R12 S9 Occurrence-Quotient Relational Compiler Preregistration

Status: CPU representation admitted; neural source and board not yet frozen

Parent result: S8.1 rejected end to end at 514/2,048 exact graphs, with 514/514 exact execution conditional on graph validity

1. Target failure

S8.1 is not failing after compilation. Its valid, exact-graph, exact-state, and exact-answer sets are the same 514 development rows. The compiler instead loses complete rosters, state permutations, card witnesses, or repeated-name bindings under unseen renderers and nonce vocabularies. Its architecture independently labels BPE tokens, although the source repeatedly refers to the same entity, position, operation, and event tag.

S9 tests whether identity before semantics is a better factorization:

1. propose nonempty surface islands from source tokens;
2. quotient byte-identical proposed islands into occurrence classes;
3. classify local relation types and argument slots using both local context and the shared class representation;
4. emit class-level roster, state, card, event, entry, next/nil, and query relations; and
5. compile those relations into the unchanged S8 graph and execute through the confirmed S7/S8 runtime.

No arithmetic or recurrent component is widened in this phase.

2. Model and host ownership

Model-owned

• each selected island's start and end;
• whether an island participates in the graph;
• its local relation kind and argument slot;
• all roster/state/card/event/entry/query records;
• every event tag, operation, entity, next link, and nil decision.

Architectural

• enumeration of bounded contiguous token-span proposals without a candidate- name dictionary;
• exact byte equality over spans selected by the model;
• quotient class renaming and relation-storage invariance;
• strict categorical relation/graph validation;
• the already disclosed S8 linked traversal, node-count safety bound, S7 cyclic compiler, and pop-insert transition.

Forbidden at inference

• gold spans, names, or candidate-name dictionaries;
• board spans, entities, positions, cards, nodes, execution_tags, initial_state, final_state, answer, depth, or source event order;
• host alias resolution, graph repair, retry/search, state transition, or answer selection.

The host may tokenize source, enumerate all spans up to the preregistered maximum width, compare the exact bytes of model-selected spans, validate the emitted relation graph, and invoke the frozen runtime once.

3. CPU theorem and result

Source seed 792451398761220486 runs the representation over all 2,048 already- closed S8.1 development sources. Frozen labeled spans stand in only for future model emissions; the compiler function receives source and emitted spans, not the row's structured graph fields. Expected graph/state/answer are scorer-only.

Report SHA-256: f77dce825314cc38b0630cd574b450284c00fc8afa23dc0ab39cfc5be8ef2c94

All 13 frozen CPU gates pass. This proves representational sufficiency and causal dependence only. It does not show that Shohin can emit the quotient.

4. Neural architecture freeze requirements

Before any board seed is drawn, source and tests must freeze:

• a frozen Shohin residual extractor;
• a trainable contextual encoder;
• a bounded span proposal scorer that cannot inspect board span labels at inference;
• exact source-byte class grouping only after model selection;
• a class-aware relation/slot decoder;
• a shuffled-relation control with equal architecture and updates;
• the complete parameter count below 150,000,000;
• fail-fast checkpoint/base/tokenizer/board hashes;
• an evaluator that records selected-span, class, relation, graph, state, answer, depth, renderer, and causal-control scores; and
• access counters fixed at zero before the board and incremented once only by the sole development evaluation.

Teacher forcing may label span proposals and relation slots in training. It may not provide final state, answer, recurrent trace, or development/confirmation relation records. Development and confirmation names, renderers, and laws must remain disjoint from training.

5. Fresh-board controls

The future board must preserve S8.1's counts and scientific exclusions unless a new source commit preregisters a smaller infrastructure canary:

• 48,000 graph-field-only training rows;
• 2,048 development rows;
• 2,048 sealed-confirmation rows;
• 23 successor cells and three zero anchors only for the S7 generator;
• depths one through eight in training and three through eight in scoring;
• split-disjoint names, laws, and renderer families;
• zero exact prompt, 13-gram, and split-name overlap;
• no train final states or answers; and
• no development or confirmation access before source, assessor, thresholds, and seeds are frozen.

Required controls are gold quotient, gold graph, S8.1 token-role parser, a same-parameter span model with equality-class messages disabled, shuffled relation labels, class-ID reindex, relation-storage reindex, operation-nonce rotation, split-reference, merged-class, swapped-witness, reversed-link, state-reset, and early-nil interventions.

6. Immutable development gates

The sole development read advances S9 only if every gate passes:

1. selected-span F1 at least 98%;
2. class membership exact at least 95%;
3. complete relation tuple exact at least 90%;
4. valid graph at least 90%;
5. exact graph at least 85%;
6. recurrent state at least 80%;
7. answer at least 85%;
8. every depth-three-through-eight state at least 70%;
9. at least +20 percentage points exact graph over frozen S8.1's 25.098%;
10. at least +5 points exact graph over the same-parameter no-class-message control;
11. shuffled relations below 10% exact graph;
12. class and relation-storage reindexing bit-identical on every valid graph;
13. operation nonce recoding bit-identical on every originally valid graph;
14. swapped witnesses, reversed links, reset, and early nil each cause their preregistered causal drop;
15. split/merge corruptions are rejected rather than repaired;
16. complete system below 150,000,000 parameters; and
17. one development access and zero confirmation accesses.

Failure closes this architecture/version. Passing authorizes one separately frozen confirmation evaluator with unchanged weights. It does not by itself establish alias resolution, unconstrained language grounding, arbitrary algebra, unbounded planning, or broad native reasoning.

7. Honest free-word boundary

Exact occurrence quotienting helps only when references share exact surface bytes. The free-word control makes every occurrence unique and correctly causes the current compiler to abstain on 2,048/2,048 cases. S9 must never describe this as general coreference. A future alias-capable phase would need a distinct, causally tested learned equivalence relation and a negative set containing similar-but-nonidentical distractors.