Scoped negative result: exact constant-row center shear optimum (no new kappa)

research/dyadic-center-anchor-bound/CERTIFICATE.json

@@ -0,0 +1,30 @@
+{
+  "basis": "binomial(h-10,j), j=0,1,2,3",
+  "difference": "cost(k)-cost(0), k=1,2,3,4",
+  "positive_newton_coefficients": [
+    [
+      20,
+      19,
+      7,
+      1
+    ],
+    [
+      5,
+      21,
+      11,
+      2
+    ],
+    [
+      53,
+      48,
+      19,
+      3
+    ],
+    [
+      122,
+      72,
+      24,
+      4
+    ]
+  ]
+}

research/dyadic-center-anchor-bound/CLAIM.json

@@ -0,0 +1,41 @@
+{
+  "track": "Complex supplier: scoped negative result for a complete center-basis family",
+  "assignment_seed": 33,
+  "randomness": "secrets.randbelow(100), backed by OS randomness",
+  "started_utc": "2026-10-13T13:51:46.586386+00:00",
+  "base_commit": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
+  "selected_at_base": {
+    "pr": 890,
+    "kappa": "1661957774647029/1000000000000000000"
+  },
+  "candidates": [
+    {
+      "task": "Bounded single-scratch dyadic coefficient synthesis",
+      "decision": "Not selected: direct overlap with PR882 and PR837."
+    },
+    {
+      "task": "Raw coordinate-total factory resynthesis",
+      "decision": "Not selected: active PR922, PR924 and PR931 overlap."
+    },
+    {
+      "task": "Classify all integral constant-row shears of the historical rank-h center, with complete gather/scatter costs",
+      "decision": "Selected: algebraic orbit classification and an all-even-h optimum, beyond PR809 one-step and PR937 second-step searches."
+    }
+  ],
+  "object": "A=I+sum(a_i E_i,p), integer a_i, fixing one constant gather row and all nonconstant gather differences; preserve gather alphabet {0,+1,-1} and scatter numerators {0,+1,-1,+2,-2}.",
+  "method": "Translate to binary anchors; reduce all subsets to cardinality orbits; certify admissibility and exact cost polynomials. Use pivot p=33 mod 26=7 for the h26 finite replay.",
+  "domain": "All integer shear vectors for every even h>=8 within the stated alphabets; finite diagnostics all 128 anchors at h8, 512 at h10, and 26 cardinality representatives at h26.",
+  "stopping_rule": "Complete the class theorem, exact polynomial certificate and stated finite diagnostics; do not expand to general nonconstant-row mixing.",
+  "expected_deliverable": "Scoped optimality/negative-result note, exact offline checker, source pins, meaningful mutation controls, one focused PR.",
+  "expected_finish_utc": "2026-10-13T14:36:46Z",
+  "verification_reserved_from_utc": "2026-10-13T14:25:31Z",
+  "coordination": "No pinned issue in live GraphQL check; local claim per sprint instructions. Open PR list covered 714 entries through PR943; targeted metadata checked PR809, PR937, PR882, PR837 and PR922.",
+  "status": "completed",
+  "result": {
+    "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/947",
+    "branch": "research/center-anchor-bound-seed33",
+    "summary": "Exact constant-row integral-shear classification; PR937 uniquely minimizes the complete cost for fixed pivot and every even h>=10. h8 has a certified size-two exception. No new kappa.",
+    "verification": "14 main controls, 9 package tests, 4 inherited tests and selected-record integrity pass.",
+    "completed_utc": "2026-10-13T14:16:18.246472+00:00"
+  }
+}