DIVERGE-ATS1: Source-Sealed Algebraic Typed State

Status: closed after the one frozen component gate on 2026-08-06.

1. Decision boundary

RSM1 selected the gold CRP1 boundary on all 480 OOD rows but decoded zero exact initial states. Its flat 24-byte state then produced only 2/2,662 exact transitions. The failure is therefore not evidence against recurrent execution from a valid state; it rejects regeneration of an exact state from six continuous packet vectors into an untyped character tape.

ATS1 changes both parts of that interface without changing CRP1 localization:

Preserve source characters through a learned role-copy compiler, seal them into a typed algebraic packet, and compose transactions in that packet rather than regenerating intermediate text.

ATS1 is a bounded internal-machine experiment. Its residue arithmetic and symbol-tape kernels are architectural primitives, analogous to adding an ALU inside the model. It does not establish unrestricted mathematical reasoning, language understanding, or novelty.

2. Source boundary

For a selected CRP1 candidate e > 0, the compiler receives the unchanged bytes of draft step e and every later draft step. It does not receive the gold state, program object, answer, correct trace, or claimed semantic fields. It predicts one role for every source byte and one complete operation class per step. Selected bytes remain in source order and become the only values written to the packet. The claimed successor on each draft step is compiled for audit but is never used during replay.

The role vocabulary is fixed before training:

OTHER, LHS_A, LHS_B, LHS_SYMBOL,
RHS_A, RHS_B, RHS_SYMBOL, ARG1, ARG2

The operation vocabulary is the union of the three frozen CRP1 families: scalar add/subtract/multiply, five two-register transactions, and symbolic reverse/rotate/swap. No operation ID or argument is supplied at candidate inference. A malformed, noncontiguous, duplicated, or type-incompatible copy fails closed.

After compilation, source bytes, source hidden states, and claimed successors are deleted. Replay receives only the sealed typed state, operation IDs, and copied arguments.

3. Algebraic packet

Numeric values are represented by residues modulo (17, 19, 23, 29, 31). Their product is 6,678,671, giving an unambiguous signed interval much larger than the complete frozen board. Decimal source bytes are folded directly into each residue; no vocabulary-sized numeric class or autoregressive digit decoder exists.

Scalar and register transactions apply componentwise modular arithmetic. Symbolic values use a hard source-copied character tape plus length, and transactions are whole-tape permutations. One tied transaction layer is used at every replay depth. Intermediate states remain typed packets and are never converted to language.

The independent assessor reconstructs signed integers by CRT only for scoring. CRT reconstruction, correct program objects, and correct successors are absent from the candidate runtime.

4. Frozen data and budget

• CRP1 train/development/evaluation boards and hashes are unchanged.
• Train depth is 4--6; OOD depth is 7--9.
• Both correct and wrong train-step renderings may teach source roles, but only wrong OOD traces enter the forced replay gate.
• One seed: 2026080606.
• Byte width 128, two Transformer encoder layers, four heads, no pretrained language-model weights.
• At most 1,600 optimizer updates and 512 source steps per update.
• AdamW, peak learning rate 3e-4, fixed cosine schedule.
• No held renderer, OOD row, answer, or threshold enters optimization.

5. Frozen component gate

The CPU reference must first show 100% extensional parity on every state and transition in all 5,760 CRP1 identities.

Forced gold-boundary OOD promotion is conjunctive:

• complete operation class exact >=99%;
• complete copied LHS state exact >=95%;
• copied operation arguments exact >=99%;
• exact terminal typed state >=432/480;
• exact terminal typed state >=136/160 in every family;
• exact complete typed trajectory >=128/160 in every family;
• zero accepted malformed packets;
• claimed RHS deletion leaves every replay result unchanged;
• initial-packet swap and within-family operation shift each reduce terminal exactness by at least 240/480; and
• all source-role parameters are finite and the frozen CRP1 checkpoint is not modified.

If the component gate fails, close ATS1 without a seed, width, depth, role, modulus, optimizer, duration, or loss repair. Do not launch autonomous CRP1 composition.

6. Ordered autonomous gate

Only a component pass authorizes one autonomous composition with the immutable guarded CRP1 selector. On wrong traces it must beat the preserved guarded language path (213/480) by at least 27 exact answers and recover at least 80% of rows whose selected boundary is no later than the true first error. On correct twins it must preserve at least 432/480. Swapping sealed typed packets must cause the predicted large collapse.

A pass would establish a bounded source-sealed model-owned transaction mechanism. It would not by itself establish broad reasoning or justify long pretraining.

7. Pre-neural qualification

The independent CPU reference passes exact extensional parity before any neural result. Across 4,800 train, 480 development, and 480 evaluation identities it executes 24,044 / 2,368 / 3,854 transitions and reaches every terminal state exactly. The complete trajectory digest is 4b7e06df1f7cd9237e7309fb74e633d9fac2c7f60583692c140f5d8ab3ca5eeb. The audit report SHA-256 is eaadb1793c3a4e40d5c7e81ec4d3f4fce75bde19b727230d67284faaaf8b1314.

Local source-role, runtime, gate, Python compilation, Ruff, Bash syntax, and two-update CPU smoke checks pass. No H100 capability result exists yet.

8. Frozen result

Smoke 743544, scientific fit 743546, and corrected evaluator 743558 complete cleanly. The 443,156-parameter compiler trains for exactly 1,600 updates / 32,253,627 source bytes in 83.393 seconds on one H100, peaks at 592,967,168 allocated bytes, and reaches zero-like final role/operation loss. Its 96-row development probe is completely exact: 96 terminals, 96 complete trajectories, and all 389 transitions.

The untouched depth/value/length-shift gate is a bounded positive/negative:

Every accepted packet executes every remaining transition and terminal exactly. The algebraic state is therefore sufficient on this board and is causally used. The failure is solely compiler transfer: exact whole-span rates fall from 100% at trained lengths to 55.79% for four-character register fields, 60% for five-character scalar fields, and 35.84%/29.36% for eight-/nine-character symbolic tapes. The dominant error swaps LHS_SYMBOL and RHS_SYMBOL while preserving the copied surface, exposing reliance on absolute positions rather than delimiter-relative structure.

The frozen gate fails and autonomous CRP1 composition is not launched. ATS1 receives no seed, width, duration, role, modulus, optimizer, or loss repair. The source compiler is replaced by one position-free finite-state transducer; the algebraic packet, data, seed family, and evaluator remain protected.

Training report/checkpoint SHA-256 values are 914b24ca87962aa13f638c628df58e1332072250a06896267df5f64cad3bae14 / 3c4fbb93be0bbc16fcbd4d58480da4594b674c693925faf5dd564a9204ed715f. Evaluation/gate SHA-256 values are b7e3bf3d45b6b5b499e0a8d8085bc544a3e7cf0927b15db0cfb8e0a93108566b / 1cb1e321263c88549c0622df344c77e73604f92c5422a254db4131a8a564904a.