=1\}^\{10\}\(y\_\{s,m\}\-\\bar\{y\}\_\{m\}\)^\{2\}\}\. For the matched comparison we computeds=ys,CN−ys,routed\_\{s\}=y\_\{s,\\mathrm\{CN\}\}\-y\_\{s,\\mathrm\{route\}\}and the two\-sided intervald¯±t0\.975,9​sd/10\\bar\{d\}\\pm t\_\{0\.975,9\}s\_\{d\}/\\sqrt\{10\}\. Correlations in §[6\.3](https://arxiv.org/html/2608.07809#S6.SS3)are Pearson over the ten seeds; the Spearman analogues agree in sign and significance \(F1F\_\{1\}vs\.Δ\\DeltaID:ρS=−0\.23\\rho\_\{S\}=\-0\.23,p=0\.53p=0\.53; NRMSE vs\.Δ\\DeltaID:ρS=\+0\.59\\rho\_\{S\}=\+0\.59,p=0\.07p=0\.07\)\. Four cells and several method comparisons make uncorrected significance hunting misleading, so we emphasize effect sizes, intervals, per\-seed differences, and average rank\. No bootstrap over evaluation episodes is used, because episodes within a trained seed do not replace independent training replicates\.

## Appendix EPer\-seed results

![Refer to caption](https://arxiv.org/html/2608.07809v1/figures/paired_causal_gain.png)Figure 4:Per\-seed return difference between CausalNav and its routed expert \(SOMBRL for CartPole; its own base controller for Pendulum\)\. Orange diamonds are paired means; bars are Student\-tt95% confidence intervals\.Tables[7](https://arxiv.org/html/2608.07809#A5.T7)–[10](https://arxiv.org/html/2608.07809#A5.T10)report every seed–method mean behind Table[1](https://arxiv.org/html/2608.07809#S6.T1), exposing the pronounced bimodality of CartPole and showing that no failed training run was removed\. Column abbreviations: CN \(CausalNav\), TF \(TF\-Policy\), GRU \(GRU\-World\), Split \(Split\-Latent\), GNN \(GNN\-RAG\), EZ2 \(EfficientZero V2\), SOM \(SOMBRL\), Flat \(FlatMBRL\)\.

Table 7:CartPole\-v1 in\-distribution return by held\-out seed\.Table 8:CartPole\-v1 physical\-shift return by held\-out seed\.Table 9:Pendulum\-v1 in\-distribution return by held\-out seed\.Table 10:Pendulum\-v1 physical\-shift return by held\-out seed\.
## Appendix FPer\-seed world\-model diagnostics

Table[11](https://arxiv.org/html/2608.07809#A6.T11)gives the per\-seed quantities behind §[6\.3](https://arxiv.org/html/2608.07809#S6.SS3): structuralF1F\_\{1\}against the CartPole ground\-truth adjacency, the exponential one\-step NRMSE, the frozen certificateρ\\rho, and the paired return differences against SOMBRL\. Seeds withρ=0\\rho=0executed the routed expert exactly\.

Table 11:Per\-seed CausalNav diagnostics on CartPole\-v1\.
## Appendix GArtifact map and implementation checks

Table 12:Primary reproducibility artifacts\.The released runner enforces the following invariants: \(i\) all methods receive identical benchmark seeds, interaction budgets, PPO hyperparameters, and identified\-state targets; \(ii\) the active CartPole route uses three deterministically seeded optimistic experts while the Pendulum route exactly disables the causal component and executes the base controller unmodified; \(iii\) optimizer state persists across rollouts; \(iv\) auxiliary gradients reach the observation encoder; \(v\) transition targets are actual successor states and never connect the final state of one episode to the first state of another; and \(vi\) evaluation actions come from learned logits without scripted outcome injection\.