R12 Sparse-Law Generator Factorization Preregistration

Trigger

The first direct set-attention completer (704748) is a clean negative:

• training transition accuracy: 91.4150%;
• development transition accuracy: 46.5000%;
• development complete maps: 0/60;
• development exact queries: 4/60; and
• direction-negated exact queries: 8/60.

The training pool already covered 184 unique fitting action maps while all 80 development action maps remained hash-disjoint. More rows from the same pool cannot test the missing generalization.

New Hypothesis

Unseen operators may generalize if represented as compositions of reusable learned permutation generators rather than decoded directly as independent table cells.

The treatment adds:

• 32 learned soft permutation generators for each cardinality;
• eight-step Sinkhorn normalization for every generator;
• an observation-set encoder that selects four generator stages; and
• differentiable matrix composition to produce the complete operator.

No generator has a predefined arithmetic, bitwise, Gray-code, or family meaning. The candidate does not enumerate the legal hypothesis union or call the exact compiler.

Frozen Canary

• board and map split: unchanged sparse-law V1;
• seed: 20260725;
• width: 128;
• recurrent byte layers: 2;
• generator count: 32;
• composition depth: 4;
• optimizer updates: 2,000;
• auxiliary fitting rows: 3,000;
• frozen fitting rows: 60;
• counterfactual direction rows: 120;
• batch size: 64;
• same-weight controls: direction negation, target shift, observation zero;
• candidate-time oracle/search/verifier calls: 0/0/0; and
• one H100, maximum one hour.

The exact held-out passive source order remains absent. Counterfactual rows use its relation words only in different source/target orders.

Decision Rule

This is a one-seed architecture canary, not promotion. Continue to the frozen five-seed gate only if it:

1. exceeds the direct attention baseline's 46.5% development transition accuracy;
2. produces at least one exact unseen development map;
3. beats every same-weight control in query exactness; and
4. retains zero train/development action-map overlap.

Failure closes this learned-generator formulation. It does not close sparse law induction generally.