Research construction: optimal dyadic-run BIT query batches (no new kappa)

research/dyadic-query-runs/CLAIM.md

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+# Sprint claim: dyadic query runs
+
+- Track: recursive interfaces. OS assignment seed **55**, drawn with
+  `secrets.randbelow(100)` at 2026-10-13 13:51:49 UTC (2026-10-14 Melbourne).
+- Exact base: `47481c89fd30a43f8f882eb4b391e89c29273fd0`.
+- Object: batches of PR840's centered native BIT shears on the **same** target
+  and unchanged source, with exponents `+/-2^j` for a finite index set J.
+- Hypothesis: keeping the target in its intermediate ADDRESS layout across
+  adjacent powers eliminates repeated query boundaries. The candidate bill is
+  `2|J| + runs(J)` ordinary children instead of `3|J|`, with no private row.
+  Investigate exact optimality only in the target-query / source-XOR alphabet.
+- Method/domain: written integer-walk argument, literal paid affine/child
+  lowering, independent Laurent and modular VALUE replay. Complete all 63
+  nonempty subsets of indices 0 through 5; seed 55 selects the gapped set
+  `{0,1,2,4,5}`. No random search or new kappa claim.
+- Deliverable: one standalone research construction with proof, complete
+  typed cost recurrence, exact certificates, source pins and adverse controls.
+- Budget: approximately 60 minutes, orientation at most 12 minutes;
+  final 15 minutes reserved for verification and handoff. Expected finish
+  2026-10-14 01:52 AEDT (2026-10-13 14:52 UTC).
+
+Three candidates were considered: (1) extend the dyadic DATA-target query
+pair across a finite exponent set, (2) move clean checkpoints among recursive
+subtrees, (3) share a dirty connector among product-shear outputs. Candidate 1
+was selected. PR714/788 already cover checkpoint placement; PR889/934/943 and
+the newly visible PR944 cover the multi-source connector neighborhood. The
+selected task extends PR840's single centered pair to a shared target batch;
+it does not repeat its arbitrary-dirty-row three-query lower bound.
+
+Initial overlap inventory: 714 open PRs through #943. Immediate claim refresh
+included #944 (signed connectors) and #945 (complex Horner). No pinned issues
+exist; the two open issues #650/#913 are not sprint coordination issues, so
+this claim is local. The review ledger marks PR521 unreviewed and has no
+exact-head acceptance for PR677/840. They are pinned pending predecessors,
+not accepted frontier dependencies. Prior fixed-menu and supplier-profile
+negative results are not reopened: the query interface changes and the
+selected supplier is not modified.
+
+At this base the selected conditional kappa is
+`1661957774647029/1000000000000000000` (PR890). Its certificate, actual T21
+construction and maintainer review were followed. The first checkout read
+saw the older PR799 snapshot while the fetch was running; that snapshot is
+not used as the accepted result here.
+
+## Result update
+
+Completed contribution: [PR953](https://github.com/CrocSwap/integer-mult-bounds/pull/953),
+**recursive-interface research construction; no new kappa**. The written
+argument proves the `2|J|+runs(J)` query optimum in the declared uniform
+target-only dyadic alphabet, including arbitrary off-support excursions.
+The seed-55 batch uses 12 children and 72 affine events instead of 15 and 90,
+with ten XOR scans and no extra full private row in both programs. Actual
+coefficient-dependent work and all inherited implementation obligations remain
+explicit in [the proof and recurrence](PROOF.md).
+
+All 63 literal cases, the separate 15-selection bounded walk census, 252 dirty
+forward/inverse case pairs, 15 rejection controls and eight package faults
+pass. The complete evidence agrees on Python 3.14.6 and 3.9.6; source Git
+objects, relocation and regeneration pass. See [validation](VALIDATION.md)
+for the exact domains and the incomplete root-suite boundary (missing SymPy).
+
+The full overlap refresh reached #947 and the immediate pre-submission check
+reached #950, again with no pinned coordination issue. PR840's consumed head
+remains unchanged. Main advanced to `007664306fff84fbb1c9a1b4053b69f439764034`
+without changing the selected record. The mathematical implementation and
+certificate were committed at `282eff4d60bacfe1d0018bc08b22a2e1bf8d5928`;
+this result update adds publication metadata only. Verification and packaging
+occupied the final part of the session, after implementation was frozen.

