{ "label": "Re-checks the programme's own ledger: dependency graph, bounded constructions (Sidon, Ramsey), external proof hashes, status propagation and independent reviews. It does not re-run an external formal proof and does not prove the mathematics beyond the bounded construction it re-checks.", "public_key_b64": "W2JA1ibUIv72UVHnEpj4x/+KMoba3ocZt+QPA/i6mfo=", "records": [ { "checks": [ { "detail": "author 'agent:explorer-1'", "id": "C1-paley17.author_registered", "ok": true }, { "detail": "depends on []", "id": "C1-paley17.dependencies_exist", "ok": true }, { "detail": "author 'agent:explorer-2'", "id": "C2-mian-chowla-12.author_registered", "ok": true }, { "detail": "depends on []", "id": "C2-mian-chowla-12.dependencies_exist", "ok": true }, { "detail": "author 'agent:explorer-2'", "id": "C3-greedy-density.author_registered", "ok": true }, { "detail": "depends on ['C2-mian-chowla-12']", "id": "C3-greedy-density.dependencies_exist", "ok": true }, { "detail": "author 'agent:explorer-1'", "id": "C4-extension.author_registered", "ok": true }, { "detail": "depends on ['C3-greedy-density']", "id": "C4-extension.dependencies_exist", "ok": true }, { "detail": "author 'agent:prover-3'", "id": "C5-lean-lemma.author_registered", "ok": true }, { "detail": "depends on ['C1-paley17']", "id": "C5-lean-lemma.dependencies_exist", "ok": true }, { "detail": "no claim depends on itself", "id": "graph.acyclic", "ok": true }, { "detail": "a CONSTRUCTION must carry the object", "id": "C1-paley17.construction_has_construction", "ok": true }, { "detail": "a CONSTRUCTION must carry the object", "id": "C2-mian-chowla-12.construction_has_construction", "ok": true }, { "detail": "an external proof records its checker and the SHA-256 of the proof artifact", "id": "C5-lean-lemma.formal_proof_recorded", "ok": true }, { "detail": "the programme calls it established; the ledger gives ESTABLISHED", "id": "summary.C1-paley17.is_established", "ok": true }, { "detail": "1 independent, current accepting review(s)", "id": "summary.C1-paley17.independently_reviewed", "ok": true }, { "detail": "the programme calls it established; the ledger gives ESTABLISHED", "id": "summary.C2-mian-chowla-12.is_established", "ok": true }, { "detail": "1 independent, current accepting review(s)", "id": "summary.C2-mian-chowla-12.independently_reviewed", "ok": true } ], "created_at": "2026-11-12T07:59:13Z", "engine": "a75-005/1.0.0", "extra": { "construction_checks": { "C1-paley17": "graph on 17 vertices: no K4 and no independent 4-set (so R(4,4) > 17)", "C2-mian-chowla-12": "12 elements in [1, 123], all 78 pairwise sums distinct" }, "independent_reviews": { "C1-paley17": 1, "C2-mian-chowla-12": 1, "C3-greedy-density": 0, "C4-extension": 0, "C5-lean-lemma": 0 }, "status": { "C1-paley17": "ESTABLISHED", "C2-mian-chowla-12": "ESTABLISHED", "C3-greedy-density": "CONDITIONAL", "C4-extension": "CONDITIONAL", "C5-lean-lemma": "EXTERNAL" } }, "failed": [], "label": "Re-checks the programme's own ledger: dependency graph, bounded constructions (Sidon, Ramsey), external proof hashes, status propagation and independent reviews. It does not re-run an external formal proof and does not prove the mathematics beyond the bounded construction it re-checks.", "prev_record_hash": "8c7c8815b698dcdf4e36e3bd44b3ca17362f0444ebc42da824c925f383080596", "public_key_b64": "W2JA1ibUIv72UVHnEpj4x/+KMoba3ocZt+QPA/i6mfo=", "record_hash": "68a6e3295f0a28b1efab7d0a62e8db377bd227d6d7ed9ad91d4590f5d1fa85c3", "schema": "cain42.a75.research.record.v1", "signature_b64": "COfQzESLCK9AtHk8G0a4+bYW/VG2WnFGNsPlhpcdxnmwvsP0Bl4+F/NU+mfgSl6UPqap4yJdYUYf4fMvqgEZCg==", "sku": "CAIN-A75-005", "subject": { "agents": [ { "id": "agent:explorer-1", "operator": "lab-a" }, { "id": "agent:explorer-2", "operator": "lab-a" }, { "id": "agent:prover-3", "operator": "lab-b" }, { "id": "agent:auditor-9", "operator": "independent-c" } ], "claims": [ { "author": "agent:explorer-1", "depends_on": [], "evidence": { "family": "ramsey_graph", "object": { "edges": [ [ 0, 1 ], [ 0, 2 ], [ 0, 4 ], [ 0, 8 ], [ 0, 9 ], [ 0, 13 ], [ 0, 15 ], [ 0, 16 ], [ 1, 2 ], [ 1, 3 ], [ 1, 5 ], [ 1, 9 ], [ 1, 10 ], [ 1, 14 ], [ 1, 16 ], [ 2, 3 ], [ 2, 4 ], [ 2, 6 ], [ 2, 10 ], [ 2, 11 ], [ 2, 15 ], [ 3, 4 ], [ 3, 5 ], [ 3, 7 ], [ 3, 11 ], [ 3, 12 ], [ 3, 16 ], [ 4, 5 ], [ 4, 6 ], [ 4, 8 ], [ 4, 12 ], [ 4, 13 ], [ 5, 6 ], [ 5, 7 ], [ 5, 9 ], [ 5, 13 ], [ 5, 14 ], [ 6, 7 ], [ 6, 8 ], [ 6, 10 ], [ 6, 14 ], [ 6, 15 ], [ 7, 8 ], [ 7, 9 ], [ 7, 11 ], [ 7, 15 ], [ 7, 16 ], [ 8, 9 ], [ 8, 10 ], [ 8, 12 ], [ 8, 16 ], [ 9, 10 ], [ 9, 11 ], [ 9, 13 ], [ 10, 11 ], [ 10, 12 ], [ 10, 14 ], [ 11, 12 ], [ 11, 13 ], [ 11, 15 ], [ 12, 13 ], [ 12, 14 ], [ 12, 16 ], [ 13, 14 ], [ 13, 15 ], [ 14, 15 ], [ 14, 16 ], [ 15, 16 ] ], "n": 17, "s": 4, "t": 4 }, "type": "construction" }, "id": "C1-paley17", "kind": "CONSTRUCTION", "reviews": [ { "by": "agent:auditor-9", "claim_sha256": "dbd5d1f11e58d21f57b6ca953721047c82a0fa37cb7f215967c1af5ca0b72dec", "verdict": "accept" } ], "statement": "The Paley graph on 17 vertices has no K4 and no independent set of size 4, so R(4,4) > 17." }, { "author": "agent:explorer-2", "depends_on": [], "evidence": { "family": "sidon_set", "object": { "N": 123, "claimed_size": 12, "set": [ 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123 ] }, "type": "construction" }, "id": "C2-mian-chowla-12", "kind": "CONSTRUCTION", "reviews": [ { "by": "agent:auditor-9", "claim_sha256": "055a47dee14d6fa970deec68d8c4f3e44197cd7c16f976b03934afcb535e4664", "verdict": "accept" } ], "statement": "The first 12 Mian-Chowla terms [1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123] form a Sidon set in [1, 123]." }, { "author": "agent:explorer-2", "depends_on": [ "C2-mian-chowla-12" ], "evidence": { "type": "none" }, "id": "C3-greedy-density", "kind": "CONJECTURE", "statement": "The greedy Sidon sequence keeps a density close to the optimal order." }, { "author": "agent:explorer-1", "depends_on": [ "C3-greedy-density" ], "evidence": { "type": "none" }, "id": "C4-extension", "kind": "THEOREM", "statement": "A consequence that holds if C3 holds." }, { "author": "agent:prover-3", "depends_on": [ "C1-paley17" ], "evidence": { "artifact_sha256": "7777777777777777777777777777777777777777777777777777777777777777", "checker": "lean4 v4.12", "type": "formal_proof" }, "id": "C5-lean-lemma", "kind": "LEMMA", "statement": "A lemma proved in Lean by another group." } ], "programme": "open-world-math-station-sample", "schema": "cain42.a75.research.ledger.v1", "summary": { "conditional": [ "C3-greedy-density", "C4-extension" ], "established": [ "C1-paley17", "C2-mian-chowla-12" ], "external": [ "C5-lean-lemma" ] } }, "subject_sha256": "7b152b9844ff9ba0e39f38e8139019a05a46164384965d3681ba16e6ca1fd56e", "verdict": "CONSISTENT" } ], "run_hash": "4f8defd0697fad8ccf78452a519097fda3a30797ccaf764ca533ce031e58ef41", "schema": "cain42.a75.research.run.v1", "sku": "CAIN-A75-005", "verdict": "VERIFIED", "verdicts": [ "CONSISTENT" ] }