# 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.