Research: batch common-factor product shears with dirty restoration

research/dirty-fanout-batch/CERTIFICATE.json

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+{
+  "base": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "binary_optimum_domain": "all ordered binary splits, unweighted n=1..64",
+  "controls": [
+    "omit_final_leaf",
+    "reverse_factor_order",
+    "change_common_source_during_batch",
+    "omit_common_restoration",
+    "negate_without_reverse",
+    "omit_one_output",
+    "empty_common",
+    "empty_output_list",
+    "insufficient_scratch",
+    "ancestor_alias",
+    "target_source_alias",
+    "coefficient_alias",
+    "boolean_sign",
+    "nonlinear_left_map_has_dirty_cross_term",
+    "rounded_left_map_is_not_exact_linear_map"
+  ],
+  "dense_cases": 795,
+  "rational_cases": 1,
+  "rounded_cases": 27,
+  "scope": "Exact linear multi-output interface; no instantiated supplier, rounded inverse theorem, or new kappa",
+  "seed": 58,
+  "seed_case": {
+    "common_factors": 8,
+    "dirty_arrays": 4,
+    "invoices": {
+      "batch": {
+        "additions": 2952,
+        "calls_by_factor": {
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+          "4": 16,
+          "5": 16,
+          "6": 16,
+          "7": 16,
+          "8": 2,
+          "9": 4
+        },
+        "coefficient_reads": 2214,
+        "coefficient_storage_words": 207,
+        "data_storage_words": 30,
+        "head_travel_word_slots": 458208,
+        "instruction_records": 246,
+        "leaf_calls": 246,
+        "multiplications": 2214,
+        "negations": 369,
+        "preflight_array_length_checks": 10,
+        "preflight_coefficient_alias_pairs": 7380,
+        "preflight_matrix_row_length_checks": 738,
+        "preflight_role_alias_entries": 10,
+        "source_reads": 2214,
+        "target_read_writes": 738
+      },
+      "grouped": {
+        "additions": 9096,
+        "calls_by_factor": {
+          "0": 80,
+          "1": 80,
+          "10": 4,
+          "11": 4,
+          "12": 8,
+          "13": 8,
+          "14": 8,
+          "15": 8,
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+          "4": 80,
+          "5": 80,
+          "6": 80,
+          "7": 80,
+          "8": 2,
+          "9": 4
+        },
+        "coefficient_reads": 6822,
+        "coefficient_storage_words": 207,
+        "data_storage_words": 30,
+        "head_travel_word_slots": 885344,
+        "instruction_records": 758,
+        "leaf_calls": 758,
+        "multiplications": 6822,
+        "negations": 1137,
+        "preflight_array_length_checks": 10,
+        "preflight_coefficient_alias_pairs": 22740,
+        "preflight_matrix_row_length_checks": 2274,
+        "preflight_role_alias_entries": 10,
+        "source_reads": 6822,
+        "target_read_writes": 2274
+      },
+      "separate": {
+        "additions": 8160,
+        "calls_by_factor": {
+          "0": 40,
+          "1": 56,
+          "10": 16,
+          "11": 8,
+          "12": 16,
+          "13": 16,
+          "14": 16,
+          "15": 8,
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+          "4": 72,
+          "5": 56,
+          "6": 48,
+          "7": 72,
+          "8": 16,
+          "9": 16
+        },
+        "coefficient_reads": 6120,
+        "coefficient_storage_words": 207,
+        "data_storage_words": 30,
+        "head_travel_word_slots": 998624,
+        "instruction_records": 680,
+        "leaf_calls": 680,
+        "multiplications": 6120,
+        "negations": 1020,
+        "preflight_array_length_checks": 10,
+        "preflight_coefficient_alias_pairs": 20400,
+        "preflight_matrix_row_length_checks": 2040,
+        "preflight_role_alias_entries": 10,
+        "source_reads": 6120,
+        "target_read_writes": 2040
+      }
+    },
+    "left_factors": [
+      1,
+      2,
+      3,
+      4,
+      5
+    ],
+    "word_sha256": {
+      "batch": "a8a8a350ea43fec5769f393de1eb077c51216a5aa2cbec7046511f58fd8fa970",
+      "grouped": "de2b43e1f8d00c93a1a6a8c90378713fdc8d59d42339f40a7a59a23b4cba7818",
+      "separate": "50f414e6ea161dc6ab1f54c90bf100ebe3ec1433d9b8fb84c8e9b2832f636828"
+    }
+  },
+  "short_star_words_rejected": 9331,
+  "status": "PASS_DIRTY_FANOUT_BATCH",
+  "symbolic_cases": 128,
+  "tape_cases": 15,
+  "weighted_cases": 384
+}

