R12 S3 Categorical Permutation Register Result
Decision: reject_s3_categorical_register
The exact categorical state representation is valid, but v1's neural update cell is not permutation-equivariant and fails immediately outside the identity state seen during atomic training.
Custody
- Source/prereg commit
dc7c13epreceded fit and every S3 score. - Job
693127completed once on H100evc29in 5m39s, exit0:0. - Training used 96,000 public rows / 192,000 independent atomic targets / 1,517
updates / one epoch / seed
2026071903. - The 717,323-parameter executor kept the full system at 134,406,873 parameters and recorded zero confirmation access.
- Training completed in 56.15 seconds; final executor state SHA-256:
8f043863138d32a89089ceaf029f89e2806d1f1c2df4c2735bf8bb1fb491b161. - Assessment SHA-256:
c9c7b545dfc85d614faaf1e943fb7932c6e54c80679bdb3ad735a09825418fdf.
Results
| Evaluation | Answers | Exact state | All transitions | Entity match |
|---|---|---|---|---|
| Two-step mean | 79.590% | 66.211% | 66.211% | 99.927% |
| Two-step ordered | 79.541% | 66.260% | 66.260% | 100.000% |
| Two-step gold | 79.541% | 66.260% | 66.260% | 100.000% |
| Lexical-OOD mean | 58.984% | 48.730% | 42.236% | 86.377% |
| Depth 3--8 mean | 53.906% | 41.260% | 17.627% | 71.879% |
| Depth 3--8 ordered | 54.834% | 42.285% | 18.750% | 73.551% |
| Depth 3--8 gold | 54.932% | 42.432% | 18.896% | 73.871% |
Depth-eight mean answers are 48.529%. Every substantive promotion gate fails.
Mechanistic diagnosis
Atomic transition loss reaches effectively zero and the forward register is always a valid S3 element. Identity is also not the problem: ordered and gold are indistinguishable at two steps, while entity match is exact. The defect is the update cell's input contract. It receives the complete assignment matrix and immutable identity vector. Atomic training presents only the identity assignment; the second recurrent call presents a non-identity assignment that is out of distribution. The unrestricted MLP therefore memorizes the initial coordinate frame rather than a local group action.
The only bounded repair is equivariant local action: compute current location by multiplying register and categorical identity, then let the tied cell depend only on location, operation kind, and amount. Those variables fully determine the relative move permutation and have complete atomic support. The raw assignment and immutable identity must not enter the transition MLP. This is a separately preregistered architecture version, not a retry or width/ epoch/data change.
No confirmation, autonomous planning, learned halt, language reasoning, or novelty claim is authorized.