Submitted:
09 July 2026
Posted:
14 July 2026
You are already at the latest version
Abstract
Keywords:
1. Introduction
2. Related Work
3. The Measurement Standard
3.1. The Acceptance Gate and the Class-Prior Control
3.2. The Seven Loophole-Closing Checks
4. Eleven Documented Failure-Mode Case Studies
4.1. Class Priors and Definitional Tautologies
4.2. Probe Strength, Data Volume, and Prediction Targets
4.3. Units, Appearance, and Episode Structure
4.4. Reading the Eleven Together
5. Discussion
6. Limitations
7. Conclusion
References
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| Check | Rule | Enforcing tool |
|---|---|---|
| 1. Class-prior control | Beat the strongest trivial baseline with a CI that excludes it, on independent units, on a morphology-varying task. | the acceptance gate (verify_claims.py) |
| 2. Strong-probe certification | Certify invariance with a strong nonlinear probe, not a linear one. | dual linear/RF probe grid |
| 3. Data-volume control | Hold the total data budget fixed before crediting diversity. | budget-by-breadth grid |
| 4. Independent-unit rule | Bootstrap over independent units, not pseudo-replicated (unit × seed) rows. | the gate’s aggregation step |
| 5. Non-degenerate target | A prediction target must have real variation, not sit at a floor. | tiny-probe budget-oracle protocol |
| 6. No observational leakage | A tiny-probe prediction must end before the event it predicts. | the same oracle protocol |
| 7. Raw-input control | Run the identity probe on the raw input; if it recovers identity, the probe read appearance. | the raw-pixel control |
| 8. Episode-blocked splits | Per-frame metrics on episodic data need episode-blocked train/test splits. | the episode-blocked split |
| # | Tested claim | Metric | Strongest baseline | Gap 95% CI, n | Verdict |
|---|---|---|---|---|---|
| 1 | Distance predicts transfer | target prior | , 42 | fails | |
| 2 | Features predict gain (oracle) | class bit | , 29 | fails | |
| 3 | Semantic state helps transfer | raw-obs | , 29 | passes | |
| 4 | A diversity scaling law | range | flat-ceiling test | 4/7 flat, 7 | fails |
| 5 | Distance predicts locomotion | zero correlation | , 12 | fails | |
| 6 | Deliberation enables multi-step transfer | reactive | , 6 | passes | |
| 7 | Body-blind action coding transfers | padded head | , 5 | fails | |
| 8 | Leaked body channels collapse transfer | leaked proprio | , 5 | passes | |
| 9 | Structured beats token coding | token | , 6 | passes |
| Tempting claim | Check | Corrected claim | Artifact | |
|---|---|---|---|---|
| a | Learnability, | 1, 5 | Geometrically trivial within one topology | stance control |
| b | Learnability governs transfer | 1 | Outcome is near-identity; gain unpredictable () | transfer law |
| c | Adversary converged everywhere | 2 | The certifier is the independent strong probe | invariance grid |
| d | Diversity scales transfer | 3 | Breadth never beats depth at fixed budget | diversity grid |
| e | An invariant latent (probe ≈ chance) | 2 | Strong probe recovers the body at | invariance grid |
| f | A budget oracle sharper | 5, 6 | It was predicting a floor; works on a real substrate | budget oracle |
| g | Gap CI , | 4 | Aggregated over 42 pairs | the gate |
| h | Distance predicts transfer | 1 | Loses to a target prior; the oracle reads class | the gate |
| i | A VLA encodes embodiment identity | 7 | Raw pixels recover it; probe read the scene | VLA probe |
| j | A linear scrub certifies invariance | 2, 8 | Vacuous under a strong probe and episode splits | action probe |
| k | Multi-agent degrades with scale | 1 | The value is the shared-term independence null | ladder null |
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