# 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.