DIVERGE-NTA1: Natural Arithmetic Transfer

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

Question

FTA1-AC1 is exact on a generated typed grammar. NTA1 asks the first external transfer question: does the unchanged finite-state compiler recognize and falsify arithmetic transactions copied from an independently answer-verified reasoning corpus when the synthetic Step N: prefix is absent?

Board

The only source is the frozen V10 verified corpus at SHA-256 2461d6f70b44a142854d56c24e1fb42d600065e5788a2c4e055ba47b12696549. The deterministic builder admits exactly 279 reasoning_gym_trace rows with two to five chained integer +, -, or * transactions, nonnegative explicit arguments, exact intermediate arithmetic, exact final answer, and CRT-safe values. It preserves each original equation substring, injects one deterministic wrong result, and recomputes the suffix from that corrupted state. The FTA1 checkpoint receives no update.

This is corpus-derived arithmetic, not broad natural language. It tests a real renderer/source shift while keeping the transaction algebra fixed.

Frozen gate

• operation >=90%, whole-role and valid-packet rates >=80%;

• =200/279 exact first-error selections, terminals, and trajectories;

• <=28 invalid rows;
• every error operation and depth 2--5 reaches >=60% terminals;
• trusting source or ignoring the conflict costs >=150 answers;
• initial packet swap and operation shift each cost >=120 answers.

The gate is zero-shot and one-pass. A pass authorizes one source-disjoint supervised natural-compiler gate; it does not authorize a general reasoning claim. A failure is localized before any natural-interface training.

Result

The builder emits exactly 279 rows / 963 transactions at board SHA-256 d71f1875ca967e2ff84cf0ff9e9940794643685c42a6298af90151b1a958d5b3. Depth counts are 78/60/78/63 for depths 2/3/4/5, and every wrong terminal differs from the verified answer.

Zero-shot operation transfer is perfect: 963/963 operation classes. Unconstrained role argmax nevertheless yields 0/963 valid packets and therefore zero autonomous selections or answers. Token audit makes the boundary precise:

• the source-free CLS position is predicted as LHS_A on all 963 segments;
• all 2,748 LHS bytes and all 2,939 RHS bytes are otherwise exact;
• 2,265/2,354 argument bytes are exact;
• the remaining 86 errors assign leading digits of long subtraction arguments to RHS_A, violating contiguous field structure.

Thus semantic operation recognition transfers, but independent token argmax does not preserve a valid finite-state field sequence after the renderer shift. Evaluation/gate SHA-256 values are c0c270778cb643316776e84b3512d7ef738d93272a20b9f57f4e8d4b9e4e4750 / ea86c3bde7a4c83b8333aafec78a5a6285c493501273d6b1db9750a5d0fb4e09.

The ordered successor is one zero-update constrained finite-state decoder that forces CLS/punctuation to OTHER and finds the highest-scoring legal LHS -> argument -> RHS field path. NTA1 is not rescored.