Research note: paid quadratic-reader restoration and exact square-repair floor

research/quadratic-reader-restoration/CLAIM.json

@@ -0,0 +1,45 @@
+{
+  "track": "recursive-interfaces",
+  "assignment_seed": 55,
+  "seed_source": "python3 secrets.randbelow(100), OS randomness, drawn once at session entry",
+  "base_commit": "ef5f39403610d231a0c27e8a6b4f08c10209bcd6",
+  "object": "Repeated quadratic dirty readers y += beta_i*a^2 with a += alpha_i*b, terminal output observation and complete source restoration",
+  "method": "Exact polynomial identity, independently interpreted rational events, complete stream/child invoices and restricted square-repair rank obstruction",
+  "pilot": "r = 2 + (55 mod 7) = 8; all-positive shears and readers",
+  "domain": "All signed reader/shear batches of lengths 1 through 5; arities 2 through 16 for deterministic cost comparison; no general circuit search",
+  "changed_hypothesis": "Extend the linear-reader model of PR1205/1246 to a specified nonlinear square reader; pay every nonlinear correction and source frame change",
+  "candidates": [
+    {
+      "task": "Linear endpoint defect repair",
+      "decision": "Rejected: already covered by PR1246"
+    },
+    {
+      "task": "Persistent order-four dirty echoes",
+      "decision": "Rejected: overlaps PR1391, PR1410 and PR1499"
+    },
+    {
+      "task": "Quadratic reader with paid bilinear repair",
+      "decision": "Chosen: distinct nonlinear observer, square-call rank floor and full tariff"
+    }
+  ],
+  "predecessors": {
+    "PR1205": "e2008d7ffcad464da7ec21c69e8d8a8c91de4930",
+    "PR1246": "5ed1ce17a9df4c853a93f9758ba903d2620c3443"
+  },
+  "claim_location": "local; GitHub GraphQL pinnedIssues was empty at 2026-10-14 01:54 UTC",
+  "overlap": "Fresh full PR/Discussion metadata checked before recording; literal quadratic/nonlinear-reader terms had no matches. This is bounded evidence, not a novelty guarantee.",
+  "expected_deliverable": "One source-pinned recursive-interface research package with exact certificate, cost threshold, rejection controls and bounded replay",
+  "expected_finish_utc": "2026-10-14T02:37:50Z",
+  "verification_starts_by_utc": "2026-10-14T02:26:35Z",
+  "stopping_rule": "One completed bounded package; stop supplier adoption if even the complete favorable tariff does not help; do not infer a new kappa",
+  "attribution": "Prepared by @theon199 with substantial OpenAI Codex assistance; Apache-2.0",
+  "result": {
+    "status": "DONE",
+    "finished_at_utc": "2026-10-14T02:23:57.254280+00:00",
+    "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1532",
+    "verified_code_commit": "7e720d66e20e7e36f0cca33dd8f38832f8784d71",
+    "summary": "Exact quadratic reader defect, fused restoring one-product repair, rank-two appended-square floor, full nonlinear tariff and literal recursion; pilot 32->31 scalar operations, no new kappa.",
+    "verification": "1364 signed batches; 36828 dirty triples; full polynomial coefficients and literal inverses; 15 cost/access arities; 4 recursion depths; 8 semantic/resource controls; optimized Python 3.12 registered relocation and 5 on-disk corruption rejections; normal Python 3.14 replay.",
+    "handoff": "Pin an admitted indivisible nonlinear reader and substitute complete backend/precision/tape/hosting costs in P+3C<(r-2)L before claiming a supplier improvement."
+  }
+}

research/quadratic-reader-restoration/CONTEXT.json

@@ -0,0 +1,21 @@
+{
+  "base_commit": "ef5f39403610d231a0c27e8a6b4f08c10209bcd6",
+  "predecessor_heads": {
+    "PR1205": "e2008d7ffcad464da7ec21c69e8d8a8c91de4930",
+    "PR1246": "5ed1ce17a9df4c853a93f9758ba903d2620c3443"
+  },
+  "files": [
+    {
+      "path": "context/pr1205-README.md",
+      "sha256": "fc672e69f4b3363fa7736efa4b4103c755fcb72f6f5d45e5d268c10e133a914d",
+      "git_blob": "7ed4d89d17c5cdeba0e5e5eb160919e0e9c5a076"
+    },
+    {
+      "path": "context/pr1246-README.md",
+      "sha256": "31a9770a4dfa057a84def481132591b5400a58f1f1ccf802747c3f0db2a54b60",
+      "git_blob": "e9263fffce7aa51fa0a86821dfbf17f817d50348"
+    }
+  ],
+  "license": "Apache-2.0",
+  "usage": "Retained source notes only; no predecessor verifier is imported or replayed."
+}

research/quadratic-reader-restoration/OVERLAP.json

@@ -0,0 +1,51 @@
+{
+  "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+  "searched_at": "2026-10-14T02:22:17.583221+00:00",
+  "terms": [
+    "quadratic reader",
+    "nonlinear reader",
+    "square reader",
+    "quadratic observer"
+  ],
+  "coverage": {
+    "open_prs": {
+      "fetched_at": "2026-10-14T02:21:43.501730+00:00",
+      "complete_pagination": true,
+      "records": 774
+    },
+    "discussions": {
+      "fetched_at": "2026-10-14T02:22:17.512137+00:00",
+      "complete_pagination": true,
+      "records": 199
+    }
+  },
+  "local_records": 329,
+  "warnings": [],
+  "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+  "matches_total": 2,
+  "matches": [
+    {
+      "kind": "local-task",
+      "title": "research/quadratic-reader-restoration/TASK.json",
+      "path": "research/quadratic-reader-restoration/TASK.json",
+      "sha256": "73f0394b163b8b5be1c17d4ffe1aabbb3f71be31c4192271cf639149a9254d23",
+      "matched_terms": [
+        "nonlinear reader",
+        "square reader"
+      ],
+      "score": 2,
+      "excerpt": "ope_change_reason\": \"Existing PR1205 and PR1246 cover linear observations and repairs; this tests a square reader with a mixed quadratic defect and separately paid square/product backends.\",\n  \"bottleneck_link\": \"Side result: specifies when eliminated source restoration survives its nonlinear child and coefficient bill; no supported supplier with this indivisible reader is established.\",\n  \"budget_minutes\": 45,\n  \"stop_rule\": \"Complete signed batches of lengths 1..5, fixed arities 2..16 and bina"
+    },
+    {
+      "kind": "local-readme",
+      "title": "research/quadratic-reader-restoration/README.md",
+      "path": "research/quadratic-reader-restoration/README.md",
+      "sha256": "eaf5278c40eeab8235014926fda17f3fe163c808ab642704802ee26dddc8ce68",
+      "matched_terms": [
+        "nonlinear reader"
+      ],
+      "score": 1,
+      "excerpt": "nd is supplied by this package.\n\n## Open next questions\n\nDoes a supported supplier have indivisible nonlinear readers whose full repair\nsatisfies `P+3C < (r-2)L`? This matters because the extra product child can erase\nthe apparent restoration saving. First pin an actual child return map and price\nits frames, private scratch, coefficient preparation, precision, transport and\nhosting in the displayed tariff. The blocker is that no such admitted child has\nbeen identified. If these toy reader calls "
+    }
+  ]
+}