R12 S3 Categorical Permutation Register Preregistration

Status: closed negative after job 693127. See R12_S3_CATEGORICAL_REGISTER_RESULT.md.

Claim class: public source-deleted execution-component development under an external operation schedule and halt. A pass authorizes only a new independent confirmation board.

Theory

The prior matched diagnostic shows that exact referent rebinding is insufficient: gold identity still reaches only 88.672% answers / 85.840% exact state because the old executor repeatedly re-encodes semantic identity into continuous vectors and mixes those vectors through a soft assignment.

The new state space is the finite group S3. The persistent register is always one of the six valid three-item permutation matrices. For each atomic update:

1. the compiler emits a categorical identity among the three introduced referents;
2. multiplying the S3 register by that one-hot identity gives its exact current location;
3. one tied neural cell predicts one of the six relative S3 permutations from current register, identity, location, operation kind, and amount;
4. a straight-through six-way gate is hard in the forward pass and soft only for gradients; and
5. exact group multiplication updates the persistent register.

Semantic equality is never relearned inside the recurrent loop, and an invalid or fractional state is structurally impossible in forward execution.

Frozen training

• immutable raw-300k base and qualified ordinary compiler;
• one 717,323-parameter tied executor, total system 134,406,873 parameters;
• one epoch / 1,517 updates / batch 64 / seed 2026071903;
• 96,000 public rows supply op0 and op1 independently from identity state, 192,000 atomic targets per epoch;
• gold categorical identity during training isolates state-update learning;
• no composed, long-program, confirmation, answer-only, or halt supervision.

Frozen evaluation

Two-step compositional development is scored with mean identity as primary and ordered/gold identity as favorable ceilings. Mean identity is also scored on lexical OOD. The existing 2,048-row public paired-name board is scored at depths three through eight with all three identity modes. The rejected ordered kernel remains a ceiling, not a promotion path.

Gates

All must pass:

1. two-step mean: at least 95% answers/state, 90% both transitions, and 94% answers on every surface;
2. lexical-OOD mean answers at least 60%;
3. long mean answers at least 87.3926% (ten points above continuous), state at least 85%, all transitions at least 65%, and depth-eight answers at least 80%;
4. long ordered answers/state at least 98%;
5. long gold answers/state at least 99%;
6. every evaluation records zero fit updates and zero confirmation access;
7. one job exits 0:0, hashes every source/input/output, and stays below 150M total parameters.

Failure rejects this register. Passing does not establish autonomous planning, learned halt, free-form language reasoning, or novelty; it only authorizes a fresh independently seeded source-deleted confirmation.