Research construction: eight-query private native shear batch (no new kappa)

[thakrarsagar]

Change and scope

Recursive-interface research construction with a scoped finite optimum. No new kappa.

Batch four DATA targets and five immutable sources through one arbitrary-dirty private row using PR521's native ADDRESS query. For the explicit rank-three incidence matrix, sharing dirt correction reduces the best separately completed PR677 rank-factor schedule from 12 recursive queries and 36 XOR scans to 8 queries and 30 scans. The eight queries include 48 ordered-affine events and all recovery children. No DATA row is queried, copied or cleared.

The package supplies the literal 38-event schedule, its arbitrary-array identity, a complete typed cost recurrence, nine source pins and exact verification. The eight-query lower bound applies only to the stated single-level excursion class. All 5,376 minimum-query schedules in that class are exhausted; 232 attain 30 XOR scans. A second enumeration through target-column bases reproduces the full histogram. This is not a general query lower bound or an admitted supplier.

Only six files under research/native-shear-batch/ are added. Exact base: bbc600db2fc15007b7c914f4f2b2ed55fa909c87. OS-random assignment seed: 52. The selected PR942 result and upstream/ are unchanged.

Reproduce and validation

python3 -I -B research/native-shear-batch/verify.py

Expected:

PASS_NATIVE_SHEAR_BATCH schedules=5376 queries=12->8 xor_scans=36->30 columns=7290 negative_controls=8 no_new_kappa

Passed on macOS arm64 with Python 3.14.8, standard library only:

• Exact Laurent-polynomial endpoint and inverse; rational forward/inverse ADDRESS lowering.
• All 7,290 input columns on the full 729-address domain, including arbitrary private dirt; complete forward and reverse replay.
• Direct-map/literal-lowering agreement on every order-three and order-five ADDRESS, including spectators.
• Eight algebraic/admission/invoice controls, a paid neutral-pair control, and four actual certificate corruption controls.
• Normal, isolated optimized and two-file relocated execution; all nine pinned Git source hashes.
• make selected-record-check, all 17 selected-record tests, and staged whitespace/scope checks.

No repository-wide make verify, cold supplier reconstruction, hosted CI or Lean build is claimed. These finite replays are not a formal proof of the full multiplication theorem. Supplier placement, permission to retain the private batch state, complete row/route admission, all-size compilation, realization, hosting, tape and analytic transfer remain open. The recurrence goes from this batch interface to an ordinary interchange child; it is not a self-recursion proving an exponent.

Predecessors and coordination

Credit Karl Appel / @applecrusher's #521 native lowering, @commdata2338's #677 restored shear contracts, @CubeJerry's #889 common-factor dirty correction sharing, and the inherited upstream stream contracts. No priority is claimed for compute/uncompute or dirty correction sharing. #938 audits a different star-word language. Concurrent #982 borrows an output instead of retaining a dedicated private row, a different scratch/query contract. #974's optimistic selected-supplier budget is not used to claim a bound here.

There was no pinned sprint issue, so CLAIM.md records the local claim, three candidate tasks and completed result. The immediate pre-submission open-PR refresh reached #989; no duplicate native private-only affine-state census was found. Upstream main advanced to 55645f9d4d806d67875c1c8b9840b0b039ece22e with the same selected kappa and no package-path overlap.

Contributed by Sagar Thakrar / @thakrarsagar, with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0; no independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at 1c3ddf6bbbe1d8f0227de6726bb8273b2cb03711.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Native multi-source shear batching for one fixed matrix with dirty restoration and complete typed costs; not a DATA-query supplier.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.