Independent verification: exact synthetic-transform physical layouts (no new kappa)

research/synthetic-layout-independent/CLAIM.json

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+{
+  "status": "completed local contribution; publication prepared",
+  "assignment_seed": 80,
+  "randomness": "OS randomness via secrets.randbelow(100), drawn once",
+  "track": "independent verification or formalization",
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "started_utc": "2026-10-13T09:09:13Z",
+  "claimed_utc": "2026-10-13T09:13:15.532680+00:00",
+  "expected_finish_utc": "2026-10-13T09:49:13Z",
+  "time_budget_minutes": 40,
+  "verification_reserve_minutes": 10,
+  "object": "upstream/build/sections/06-transforms.tex, lem:synthetic-transform-cost; L B F- and F+ B^-1 L^-1 for mixed long/short axes",
+  "method": "Two independent exact implementations: literal named-slot prefix/chunk movement plus physical butterfly/twiddle rounds, versus direct tensor Fourier coefficients and a closed-form address map. Exhaustive bounded layouts and all basis columns of small configurations, with ordering/twiddle/normalization controls.",
+  "expected_deliverable": "Standalone reproducible independent verification package, exact receipt, source pins and mathematical scope note; no new kappa.",
+  "candidates": [
+    {
+      "task": "X4 subset scalar identity",
+      "decision": "not chosen; PR874 covers all 16 subsets"
+    },
+    {
+      "task": "cold-wrapper all-column identity",
+      "decision": "not chosen; PR702 and PR712 provide distinct completed independent methods"
+    },
+    {
+      "task": "mixed-axis synthetic transform physical layout",
+      "decision": "chosen; PR673 has six arithmetic/convolution configurations but physical L and complete chunk-group layout are distinct obligations"
+    }
+  ],
+  "overlap": {
+    "open_pr_count": 668,
+    "highest_pr": 875,
+    "pinned_issues": 0,
+    "related_pr": 673,
+    "related_head": "0b4f514c60d9bc7786415d7cbc24754f24d6dc3b",
+    "prior_negative": "PR673 rejects its dirty-echo adapter cost; this check does not reopen that supplier search or price a replacement. No construction search is performed."
+  },
+  "seed_diversification": "Even seed prioritizes mixed axis lengths and the b=0/nonzero chunk-remainder boundary; seed 80 also fixes dense and large-layout sample inputs.",
+  "stopping_rule": "Complete predeclared bounded domains, no adaptive search for a better supplier; reserve final ten minutes for controls, independent review and handoff.",
+  "result": {
+    "completed_utc": "2026-10-13T09:27:34.918431+00:00",
+    "status": "independent finite verification; no new kappa",
+    "summary": "9486 layouts; 200434 complete addresses; 4340 ring columns; 1244 extra scalar columns; 16 source-illustration columns; 11 sensitive controls; all scoped checks pass",
+    "result_file": "EXPECTED.json",
+    "contribution_link": "https://github.com/mightyOil/integer-mult-bounds/tree/research/synthetic-layout-independent-seed80/research/synthetic-layout-independent",
+    "final_overlap": "669 open PRs through 877; no pinned coordination issue; PR673 source head unchanged; no duplicate scope found",
+    "verification_reserve": "Implementation completed before final verification, independent review, metadata refresh and handoff; remaining work is publication only."
+  }
+}

research/synthetic-layout-independent/DOMAIN.json

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+{
+  "seed": 80,
+  "symbolic_layouts": {"ell": [2, 18], "axis_count": [1, 5], "long_short_masks": "all", "K": "all integers 1 <= K < ell"},
+  "complete_addresses": {"ell": [2, 7], "axis_count": [1, 4], "long_short_masks": "all", "K": "all integers 1 <= K < ell", "maximum_total_address_bits": 12},
+  "ring_basis_columns": {"ell": [2, 4], "axis_count": [1, 2], "long_short_masks": "all", "K": "all integers 1 <= K < ell", "directions": ["forward", "opposite"], "additional_cases": [[2, 1, [false, false, true]]]},
+  "extra_scalar_basis_columns": "every coefficient 1..r-1 for every record in ell=2 basis cases, plus ell=3,K=2 and both mixed two-axis orders",
+  "dense_inputs": "one signed integer array per ring-basis configuration, generated in declared order with random.Random(80); both direct operators and opposite composed with forward",
+  "source_illustration": {"ell": 6, "K": 2, "long_axes": [true, false], "input_records": [0, 1, 80, 2047], "input_coefficients": [0, 63], "directions": ["forward", "opposite"]},
+  "stopping_rule": "complete all declared cases; no optimization or adaptive supplier search"
+}