{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D4EI2QRQAF5XBPZHVHPZHF6AHE","short_pith_number":"pith:D4EI2QRQ","canonical_record":{"source":{"id":"1211.3561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-15T10:23:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"17e0950bea9d26ae310e8adf38d746147bf03c583cd408285156e73c7c23feb4","abstract_canon_sha256":"b7ec8a75672456568b462921368dce06993c1d61d8b99d5f35f815b0bd18dd37"},"schema_version":"1.0"},"canonical_sha256":"1f088d4230017b70bf27a9df9397c0390305fa5912a7cd40fab083295b3faf65","source":{"kind":"arxiv","id":"1211.3561","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3561","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3561v2","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3561","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"D4EI2QRQAF5X","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D4EI2QRQAF5XBPZH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D4EI2QRQ","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D4EI2QRQAF5XBPZHVHPZHF6AHE","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-15T10:23:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"17e0950bea9d26ae310e8adf38d746147bf03c583cd408285156e73c7c23feb4","abstract_canon_sha256":"b7ec8a75672456568b462921368dce06993c1d61d8b99d5f35f815b0bd18dd37"},"schema_version":"1.0"},"canonical_sha256":"1f088d4230017b70bf27a9df9397c0390305fa5912a7cd40fab083295b3faf65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:55.479160Z","signature_b64":"vUWQUgZDq7OpW6xQS1dThFVpEloqXP1pH2cRsuEtOYVjw+ssCFSOT0rYTfJXl7hSFJ53l75LapnyG/1NDjGPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f088d4230017b70bf27a9df9397c0390305fa5912a7cd40fab083295b3faf65","last_reissued_at":"2026-05-18T01:39:55.478621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:55.478621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3561","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5X7f0VipfQBi2ZEK9gRiC+UEUy3M9hMyiJeYOOyZmatPD7Rr08TnSkkVEBN6HkV0PX1uDMqSbTiIO7lI02hhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:34:45.627415Z"},"content_sha256":"4ec13fd1c100c920190449c2ab0f625afd9d1a785edad79a47e3892a458a6dd0","schema_version":"1.0","event_id":"sha256:4ec13fd1c100c920190449c2ab0f625afd9d1a785edad79a47e3892a458a6dd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D4EI2QRQAF5XBPZHVHPZHF6AHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing partition functions of the edge-coloring model by rank growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver","submitted_at":"2012-11-15T10:23:50Z","abstract_excerpt":"We characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3561","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZM+e/7DZftbW3Y4o/4oIRao+1Y3ab6Thi2+XtQ5CcOG0kgM00wVwIC00FIrZv8RgmBwu/1eB9TbBo+bWfFhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:34:45.627757Z"},"content_sha256":"58f309fbc905b9cdfc015256fe397366670ea1afc98dc818bb40f9184a1326a8","schema_version":"1.0","event_id":"sha256:58f309fbc905b9cdfc015256fe397366670ea1afc98dc818bb40f9184a1326a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/bundle.json","state_url":"https://pith.science/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T15:34:45Z","links":{"resolver":"https://pith.science/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE","bundle":"https://pith.science/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/bundle.json","state":"https://pith.science/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4EI2QRQAF5XBPZHVHPZHF6AHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D4EI2QRQAF5XBPZHVHPZHF6AHE","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":"b7ec8a75672456568b462921368dce06993c1d61d8b99d5f35f815b0bd18dd37","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-15T10:23:50Z","title_canon_sha256":"17e0950bea9d26ae310e8adf38d746147bf03c583cd408285156e73c7c23feb4"},"schema_version":"1.0","source":{"id":"1211.3561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3561","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3561v2","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3561","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"D4EI2QRQAF5X","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D4EI2QRQAF5XBPZH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D4EI2QRQ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:58f309fbc905b9cdfc015256fe397366670ea1afc98dc818bb40f9184a1326a8","target":"graph","created_at":"2026-05-18T01:39:55Z","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 characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'.","authors_text":"Alexander Schrijver","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-15T10:23:50Z","title":"Characterizing partition functions of the edge-coloring model by rank growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3561","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":"sha256:4ec13fd1c100c920190449c2ab0f625afd9d1a785edad79a47e3892a458a6dd0","target":"record","created_at":"2026-05-18T01:39:55Z","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":"b7ec8a75672456568b462921368dce06993c1d61d8b99d5f35f815b0bd18dd37","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-15T10:23:50Z","title_canon_sha256":"17e0950bea9d26ae310e8adf38d746147bf03c583cd408285156e73c7c23feb4"},"schema_version":"1.0","source":{"id":"1211.3561","kind":"arxiv","version":2}},"canonical_sha256":"1f088d4230017b70bf27a9df9397c0390305fa5912a7cd40fab083295b3faf65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f088d4230017b70bf27a9df9397c0390305fa5912a7cd40fab083295b3faf65","first_computed_at":"2026-05-18T01:39:55.478621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:55.478621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vUWQUgZDq7OpW6xQS1dThFVpEloqXP1pH2cRsuEtOYVjw+ssCFSOT0rYTfJXl7hSFJ53l75LapnyG/1NDjGPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:55.479160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ec13fd1c100c920190449c2ab0f625afd9d1a785edad79a47e3892a458a6dd0","sha256:58f309fbc905b9cdfc015256fe397366670ea1afc98dc818bb40f9184a1326a8"],"state_sha256":"002ce06fd876509708d70e6cbb779bcde35f1dc3ef3a6d9cfc2a0ba9bd2f1cbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MhWYAUOosJobFSmWuK99Bx7e1+QXLqyIAzVCPvV71dVhSCGLg79mMFVTjleYXfZxUIj8mz+XAB6FkoPTgUBhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:34:45.629573Z","bundle_sha256":"356e5c07fd1fc6063666e1a23c2b65b5ee54ca1b17232621b80e1230e64e5e3d"}}