Research012 — an equivariant external policy can still be wrong¶

New bounded follow-up after verified010/011: test whether imposing exact D4 output symmetry by group aggregation replaces the correctness supplied by canonicalization. It does not. This is four frozen offline postprocessing policies, not training, a deployed replacement, or learned network equivariance.

Predeclared algorithms and source¶

manifest012.json / root experiment-study012.json fixes all four policies before aggregate outcomes. All8 D4 elements are equally weighted, including stabilizer repetitions. The source is the immutable010 trace SHA-256 7d0e07c6e406925530a6b3feb1bf9422c536a9c168786c9bb5eaafef7679aad5. This reuses4,520 measured direct network inputs expanded to5,016 canonical-orbit observations; there are zero new neural forwards. All boards were already trained/audited.

• Mean: exact sum of eight aligned integer logits is nonnegative. This tests the exact rational mean sign without rounding; no tiny negative mean can become a zero member.
• Intersection: all8 signs are nonnegative.
• Union: at least1 sign is nonnegative.
• Vote-at-least-half: at least4/8 signs are nonnegative; ties are included by preregistration.

The actual external legal mask and original raw-coordinate priority ebdfhcgia still apply. Nonnegative logits encode membership, not calibrated probabilities. Mean aggregation is a declared diagnostic algorithm, not a confidence average. It uses exact int64 host sums; no deployable accumulator/RAM/speed claim is made.

Exact unique-raw outcomes¶

The fixed canonicalizing wrapper remains4,520/4,520 exact sets and correct raw ties. Every aggregate above is exactly full-set equivariant, exhaustively checked on36,160 raw-board/transform observations per policy. Symmetry is therefore insufficient for the complete tactical-policy contract. Equivariance is enforced by external averaging/logic; it was not learned by the network.

Canonical counts are separate, not multiplied by8¶

Exact constraints and controls¶

The eight branches include a canonicalized orientation with the correct full set. Consequently intersection has no false legal members, but can remove every valid member; union omits no optimal members, but can add nonoptimal members that the raw-coordinate tie later selects. Both theoretical constraints pass.

Order reversal and duplicating all8 branches to16 leave every policy unchanged (votes threshold scales to8/16). The single canonical branch recovers the baseline627 full sets. Independent audit recomputes each policy from all8 measured branches for every4,520 raw input instead of trusting canonical expansion, independently checks minimax/metrics and allD4 set equalities.

Chosen moves are freshly tied in actual raw coordinates. Transforming an old chosen move is not used as a substitute. The selected-move map itself need not be equivariant because fixed priority is coordinate dependent.

Actual predeclared example¶

First canonical ID with a mean full-set disagreement: 2. All branch logits, legal masks, exact sum/min/max/vote values and four full sets are retained in examples012.json; the figure is not a synthetic illustration. The separately declared first nonoptimal nonempty mean-choice example is retained if it exists; no panel is expanded to hunt for failures.

Limits and stopping decision¶

No model bytes, stages, routes, gates or expert computations are changed. Original frozen source SHA-256 remains fe180f8a931f9d92d8aa39da337bc819d0dbe4e6d971edcba00324fbc18a91c1. Normally inactive expert observations remain unobserved in010/011; this study only consumes final measured logits. Neural stage restoration is not applicable because no neural parameter/stage is edited.

The result neither proves that every possible ensemble fails nor licenses a broader post-hoc ensemble search. It evaluates exactly the four declared policies on an already trained/audited domain. Their perfect imposed symmetry does not establish hidden-layer invariance, strategic component identities or new-domain generalization. It makes no target speed/RAM claim and does not run on or alter the accepted game.

This is the one optional follow-up. Stop here: no study013, larger aggregation panel, relaxed matching or retraining. See FINAL-STUDY-012.json, root verification/source bundle and README-REPRODUCTION012.md. Research010/011, all older evidence and accepted application010 remain untouched.