research/dirty-fanout-batch/CLAIM.md

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+# Sprint claim: dirty common-factor fanout
+
+- Track: recursive interfaces; OS-random seed **58** (Python secrets.randbelow(100)).
+- Exact base: `f567884aeb8851b6e794af1184119a3bfbe1e631`.
+- Object: simultaneous independent output shears `y_i += A_i B x` with a shared, unchanged input and entirely dirty workspace.
+- Method: one batched dirty commutator, exact noncommutative replay, a restricted-query lower bound, and complete weighted recursive cost/storage accounting.
+- Seed choices: fanout `2 + 58 % 5 = 5`, common factor length `1 + 58 % 17 = 8`; left lengths 1 through 5.
+- Deliverable: scoped interface construction and standalone exact verifier/certificate; no new kappa.
+- Finish target: 2026-10-13 08:29 UTC (19:29 Australia/Melbourne). Final 10 minutes reserved for verification and handoff.
+
+Three candidates were considered: cancellation of repeated transparent calls; deferred sibling cleanup; shared common-right-factor output batching. The first overlaps PR840's native dyadic pair; the second overlaps PR822's dirty connector reuse and PR714/788 clean checkpoints. The third changes the multi-output contract and retains conservative private scratch.
+
+At claim time the public issues page listed only #650, with no pinned sprint coordination issue. GitHub API read access returned `Forbidden`; no claim was posted. Public open-PR metadata was checked through #856, plus searches for boundary, echo/checkpoint/batch/prefix, common right factor, fanout and multiple outputs. Relevant context: #628, #663, #673, #689, #714, #730, #788, #822, #840. Existing echo work changes decomposition/scratch for one product output; this work batches distinct outputs sharing B. No claim of general algebraic novelty or first discovery is made.
+
+Selected state read: #799/#589, kappa `1661634653669567/10^18`, its actual X4 proof note and maintainer review. This package does not change that construction.
+
+## Result update
+
+Completed one scoped construction: common-factor multi-output batching with
+246 versus 680 complete binary factor-shear calls and four dirty arrays.
+The proof, full weighted/storage/routing/precision bill, exact certificate,
+independent checks and controls are in [README.md](README.md) and
+[VALIDATION.md](VALIDATION.md). There is no new κ or admitted supplier.
+
+The overlap refresh reached #859 and explicitly distinguished #793's scalar
+coefficient batching. No coordination issue was found. API access is denied,
+so the completed contribution is handed off as one local commit and clean patch;
+no external claim or PR was posted. Existing source and the selected frontier
+remain unchanged.

research/dirty-fanout-batch/NOTICE.md

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+# Attribution and scope
+
+Prepared for the requesting contributor with substantial OpenAI Codex assistance
+in the mathematical argument, implementation, tests and prose. The user's human
+identity is not asserted. This package uses the repository's Apache-2.0 license.
+
+Chafik Boukhalfa / chafreaky's PR628 supplies the dirty product commutator,
+literal-inverse convention, exact restoration contract and rounded-error
+analysis. Its reference source, proof and notice are retained byte for byte.
+Ali Romman's PR621 and OpenAI's exact-DFT/Newton framework are inherited context;
+we do not use their analytic kernel claims to certify the abstract matrices here.
+The commutator and batching algebra are classical; no literature-priority claim
+is made.
+
+Relevant concurrent work inspected: androolloyd's PR673 (multiway dirty echo),
+commdata2338's PR677 (native DATA-query contract), Dillon Amburgey's PR689
+(ternary placement), FanPUYen's PR714 (clean root checkpoint), Sagar Thakrar's
+PR730 (fixed scratch optimization), nightangelflowerwin-ops's PR788 (reusable
+clean checkpoint), PR822 (dirty sibling connector reuse), and Wentao Li's PR840
+(dyadic ADDRESS-query pair). These concern different contracts or one-output
+schedules. Their code is not consumed; no relative optimality against their
+broader classes is claimed. Varun Mittal's PR793 batches scalar coefficient
+preparation in historical JP8 compensation and preserves its recursive profile;
+this package instead batches full product-query calls under a different abstract
+multi-output contract. No PR793 code or claimed savings are consumed. PR663's nonlinear-restoration distinction is
+acknowledged and explicitly respected by the rounded controls.
+
+The accepted frontier's authors and source lineage retain all attribution.
+This local multi-output result supplies neither a new κ nor an instantiated
+current supplier, physical tape compiler, full theorem formalization, human
+peer review or measured performance result.