research/dyadic-query-runs/EVIDENCE.json

@@ -0,0 +1,167 @@
+{
+  "all_cases_baseline_queries": 576,
+  "all_cases_fused_queries": 496,
+  "ancestral_source_files": 7,
+  "cases": 63,
+  "dirty_execution_sha256": "3a6aa40fd16e230b40e9b0cd7f19afac8276b85947892a1193f93eada0ae9f46",
+  "dirty_forward_cases": 252,
+  "dirty_inverse_cases": 252,
+  "format": "dyadic-query-runs-evidence-v1",
+  "full_address_moduli": [
+    3,
+    5
+  ],
+  "graph_records_sha256": "3964f2b66ba03ade78eb7b96f0e2400932dcb4d6a35e85d152e31ae7e6bb3fe2",
+  "independent_bounded_walk_census": {
+    "completed_selections": [
+      [
+        1,
+        3
+      ],
+      [
+        2,
+        3
+      ],
+      [
+        3,
+        5
+      ],
+      [
+        4,
+        3
+      ],
+      [
+        5,
+        6
+      ],
+      [
+        6,
+        5
+      ],
+      [
+        7,
+        7
+      ],
+      [
+        8,
+        3
+      ],
+      [
+        9,
+        6
+      ],
+      [
+        10,
+        6
+      ],
+      [
+        11,
+        8
+      ],
+      [
+        12,
+        5
+      ],
+      [
+        13,
+        8
+      ],
+      [
+        14,
+        7
+      ],
+      [
+        15,
+        9
+      ]
+    ],
+    "directed_edges_examined": 156672,
+    "indices": [
+      0,
+      1,
+      2,
+      3
+    ],
+    "max_dyadic_step": 64,
+    "position_interval": [
+      -32,
+      32
+    ],
+    "reachable_states": 15616,
+    "scope": "Complete bounded walk census; universal bound is the written proof."
+  },
+  "modular_columns": 756,
+  "native_address_comparisons": 228956,
+  "odd_moduli": [
+    3,
+    5,
+    7,
+    9,
+    15,
+    25,
+    27,
+    49,
+    81
+  ],
+  "positive_scope_controls": [
+    "nondyadic five-query endpoint",
+    "modulus-three zero target"
+  ],
+  "rational_columns": 84,
+  "rejection_controls": [
+    "omitted final return",
+    "omitted source tap",
+    "wrong query sign",
+    "VALUE-address confusion",
+    "source query outside alphabet",
+    "unpaid children",
+    "unpaid affines",
+    "unpaid xor_scans",
+    "removed native child",
+    "control after target",
+    "nonunit at odd radix",
+    "scalar-valid wrong native sign",
+    "even radix admission",
+    "nondyadic shortcut",
+    "valid nonoptimal invoice"
+  ],
+  "seed_baseline_invoice": {
+    "affines": 90,
+    "children": 15,
+    "query_multiplicities": {
+      "-1": 2,
+      "-16": 2,
+      "-2": 2,
+      "-32": 2,
+      "-4": 2,
+      "2": 1,
+      "32": 1,
+      "4": 1,
+      "64": 1,
+      "8": 1
+    },
+    "xor_scans": 10
+  },
+  "seed_indices": [
+    0,
+    1,
+    2,
+    4,
+    5
+  ],
+  "seed_invoice": {
+    "affines": 72,
+    "children": 12,
+    "query_multiplicities": {
+      "-32": 2,
+      "-4": 2,
+      "1": 2,
+      "16": 2,
+      "2": 3,
+      "32": 1
+    },
+    "xor_scans": 10
+  },
+  "source_files": 11,
+  "spectator_configurations_per_address": 4
+}

research/dyadic-query-runs/NOTICE.md

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+# Attribution and assistance
+
+New material prepared by **Ross Richardson (@RossRichardson)** with substantial
+**OpenAI Codex assistance** in mathematical derivation, implementation,
+verification and writing. Licensed under the repository's Apache-2.0 license.
+No independent human review, proof-assistant verification, official endorsement
+or literature-priority claim is made. No delegated agents were used.
+
+- **Wentao Li / VictorLiwentao, PR840**, exact head
+  `da2cd0dd2229e08b61b174a8835a2c2bb99d2230`: centered dyadic DATA shear,
+  signed dyadic one-child lowering, three-query single-pair construction,
+  full target ownership contract and typed cost recurrence. Its proof,
+  notice, source manifest and license are retained byte for byte. The present
+  construction concatenates runs of dyadic indices; its lower bound is in
+  the narrower target-only alphabet, not PR840's arbitrary-row chart model.
+- **Karl Appel / applecrusher, PR521**, head
+  `a190fdb39f31647fc6f651625353710624627348`: native unipotent ADDRESS map
+  and paid one-child lowering. The original proof and source pins are
+  retained unchanged through PR840's archive and checked against original
+  Git objects.
+- **commdata2338, PR677**, head
+  `613c02b8b4411f991f108dcc1481b3f9100b996f`: completed first-difference
+  DATA-target shears, dirty-role contract and query-cost distinctions. The
+  original proof and notice are retained, including their predecessor
+  attribution to eumemic/PR288 and Ali Romman/PR468 and AI-assistance notices.
+- **OpenAI's original integer-multiplication framework**, maintained here
+  by **Douglas Colkitt**: ordered affine streams, complete row volumes,
+  ordinary ADDRESS interchange and tape/head-return contracts. Full source
+  sections 02 and 04 and their license are retained unchanged at the original
+  revision pinned in PR840's source manifest.
+
+The selected PR890 construction by Chafik Boukhalfa builds on Jeremy Kothe,
+Hao Yan, DreamingOfClouds, eumemic and the repository's cumulative contributors.
+Its conditional exponent is context, not a result established by this package.
+PR714/788 checkpoint work and PR889/929/934/938/940/943/944 were inspected for
+overlap. Their different storage and query contracts are not consumed here.
+The cross-family split obstruction and PR83 fixed-menu barrier remain intact:
+no recursive child is split or repriced as a different operation.
+
+The graph-component counting argument and retained-layout scheduling are
+elementary methods; no claim of new mathematics beyond this precise
+repository interface and its finite implementation evidence is made.