[RossRichardson]

Completing each PR840 centered BIT shear separately repeats the target's ADDRESS-layout restoration. For a shared target and unchanged source, this contribution batches dyadic indices into consecutive runs: r indices in c runs use 2r+c ordinary recursive children instead of 3r, with no additional full private row. Seed 55 selects {0,1,2,4,5}: 15 → 12 children, 90 → 72 affine events, ten XOR scans unchanged.

Status: recursive-interface research construction; no new kappa. The written proof establishes the exact query minimum only in the uniform target-query/source-XOR alphabet with signed dyadic powers, including arbitrary off-support excursions. Concrete controls show why nondyadic queries and fixed-modulus cancellation lie outside that theorem. The coefficient-aware work and storage recurrence pays every native affine event, full child, source scan, layout return, preparation and tape obligation. This is not a selected supplier, a general circuit lower bound or a measured runtime improvement.

Review entrypoint: research/dyadic-query-runs/README.md. Only that new directory is added, including the proof, literal certificate, deterministic evidence, source pins, local sprint claim and validation record.

python3 -I -O -B research/dyadic-query-runs/verify.py
python3 -I -O -B research/dyadic-query-runs/test_package.py

Expected: PASS_DYADIC_QUERY_RUNS cases=63 seed=55 children=15->12 affines=90->72 XOR=10 and PASS_DYADIC_QUERY_RUNS_PACKAGE relocation=1 regeneration=2 corruptions=8.

Validation:

• All 63 declared index sets, both complete invoices and exact Laurent endpoints/inverses. A separate bounded shortest-walk census exhausts 15,616 states and 156,672 edges for all 15 smaller index sets; it is distinct from the written unbounded argument.
• Fourteen native lowerings: 84 rational columns, 756 modular columns and 228,956 complete native-address comparisons with all four configurations of two intervening spectator fields. 252 dirty forward and 252 inverse VALUE executions pass.
• Fifteen rejection controls, two positive scope controls, offline relocation, exact regeneration and eight package-corruption controls pass. CPython 3.14.6 and 3.9.6 agree on the full evidence receipt. Retained files match original Git objects.
• Selected-record integrity and all five existing selected-result tests pass. One root make verify in an untouched base archive completed six historical groups, then was deliberately stopped during entrance banks after the mandatory gen4-bank-verify gate separately failed for missing SymPy. No full-suite, selected-supplier cold replay, hosted-CI or formal multiplication-proof pass is claimed.

Exact development base: 47481c89fd30a43f8f882eb4b391e89c29273fd0. Direct predecessor: Wentao Li / PR840, da2cd0dd2229e08b61b174a8835a2c2bb99d2230; credit also Karl Appel / PR521, commdata2338 / PR677, and the original OpenAI tape framework. Their original proofs, notices and licenses are preserved with source pins. The selected PR890 certificate is unchanged and remains complex-bound; this local BIT construction supplies no new exponent.

The refreshed full queue covered 700 open PRs through #947; the immediate pre-submission check reached #950. PR840 covers one pair; this adds batching across an arbitrary finite dyadic index set and a restricted exact optimum. PR934/943/944 use different multi-source dirty-connector contracts. No pinned coordination issue exists, so the claim and result are local. Main advanced to 007664306fff84fbb1c9a1b4053b69f439764034 without changing the selected record. No duplicate of this scoped result was identified.

Prepared by Ross Richardson (@RossRichardson) with substantial OpenAI Codex assistance, under Apache-2.0. No independent human review or literature-priority claim. All-size compilation, realization, physical frames/owners, whole-row hosting, tape/precision and analytic transfer remain obligations. Nothing is merged and the selected frontier is not edited.