R12 Gate Vacuity Correction and WGRQ Preregistration

Status: gate correction adopted. Independent audit rejects WGRQ as a new state, algorithm, or oracle advantage. The narrower Stage-A neural optimization falsifier is frozen separately in R12_WGRQ_CPU_PREREG.md; this document alone authorizes no implementation or job.

1. Why the gate changed

The first R12 wording accidentally made acceptance impossible. Every bounded finite-precision classical mechanism has a finite acyclic unrolling, while the old exact-collapse gate treated successful unrolling as rejection evidence. Therefore every realizable candidate failed before its resource claim could be examined.

There was a second tautology. If a comparator class contains the candidate, then the best member of that class cannot be asymptotically worse than the candidate under the same resource measure. A universal recurrent control that is explicitly allowed to execute the candidate's identical algorithm is a correct expressivity ceiling but cannot test whether a training protocol finds that algorithm more reliably or with different data/compute.

The corrected rule is narrow:

A reduction rejects a novelty or resource claim only when it preserves behavior, information access, and the preregistered resource vector within constant or polylogarithmic overhead.

The vector is

(parameters, retained bits, precision, source bytes, training examples,
 oracle calls, training FLOPs, inference FLOPs, sequential depth,
 external memory, external execution).

Finite unrolling still blocks ontological claims. Known machinery still blocks primitive-novelty claims. Neither is an automatic veto of a bounded training- protocol experiment.

2. Absolute no-go results retained

The correction does not weaken:

• residual-state information lower bounds;
• arbitrary late-query information conservation;
• hidden-coordinate nonidentifiability under conjugacy;
• finite off-support and delayed-sabotage constructions;
• passive rare-witness/sample lower bounds;
• exact accounting of precision, caches, source access, and external execution;
• the closed-deliberation theorem when no new target information enters.

OOD correctness must still receive at least one honest source: a restrictive hypothesis class, distinguishing data/interventions, or a bounded distributional claim. Hiding that source is claim-killing.

3. Candidate training protocol: WGRQ

Witness-Guided Residual Quotienting manipulates supervision and information access, not model-module vocabulary.

For a history h, an encoder commits to a query-blind state z(h). After the commit:

1. source tokens and their KV cache are deleted;
2. histories with equal future behavior receive an interchange/merge target;
3. suspected false merges receive a training-only distinguishing continuation and late query;
4. transition closure requires equivalent states to remain equivalent after every shared event;
5. counterfactual state swaps test whether consumers use causal state rather than lexical identity;
6. one committed state must answer many late queries and accept appended continuations without source recovery;
7. no simulator, witness generator, source retrieval, or verifier is available at inference.

The manipulated variable is future-equivalence supervision under a hard source barrier. Recurrence, state width, decoder, token budget, and inference compute are held identical in the principal control.

4. Capability and resource hypothesis

Use one protocol and one hyperparameter set on two unrelated exact families:

• noncommutative adjacent-transposition composition with late image queries;
• visible-coordinate reversible Boolean actions with late bit/readout queries.

The bounded hypothesis is:

At matched parameters, retained bits, training examples, training/inference FLOPs, sequential depth, and target-oracle calls, witness-guided quotient supervision increases exact source-free length/scale extrapolation by at least five confidence-separated percentage points over identical recurrent controls that lack quotient supervision.

This is not a claim of sample information creation. Training-only witnesses are oracle calls and must be counted. The test asks whether spending that fixed oracle budget on distinguishing residual collisions is more effective than random or answer-only supervision.

5. Required controls

• answer/visible-trace SFT with identical training-token and target-call budget;
• identical tied-recurrent architecture without quotient losses;
• identical architecture with random rather than adversarial witnesses;
• identical architecture without source deletion;
• a PSR/OOM, weighted-automaton, or partition-refinement control with matched retained state and every target call counted;
• exact symbolic realization as a ceiling, not a novelty comparator.

Every neural arm starts from identical initialization and sees an immutable, hash-bound training generation. No arm may see confirmation examples.

6. Frozen CPU falsifier requirements

Before implementation, an independent audit must freeze the exact data, architecture, optimizer, seeds, resource ledger, and decision rule. The minimum board then requires:

• exhaustive no-collision residual checks on the smallest scales;
• randomized symbol relabelings so lexical labels cannot identify state;
• train on short compositions and evaluate at at least eight times train length;
• unseen state scale as well as unseen length;
• 32 late queries and appended continuations from one source-deleted state;
• equivalent-state interchange and non-equivalent-state separation;
• exact target-call accounting for witness, random-witness, and control arms;
• at least 95% exact candidate accuracy and a confidence-separated gain of at least five points over every matched neural control on both families.

One failed family, residual collision, source/KV leak, hidden solver path, or resource mismatch rejects the protocol. A finite pass permits an isolated Shohin-scale design review; it does not establish asymptotic reasoning.

7. Allowed claim if every gate passes

WGRQ is a tiny-model training protocol that learns reusable query-blind causal states and improves source-free compositional extrapolation at matched state, compute, data, and oracle budgets on two frozen exact families.

It is not a new computational primitive, a proof of general intelligence, compression below causal entropy, or a universal context solution.

8. Independent audit verdict

The original two-family draft is no-go as written:

• adjacent permutations and fully visible Boolean coordinates both have immediate distinguishing queries, so they do not test nonempty witness discovery;
• equal oracle-call counts do not equalize returned witness identities, response bits, adaptive rounds, or teacher search compute;
• whenever quotient labels are derived from ordinary public answers, a fair active answer-only learner can replay the identical transcript and derive the identical labels;
• residual merging is automata minimization/bisimulation, distinguishing suffixes are active automata learning/CEGIS, and query-blind future state is PSR/OOM machinery;
• the current flat Shohin SFT corpus lacks certified semantic states and cannot support a residual-equivalence language claim.

R12_ACTIVE_WITNESS_ALLOCATION_NO_GO.md freezes the active-answer-only simulation theorem. R12_CANONICAL_RESIDUAL_NAMING_CONTROL.md defines the symbolic ceiling. R12_CERTIFIED_LANGUAGE_BRIDGE_BOUNDARY.md defines the later language barrier.

The only surviving empirical question is whether a behavioral relational loss optimizes an information-identical recurrent learner better than favorable controls under hard source deletion. R12_WGRQ_CPU_PREREG.md replaces the two immediate-readout families with a delayed-witness edge-parity ring and freezes that bounded falsifier. A pass would not restore any rejected novelty claim.