{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JDROHJOKKAHMRPW36YTCPFKAEE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"79cd0fcaa138ea436b806f1b9b4ee15936800a241022fe2ddf9d83fbff0c937e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-31T21:09:40Z","title_canon_sha256":"cda799c84134958998a9d60085892a6402b0bb5fd0a9f2d2386ad5de2e52a6db"},"schema_version":"1.0","source":{"id":"1504.00040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00040","created_at":"2026-05-18T01:33:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00040v2","created_at":"2026-05-18T01:33:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00040","created_at":"2026-05-18T01:33:43Z"},{"alias_kind":"pith_short_12","alias_value":"JDROHJOKKAHM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDROHJOKKAHMRPW3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDROHJOK","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:f565de02ff31c931a24c5777689fe0d81d52a8b38cec25f7789802c2bbea84d7","target":"graph","created_at":"2026-05-18T01:33:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove, by means of an exact structural description, that every simple triangle-free binary matroid $M$ with $|M| > \\tfrac{33}{128}2^{r(M)}$ has critical number at most $2$.","authors_text":"Jim Geelen, Peter Nelson, Rutger Campbell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-31T21:09:40Z","title":"On the structure of dense triangle-free binary matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00040","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f01fcd7ab65cc0ace6d3bf20e23338460d827ed241fd07c3a755303d62ee047","target":"record","created_at":"2026-05-18T01:33:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"79cd0fcaa138ea436b806f1b9b4ee15936800a241022fe2ddf9d83fbff0c937e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-31T21:09:40Z","title_canon_sha256":"cda799c84134958998a9d60085892a6402b0bb5fd0a9f2d2386ad5de2e52a6db"},"schema_version":"1.0","source":{"id":"1504.00040","kind":"arxiv","version":2}},"canonical_sha256":"48e2e3a5ca500ec8bedbf6262795402139d20a7271a66ac064839b4f109cd5c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e2e3a5ca500ec8bedbf6262795402139d20a7271a66ac064839b4f109cd5c8","first_computed_at":"2026-05-18T01:33:43.652559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:43.652559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ND2LpbL1H5EbzuO7cMLjEqr8E1ykT3zPOa+moMg+G8p0F4YMN+v8bc+9yXehOAajEJ8FEZx+rA+f/MO0WFwYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:43.653079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f01fcd7ab65cc0ace6d3bf20e23338460d827ed241fd07c3a755303d62ee047","sha256:f565de02ff31c931a24c5777689fe0d81d52a8b38cec25f7789802c2bbea84d7"],"state_sha256":"516764912c8f0548bc6a63405673f996f4429657acb8d3aaeef03e603623809a"}