DIVERGE-OQB1: Occurrence-Quotient Register Bus

Status: confirmed across development and five fixed confirmation seeds

Parents: confirmed NCP1 command owner, confirmed EAL2 temporal owner, closed CAB1 attribution

Capability hypothesis

CAB1's learned source-to-name similarity did not discover a robust equality operation. Its terminal accuracy was flat across recurrent depth and followed episode-law commits, while an absent-name control exploited shared generator suffixes. OQB1 changes the computational primitive rather than retraining that metric:

Exact repetition identity is an architectural quotient, while the neural owner learns which anonymous occurrence class supplies each semantic value role.

The runtime receives one declared two-name episode table. A generic exact surface-occurrence operator replaces every whole-word occurrence with an anonymous table-position marker. Raw names are then deleted. One shared neural owner reads only the anonymized source and predicts the slot attached to each numeric observation and late query. The already-qualified EAL2 owner predicts BEFORE versus AFTER, NCP1 predicts the operation program, and the existing table-relative recurrent executor consumes one coherent packet.

This is structurally different from CAB1: there is no register-name encoder, learned name-similarity projection, source-to-candidate dot product, or decoy name table. Exact surface equality is disclosed as an architectural primitive, not claimed as learned semantics. Numeric mention boundaries, the declared two-name table, exact bounded law support, Z/97 arithmetic, and the modular executor remain engineered limitations.

Frozen architecture

The trainable owner has 200,069 parameters:

1. a shared 128-wide two-layer bidirectional byte GRU;
2. an MLP that assigns each exact numeric mention to anonymous slot 0 or 1;
3. token-level late-query evidence aggregated by logsumexp; and
4. one shared state across evidence, initial-state, and query sources.

The occurrence quotient itself is deterministic and permutation equivariant. Reversing the declared table reverses every anonymous marker. It never assigns a semantic role, associates a numeric value, scans for BEFORE/AFTER language, or inspects assessor targets. Missing declared occurrences fail closed.

Frozen data and optimization

• training seed: 2026080831;
• development seed: 2026080832;
• conditional confirmation seeds: 2026080833--2026080837;
• 100,000 training records;
• 256 episodes per development/confirmation board;
• 24 evidence transitions, 16 noncommuting programs at depths 12--32, and 32 late queries per episode;
• opaque training names are independent SHA-derived lowercase words with no serial/index suffix shared across namespaces;
• final sources, names, and identities must be disjoint from the complete transitive CAB1 lineage and regenerate byte-for-byte.

Treatment and broken-quotient control start from the same initialization and receive the same sampled records, targets, optimizer, and charged examples:

• 1,000 AdamW updates;
• batch 128;
• learning rate 0.001;
• weight decay 1e-4; and
• unweighted evidence, initial, and query cross-entropies.

The treatment uses one coherent occurrence class for every repetition of a declared name. The control independently hashes each occurrence into an anonymous marker before the same neural owner sees it; the true table-position targets are unchanged. Raw names are deleted in both arms, so the control cannot recover identity from lexical suffixes.

Frozen development arms

1. treatment on ordinary names and table;
2. unseen consistent renaming;
3. coherent whole-table reindexing as a positive equivariance arm;
4. cross-owner reindexing of evidence only;
5. declared-name source scrub, which must fail closed;
6. inference-time independent occurrence break; and
7. the independently trained broken-quotient model on coherent input.

Confirmation data are materialized and sealed before development scoring. No confirmation file may open unless the unchanged development report passes.

Conjunctive gate

OQB1 passes only if all conditions hold:

• qualified EAL2/NCP1 hashes and reports match and their weights remain bit-identical;
• NCP1 program exactness is at least 99%, with at least 95% at every depth;
• treatment, unseen rename, and coherent reindexing each reach at least 99% evidence, temporal, complete-role, initial, query, law-commit, terminal-state, and answer exactness;
• each positive arm has at least 95% terminal-state exactness at every depth;
• cross-owner reindexing is at most 5% state and 55% answer exactness;
• source scrub is at most 1% on each component, state, and answer measure;
• occurrence break and the broken-quotient model are each at most 30% evidence, 35% initial, 55% query, 20% state, and 35% answer exactness;
• treatment/control schedules, data, parameters, and initialization match;
• runtime source contains the declared occurrence quotient, no local semantic register scanner, and no learned raw-name similarity; and
• typed initial states, typed programs, and typed query indices remain absent from candidate-visible boards.

Every one of the five fixed confirmation boards must independently pass. A development miss closes this exact mechanism without width, duration, seed, threshold, renderer, loss, marker, or quotient variants. One read-only attribution may identify the failed owner but cannot rescue the result.

Decision boundary

A confirmed pass qualifies one episode-local discrete identity bus inside the controlled EAL2/NCP1 system. It does not establish alias/coreference reasoning, open-domain language understanding, or public benchmark capability. It permits composition with the already-confirmed model-owned executor and the next single scaffold-removal gate. A failure closes exact-occurrence quotient plus this neural semantic attachment owner.

Immutable result

OQB1 passes every frozen gate. Final data data_2ead185_r1 contains 100,000 training records, 256 development episodes, and five 256-episode confirmation boards. It independently regenerates byte-for-byte and has zero source, name, or identity overlap against the transitive CAB1 lineage. Data-report and training SHA-256 values are a11e062cb41f81096de32f164a181928908a4750b6c9a8bd0d924f4cec6c5e94 and 9622737f0c36ae80bd5f3acdf0e1f57e5ef79fa6a918ef58bb75c6411d3eb4fb. The immutable Newton runtime has SHA256SUMS SHA-256 9b2d6112b09b97e8a9446de3dde60f172cf13531d1c4b0b9b618b4cd111981e8.

Matched jobs 744843/744844 complete all 1,000 updates from identical initialization. Treatment fits 2048/2048 fixed rows in 82.29 seconds. The broken-quotient control fits only 17/2048 = 0.8301%; its final loss remains 2.0835, approximately three independent binary cross-entropies. Treatment and control checkpoint SHA-256 values are 8c4e9b83230e75edbc146d1aa43375d14202783057eeb22bbb8ec6c5b60c8ab7 and ec353abfd212e6a166504dc258b3a9e96095b05cc4c2f32517da43ae57042baa.

Development job 744845 passes every condition. NCP1 programs, evidence, temporal role, complete role, initial state, late query, law commit, terminal state, late answer, and every depth are exactly 100% for treatment, unseen renaming, and coherent table reindexing. Source scrub and inference-time occurrence break produce zero committed laws, states, and answers. The independently trained broken model also produces zero states/answers. The evidence-only basis break reaches 3/4096 = 0.0732% states and 76/8192 = 0.9277% answers. Development report SHA-256 is d78e1622746a951cb7a82207986aa5c8a8ef93e16587976f759eb183287c87e9.

Confirmation jobs 744846--744850 each pass unchanged. Across all five seeds, treatment, unseen renaming, and coherent reindexing are each 20,480/20,480 terminal states and 40,960/40,960 late answers. Source scrub, occurrence break, and the broken model are each 0/20,480 states and 0/40,960 answers. Cross-owner reindexing is 9/20,480 states and 453/40,960 answers. Aggregate SHA-256 is da5f88071ffd75ec64a3637d5657592cd9c494566d4b57212f1b762163f344a3.

The qualified claim remains narrow but useful: exact repeated surface identity is now a stable discrete address primitive, and the neural owner learns renderer-general semantic attachment into that anonymous basis. OQB1 does not learn alias/coreference equivalence. The next scaffold-removal target is the exact numeric-span carrier; qualified OQB1/EAL2/NCP1 weights remain immutable.