Scoped negative: PR589 A-triple fixed single-move options (210 cases)

research/bit589-shared-register-triple-seed05/LICENSE

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research/bit589-shared-register-triple-seed05/PROOF.md

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+# Exact finite census on a fixed single-move-option product
+
+## Claim and scope
+
+For the seed-selected A-section triple `(927, 928, 930)` in the pinned
+PR589 `v=111`, `R=439` word, let `D_i` denote the frozen `(slot, frame)`
+choices certified for moving operation `i` **individually** by the PR1345
+atlas on the unchanged word. Every tuple in `D_927 x D_928 x D_930`,
+under the verifier's specified deterministic reinsertion, either fails the
+full chain-nesting replay, preserves the paid profile, or strictly raises
+its exact moment cost. There are no improvements or unresolved tuples in
+**this fixed product**. No completeness for jointly enabled frames or
+commutation-dependent placements is asserted.
+
+## Fixed inputs
+
+`SOURCES.json` pins the selected-result record, review, assembly, selected word
+bytes, bit-cost record and moment-cost implementation to base commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. It separately pins the exact
+PR1345 atlas source and the relevant predecessor heads. `verify.py` checks both
+Git blob IDs and SHA-256 hashes before using these inputs. It also checks that
+the selected certificate still names
+`836330098538459/500000000000000000` and that PR589's bit saving is exactly
+`1733427039589844234749/1000000000000000000000000`.
+
+The vendored atlas is loaded only through the definitions needed for legal
+options and exact scoring. The verifier stops before executing PR1345's own
+single/pair census, so this package independently applies those definitions to
+the new triple.
+
+## Domain construction
+
+Let each A operation's legal options be its exact `(slot, frame)` pairs from
+the pinned atlas. Form the graph on movable A operations, joining operations
+whose source/target register sets intersect. Keep components whose product of
+individual option counts exceeds 200,000. Within that large component, collect
+same-register triples with option-product at most 5,000 and with more than one
+distinct legal frame for each member. Sort by `(option product, operation
+indices)`. This gives 200 tuples; seed `5 mod 200` selects index 5,
+`(927, 928, 930)`.
+
+The selected operations all write register 325 at frame 282, from sources
+256, 442 and 392. Their frozen **single-move** option lists contain 7, 6
+and 5 entries, so the Cartesian product has exactly 210 tuples. This is
+complete enumeration of the specified product, not a proof that the product
+contains every globally legal triple placement. In particular, the atlas
+single-move lists need not include choices enabled only after another move,
+and alternative commutations/reinsertions are outside this finite model.
+No random sampling is used within the selected product.
+
+## Classification and pricing
+
+For each Cartesian-product tuple, the verifier reinserts the three selected
+A operations according to the fixed key `(slot - 0.5, original_index)`,
+while all other A operations retain their original index order; the C section
+is then rebuilt. The pinned PR1345 chain scorer checks nesting for precisely
+this joint reconstruction. If it returns no score, the reconstructed word
+is also replayed and required to fail the full map check. Otherwise, the
+candidate preserves the selected gates and operands, and the exact paid
+profile is computed by replaying all 661 registers. This reconstruction
+does not enumerate other commutation schedules with potentially different
+legal frame options.
+
+It then prices the profile difference against the original using the pinned
+rank-cost intervals. The independently aggregated profile interval must be
+contained in the full-chain scorer's interval. Equal profiles have exact zero
+direct delta. For changed profiles, the reported interval is strictly positive;
+all 64 such assignments have the same changed profile. This establishes a
+negative result only over the 210 assignments in the stated finite domain.
+
+The full census is: 46 nesting-incompatible assignments, 100 valid assignments
+with the baseline profile, and 64 valid assignments with a strictly higher
+profile cost. There are zero improvements and zero unresolved assignments.
+
+## Controls and limitations
+
+The replay checks an all-home identity, rejects a changed source operand, and
+rejects a word with the selected A ADD omitted. These controls check the input
+identity and coverage paths used by this finite verifier; they do not turn the
+census into a formal proof of all PR589 transports.
+
+Jointly enabled placements not present in the fixed single-move option
+lists, alternative admissible gate commutations/reinsertions, other triples,
+four-way changes, cross-section triples, structural changes, and other
+supplier words remain open. No optimum theorem,
+new supplier admission, or new `kappa` is claimed. Inherited PR589/compiler,
+realization, hosting, precision/tape, and analytic assumptions are unchanged.