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

research/native-shear-batch/CERTIFICATE.json

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+{
+  "matrix_rows": [5, 30, 11, 14],
+  "census": {
+    "sample_sets": 224,
+    "ordered_schedules": 5376,
+    "xor_histogram": {"30": 232, "32": 924, "34": 1820, "36": 1640, "38": 624, "40": 124, "42": 12},
+    "best": {
+      "xor_scans": 30,
+      "source_states": [0, 5, 11, 27],
+      "target_reads": [5, 11, 12, 2],
+      "source_scans": 10,
+      "private_read_scans": 8,
+      "direct_scans": 12,
+      "queries": 8,
+      "affine_events": 48
+    },
+    "separate": {
+      "bases": 28,
+      "xor_scans": 36,
+      "basis": [5, 14, 16],
+      "target_reads": [5, 14, 2],
+      "queries": 12,
+      "affine_events": 72
+    }
+  },
+  "program": [
+    ["query", 9, 1],
+    ["xor", 0, 9],
+    ["xor", 2, 9],
+    ["query", 9, -1],
+    ["xor", 9, 4],
+    ["xor", 9, 6],
+    ["query", 9, 1],
+    ["xor", 0, 9],
+    ["xor", 1, 9],
+    ["xor", 3, 9],
+    ["query", 9, -1],
+    ["xor", 9, 5],
+    ["xor", 9, 6],
+    ["xor", 9, 7],
+    ["query", 9, 1],
+    ["xor", 2, 9],
+    ["xor", 3, 9],
+    ["query", 9, -1],
+    ["xor", 9, 8],
+    ["query", 9, 1],
+    ["xor", 1, 9],
+    ["query", 9, -1],
+    ["xor", 9, 4],
+    ["xor", 9, 5],
+    ["xor", 9, 7],
+    ["xor", 9, 8],
+    ["xor", 0, 4],
+    ["xor", 0, 6],
+    ["xor", 1, 5],
+    ["xor", 1, 6],
+    ["xor", 1, 7],
+    ["xor", 1, 8],
+    ["xor", 2, 4],
+    ["xor", 2, 5],
+    ["xor", 2, 7],
+    ["xor", 3, 5],
+    ["xor", 3, 6],
+    ["xor", 3, 7]
+  ]
+}

research/native-shear-batch/CLAIM.md

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+# Sprint claim
+
+- Track: recursive interfaces, OS-random assignment seed 52, drawn with Python `secrets.randbelow(100)`.
+- Exact base: `bbc600db2fc15007b7c914f4f2b2ed55fa909c87`.
+- Started: 2026-10-13 15:38 UTC. Planned finish: 16:18 UTC. Verification and handoff reserved from 16:08 UTC.
+- Object: PR #677's private-only restored DATA shear for PR #521's native BIT query. Batch a rank-three matrix of shears through one arbitrary-dirty private row.
+- Hypothesis: share dirty-offset correction across four query excursions, reducing twelve rank-factored recursive queries to eight. Enumerate affine exposure bases and source transitions to price every XOR scan.
+- Deliverable: exact schedule, written identity and complete local recurrence, source pins, reproducible checker, meaningful rejection controls, and an exhaustive finite schedule-cost certificate. No new kappa or supplier admission claim.
+- Three candidates considered: batch PR #677's private-only DATA boundaries; extend PR #822's dirty connector reuse; extend PR #889's common-factor output batching. The latter two already have dedicated constructions and broader follow-ups. The selected task studies a fixed native ADDRESS query and explicitly prices its lowering and VALUE scans.
+- Overlap checked: all 703 open PRs, followed by all-state metadata through #976; PRs #677, #822, #889, #938, #943, #951 and #974. PR #889 is credited for related common-factor dirty correction sharing. PR #974 studies optimistic selected-profile budgets, a different question. No pinned sprint coordination issue exists, so this local claim is used.
+- Selected result at base: conditional kappa `1661960547713947/1000000000000000000`, PR #942 T37 with PR #589 on #555. The selected certificate was followed to `docs/research/community-batch952-review.md`, the source manifest and `research/complex-t37-owners/README.md`.
+
+Prepared for Sagar Thakrar / @thakrarsagar with substantial OpenAI Codex assistance. Apache-2.0. This claim does not reserve work against other contributors.
+
+## Completed result, 2026-10-13 16:05 UTC
+
+Submitted as [PR #990](https://github.com/CrocSwap/integer-mult-bounds/pull/990). The exact rank-three fixture uses eight complete native queries and 30 XOR scans, compared with twelve queries and 36 scans for the best separately completed rank-factor schedule. All 5,376 minimum-query excursion schedules were checked by two enumeration formulations; 232 attain the minimum. The complete paid recurrence and limited optimization class are in README.md. No new kappa is claimed.
+
+Normal, optimized and relocated verification passed, including 7,290 full-domain input columns and their inverse, eight built-in negative controls, a paid neutral pair and four actual-certificate corruptions. All nine source hashes, selected-record integrity and 17 selected-result tests passed. Existing files and upstream/ are unchanged. Full supplier replay, repository-wide make verify, hosted CI and Lean were not run.
+
+Construction finished before the final verification/packaging phase, which began by 15:57 UTC. The submission refresh covered all 694 then-open PRs through #984 and the latest metadata immediately before posting through #989. No pinned coordination issue existed. Related concurrent #982 is credited for its different output-borrowed contract. Main advanced to `55645f9d4d806d67875c1c8b9840b0b039ece22e`, retaining the same selected kappa and with no package-path overlap. The original investigation base remains the commit above.

