DIVERGE-RSM1: Persistent Discrete State Replay

Status: architecture and component gate frozen before neural execution.

Why this is not a CRP1 repair

CRP1 established that guarded first-error packets can cause complete arithmetic and register corrections. It failed because the selected packet was only converted into a short prefix for a frozen autoregressive generator. The generator could independently solve some rows, ignore packet identity on others, and never transferred to held symbolic tapes. RSM1 does not change the CRP1 packet, its training, its checkpoint, its selector, or its thresholds.

RSM1 replaces the entire post-selection substrate. A frozen selected packet must initialize one bounded discrete state. A tied transition core then consumes the remaining step surfaces one at a time, emits a hard state after every transition, and receives only that emitted state at the next transition. The terminal answer is the terminal state itself. There is no language-model generation, answer prompt, hidden host execution, beam, retry, or fieldwise averaging.

Capability hypothesis

The large CRP1 localization delta (313/480 guarded versus 64/480 unguarded) should become a material answer delta only when the selected fault line owns downstream execution. A hard state bottleneck should also reveal whether symbolic failure came from free-form language replay or from the packet/source representation itself.

Runtime

complete problem + complete draft
  -> frozen SmolLM3 source features
  -> frozen CRP1 candidate packet and hard selection
  -> initial state-byte distribution from selected whole packet
  -> hard straight-through byte state
  -> tied recurrent transition over each remaining surface step
  -> hard byte state after every step
  -> exact terminal byte decoding

State vocabulary is deliberately small and domain-neutral: digits, lowercase letters, minus, comma, EOS, and PAD, in 24 fixed positions. Scalar values, ordered register pairs, and symbol tapes use the same state machine. Surface step spans come from the rendered draft. Exact program objects and state trajectories exist only in the supervisor and assessor; they are never passed to the candidate runtime.

The selected candidate controls both the initial packet and the replay start. NO_ERROR performs no transition. Candidate e > 0 starts immediately before step e and executes steps e..N. Selecting an earlier valid rollback point is allowed to recover; selecting after the true first error begins from a corrupted lineage and should fail.

Ordered experiment

1. Reconstruct and hash exact state trajectories for the existing CRP1 board. Validate final-state parity, state-code round trips, and surface-only operation extraction on every row.
2. Load the immutable guarded CRP1 checkpoint and freeze the full source plus packet. Train only RSM1 with gold packet selection. This is the oracle- selection component gate.
3. Evaluate the same checkpoint twice: forced gold packet and autonomous packet. Do not train a matched control unless the forced component gate passes.
4. On component pass, train the identical RSM1 from the same initialization on the immutable unguarded packet and run autonomous guarded/unguarded, reset, shift, and packet-swap evaluations.

Training uses three declared losses with equal weight: selected-boundary state decoding, full hard free-running replay, and one-step transition supervision from gold predecessor states. The one-step term teaches the tied transition algebra without changing autonomous inference; the free-running term is always active and receives only model-emitted hard states. No scheduled-sampling ratio or teacher-forcing curriculum is tunable after the gate begins.

The one frozen component run uses seed 2026080605, 1,600 optimizer updates, four board identities per microbatch, accumulation two, and therefore eight wrong/correct identity pairs (16 rendered traces) per update. This is 12,800 identity exposures, about 2.67 passes over the 4,800-row board. AdamW uses lr=3e-4, betas (0.9, 0.95), weight decay 0.01, unit gradient clipping, and one cosine decay to zero. State width is 256 with 24 hard byte slots, eight attention heads, and a four-times feed-forward expansion. A two-update smoke may test mechanics and memory only; it cannot alter this scientific budget.

Frozen component gate

All conditions are conjunctive:

• exact terminal state at least 432/480 under forced gold packet selection;
• at least 136/160 forced exact states in every family;
• exact free-running intermediate state trajectories at least 80% per family;
• zero invalid byte strings, overflow, host semantic calls, or changed frozen source/packet tensors; and
• finite loss, gradients, and hard-state feedback throughout.

Failure closes RSM1 before matched autonomous composition. No seed, width, state vocabulary, duration, teacher-forcing, loss, or family-specific repair is allowed.

Frozen autonomous promotion gate

If and only if the component gate passes:

• guarded exact terminal states at least 288/480 and 80/160 per family;
• guarded beats matched unguarded by at least 48 answers and by at least ten answers in every family;
• guarded preserves at least 432/480 correct no-op twins;
• reset, shifted selection, and packet swap each cost at least 48 answers;
• at least 80% of guarded autonomous answers have an exactly correct complete hard-state replay; and
• parameter, update, source-feature, packet, and transition-FLOP receipts match.

A pass establishes only a bounded model-owned packet-to-state replay mechanism. Natural verified traces remain a separate transfer gate.

Result

RSM1 fails the oracle-selection component gate and is closed. Job 743478 completed the frozen 1,600 updates in 614.601 seconds with 3,583,784 trainable parameters, 8,133,819 source tokens, 4,919,496 state-target tokens, 13,234.3 source tok/s, and 6.64GB peak allocated CUDA memory. Frozen source and packet tensors remain unchanged.

Forced OOD evaluation 743484 selects the gold packet on all 480 rows, but scores 0 exact selected-boundary states, 0 exact terminal states, and 0 exact complete trajectories. Only 2/2,662 active transitions are exact and 356 terminal strings are malformed. Every family scores 0/160. Development free-running transition exactness is 0.2315% and oracle one-step exactness is 0.4276%.

Emitted states collapse to frequent templates such as 1,, 1,,1, and vizzz. The failure is therefore upstream of recurrent composition: the selected continuous CRP1 packet never enters an exact decodable byte-state manifold. This gate rejects flat hard-byte serialization as that interface; it does not show that a correctly initialized structured executor cannot reason. No autonomous, unguarded, seed, width, duration, loss, or vocabulary repair is authorized.