DIVERGE-NFE1 Natural Fault Evidence Result

Status: PASS on the one frozen run, 2026-08-06.

Question

Can a learned whole-mention interface compile source-bound numeric evidence from a dataset-disjoint natural arithmetic source and use that packet to refine the protected DIVERGE version space, without exposing raw source after sealing?

NFE1 is an interface/mechanism gate. It is not a public benchmark, continuation pretraining result, or claim of unrestricted reasoning.

Frozen inputs

• implementation commit: f9a70b7
• source corpus SHA-256: 2461d6f70b44a142854d56c24e1fb42d600065e5788a2c4e055ba47b12696549
• 2,179 deduplicated verified reasoning_gym_trace training equations: e05d05abb4fa01c4a38cd3126ec9e09887fcd1c8fcc291b23341c586a30fa7e9
• 96 source-disjoint augmented_gsm8k confirmation episodes, 222 transactions: 854395449c78eaf65e07d6e428336045e8604dcd9d4a6bced130def97d1f9858
• data report SHA-256: dc85f6b833d48313451f4f4af27543d7ed1cbf8c57a14f9d876a6db04d802c95
• unchanged FTA1 checkpoint SHA-256: 9321b78372d9926930d4de073d70e82c94e8360a69e09be695bab91b2e479f2d

The exact-overlap audit finds 109 eligible confirmation rows with depth counts 85/20/2/2. Selection retains all 24 depth-three-or-greater rows and the first 72 hash-sorted depth-two rows. The final board has depth counts 72/20/2/2 and operation counts 58 add, 88 subtract, and 76 multiply.

Learned interface

The only newly trained component is a 183,043-parameter, two-layer, bidirectional byte GRU with width 128 and no position embeddings. A lexical scanner proposes three complete signed-integer mentions. The model assigns a hard one-to-one LHS/ARGUMENT/RHS permutation over those complete mentions.

The frozen schedule is seed 2026080608, 1,000 AdamW updates, batch 256, learning rate 0.003 with cosine decay, and zero dropout. CPU training consumes 4,543,408 source bytes in 154.078 seconds. Training assignment/value accuracy is 2,179/2,179. Checkpoint SHA-256 is c7ef7b4c0dd0b3738a9356bded7d9aa6f1eaff08da24677197388f3474c68764; model-state SHA-256 is ad5923dc78ed5c4462b90ed8b90b86bd32e8a308cc170adc5c578ea6db0d41cb; training-report SHA-256 is 16350f099eebd4f21ad53277d78c7ed9b5af4562a0475b3abc155e2bce0857f8.

Confirmation result

The source-disjoint component gate is exact:

• learned whole-mention assignment: 222/222;
• all-three-operation support: 222/222;
• distinct immediate operation outcomes: 222/222;
• initially wrong FTA1 top operation: 221/222 transactions and 96/96 episodes.

The end-to-end source-sealed results are:

Full DIVERGE recovers 96/96 episodes whose initial top-1 assignment is wrong. Exact state-group execution matches independent assignment enumeration with and without evidence on all 96 episodes. Every depth and every operation slice is exact.

Causal and integrity controls

• shuffled evidence: 0/96;
• initial-state reset: 0/96;
• operand-semantic shift: 0/96;
• packet/query swap: 96/96 reject;
• post-seal source poison: 96/96 bit-invariant;
• wrong-source, wrong-step, wrong-mention, or wrong-value evidence accepted: zero;
• false commitments, malformed accepted packets, and overflow: zero.

Canonical complete-particle storage is 3,654,126 bytes versus 244,490 bytes for factorized packet/execution/evidence/query receipts, a 14.946x ratio. The equal-memory control funds one highest-ranked complete particle per episode. Factorized execution performs 2,610 logical applications through 666 unique state-group applications, a 3.919x sharing ratio. Peak surviving state groups after each evidence step is one.

Evaluation SHA-256 is ad77a3b2d6b32cf2ad10727a6e85cfbcbc811d06f4ab2ff93c62269f2b22eb7f.

Decision and boundary

NFE1 passes the intended boundary: learned, source-disjoint, whole-mention evidence packets can drive exact delayed version-space commitment without raw source access after sealing. This materially extends TFS1 beyond assessor- issued typed evidence.

The claim remains narrow. The lexical scanner still proposes numeric spans; the operation domain is three engineered scalar functions; FTA1 supplies the operation support; and the arithmetic verifier/executor is exact code. NFE1 does not establish general language reasoning or justify continuation pretraining. Freeze this result with no seed, width, duration, renderer, or loss variants. The next admissible boundary is one learned natural program/evidence compiler with variables, predicates, and noncommuting stateful updates, using the same source-sealed factorized runtime and explicit single-state/particle controls.