research/native-shear-batch/NOTICE.md

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+# Attribution and scope
+
+Contributed by Sagar Thakrar / @thakrarsagar with substantial OpenAI Codex assistance in task selection, mathematics, implementation, verification and writing. New code and prose are under the repository's Apache-2.0 license. No independent human review or official OpenAI endorsement is claimed.
+
+- Karl Appel / @applecrusher, PR #521 at `a190fdb39f31647fc6f651625353710624627348`, supplies the native unipotent ADDRESS map and seven-event lowering. The lowering in `verify.py` is an attributed transcription, checked against an independently written direct map.
+- @commdata2338, PR #677 at `613c02b8b4411f991f108dcc1481b3f9100b996f`, supplies the completed DATA-shear contracts, single-shear private-only construction, query-model distinctions and typed cost accounting used here. Its notice discloses OpenAI Codex and Claude Code assistance.
+- @CubeJerry, PR #889 at `e2021d1c9e06948528cbc0a8fd7079b671da981d`, supplies related common-factor multi-output dirty correction sharing. We claim no priority for that mechanism. Ross Richardson's PR #938 independently audits the corresponding star-word minima; our census concerns native-query excursions and their scalar scan costs, not that star language.
+- PR #822 studies connector reuse in recursive product trees. PR #974 studies optimistic budgets for the selected T21/T37 interfaces. They are distinct concurrent work, credited and excluded from this packet's claims.
+- Concurrent PR #982 at `5eca5b435d2ce172edf6ffb85694c7efa31bf114` borrows an output in place of a dedicated connector for common-factor batches. This packet keeps a dedicated private row and forbids DATA queries; no priority or dominance over that different contract is claimed.
+- OpenAI #109 and the retained upstream stream/interchange sources supply the ordered-affine, complete-range, tape and restoration contracts. Those contracts remain premises. The original source and license notices in `upstream/` are unchanged.
+- Jonathan Capalbo's selected PR942 T37 composition, its complex lineage and DreamingOfClouds' PR589 on eumemic's PR555 bit supplier retain their existing attribution and selected status. Their full proof and validation are not rerun or replaced here.
+
+The contribution is the explicit private-only batch boundary, paid recurrence and finite affine-state scheduling evidence. It does not claim a new kappa, an installed supplier, a general optimum, a practical multiplication speedup or a full formal multiplication theorem.