{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:BSFSVJJLOAZ4SRXYXUQ2PEJWJ7","short_pith_number":"pith:BSFSVJJL","canonical_record":{"source":{"id":"0712.1884","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-12-12T09:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"12554bece2588596902737b9b51cb4477232474856407df197de5cad143db984","abstract_canon_sha256":"1fee8e46afe36084566cc7909bcbedf02a235db6c889265cebf3cb628965c1f3"},"schema_version":"1.0"},"canonical_sha256":"0c8b2aa52b7033c946f8bd21a791364fd43e3791b32d29000a1a6bedd66f8089","source":{"kind":"arxiv","id":"0712.1884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1884","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1884v1","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1884","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"BSFSVJJLOAZ4","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"BSFSVJJLOAZ4SRXY","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"BSFSVJJL","created_at":"2026-07-04T15:06:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:BSFSVJJLOAZ4SRXYXUQ2PEJWJ7","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1884","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-12-12T09:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"12554bece2588596902737b9b51cb4477232474856407df197de5cad143db984","abstract_canon_sha256":"1fee8e46afe36084566cc7909bcbedf02a235db6c889265cebf3cb628965c1f3"},"schema_version":"1.0"},"canonical_sha256":"0c8b2aa52b7033c946f8bd21a791364fd43e3791b32d29000a1a6bedd66f8089","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:06:13.775435Z","signature_b64":"mUrfWckIXqEyoMAiUa3qH+ZfDYZR1h07VEG8XjAjScYvv/UyoeuSBQVkDiAvfVkwnjpzjfN6XqHPLgrUb1oYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c8b2aa52b7033c946f8bd21a791364fd43e3791b32d29000a1a6bedd66f8089","last_reissued_at":"2026-07-04T15:06:13.775007Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:06:13.775007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1884","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9A+DsKgu8AW8CoL46xBlaeK7fWU6DsC9Dy0rVlsG/NZ5kKDhC5z3XK3kpKjzPVLI8PBkbmUDq7W95bKbuZM4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:15:39.700164Z"},"content_sha256":"88b15b36cf5788d3fbfa5a108670d3f138d1595f16b66be12b34c0aa1e5525fd","schema_version":"1.0","event_id":"sha256:88b15b36cf5788d3fbfa5a108670d3f138d1595f16b66be12b34c0aa1e5525fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:BSFSVJJLOAZ4SRXYXUQ2PEJWJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Criterion for Vertex Colorability of a Graph Stated in Terms of Edge Orientations","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yu. V. Matiyasevich","submitted_at":"2007-12-12T09:27:48Z","abstract_excerpt":"L.M.Vitaver [1962] and G.I.Minty [1962] suggested criteria for vertex colorability of a graph in at most a given number of colors; these criteria are stated in terms of the orientation of the edges. One additional criterion of this kind is given here."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1884","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0712.1884/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNADRWMofI8qeXnuLMRqAXCFKqaPHfFf8YKmeus8ZFHEIuxjqe+bpqnoEmIKtABYIwSm8//TiE/M3CLU+DDSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:15:39.700725Z"},"content_sha256":"ba76492fc662f399022c9fa2a63767a3b589bde47d3c0dfd6d48a7bbc2894a55","schema_version":"1.0","event_id":"sha256:ba76492fc662f399022c9fa2a63767a3b589bde47d3c0dfd6d48a7bbc2894a55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/bundle.json","state_url":"https://pith.science/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/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":"2026-08-13T03:15:39Z","links":{"resolver":"https://pith.science/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7","bundle":"https://pith.science/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/bundle.json","state":"https://pith.science/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSFSVJJLOAZ4SRXYXUQ2PEJWJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BSFSVJJLOAZ4SRXYXUQ2PEJWJ7","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":"1fee8e46afe36084566cc7909bcbedf02a235db6c889265cebf3cb628965c1f3","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-12-12T09:27:48Z","title_canon_sha256":"12554bece2588596902737b9b51cb4477232474856407df197de5cad143db984"},"schema_version":"1.0","source":{"id":"0712.1884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1884","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1884v1","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1884","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"BSFSVJJLOAZ4","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"BSFSVJJLOAZ4SRXY","created_at":"2026-07-04T15:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"BSFSVJJL","created_at":"2026-07-04T15:06:13Z"}],"graph_snapshots":[{"event_id":"sha256:ba76492fc662f399022c9fa2a63767a3b589bde47d3c0dfd6d48a7bbc2894a55","target":"graph","created_at":"2026-07-04T15:06:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0712.1884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"L.M.Vitaver [1962] and G.I.Minty [1962] suggested criteria for vertex colorability of a graph in at most a given number of colors; these criteria are stated in terms of the orientation of the edges. One additional criterion of this kind is given here.","authors_text":"Yu. V. Matiyasevich","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-12-12T09:27:48Z","title":"A Criterion for Vertex Colorability of a Graph Stated in Terms of Edge Orientations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1884","kind":"arxiv","version":1},"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":"sha256:88b15b36cf5788d3fbfa5a108670d3f138d1595f16b66be12b34c0aa1e5525fd","target":"record","created_at":"2026-07-04T15:06:13Z","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":"1fee8e46afe36084566cc7909bcbedf02a235db6c889265cebf3cb628965c1f3","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-12-12T09:27:48Z","title_canon_sha256":"12554bece2588596902737b9b51cb4477232474856407df197de5cad143db984"},"schema_version":"1.0","source":{"id":"0712.1884","kind":"arxiv","version":1}},"canonical_sha256":"0c8b2aa52b7033c946f8bd21a791364fd43e3791b32d29000a1a6bedd66f8089","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c8b2aa52b7033c946f8bd21a791364fd43e3791b32d29000a1a6bedd66f8089","first_computed_at":"2026-07-04T15:06:13.775007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:06:13.775007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUrfWckIXqEyoMAiUa3qH+ZfDYZR1h07VEG8XjAjScYvv/UyoeuSBQVkDiAvfVkwnjpzjfN6XqHPLgrUb1oYBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:06:13.775435Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88b15b36cf5788d3fbfa5a108670d3f138d1595f16b66be12b34c0aa1e5525fd","sha256:ba76492fc662f399022c9fa2a63767a3b589bde47d3c0dfd6d48a7bbc2894a55"],"state_sha256":"5aef6a442631945bae423ab021236ad181fb3f11bd031884c76ae011331461bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AjdS1rXPd8Pb3tfii7Ee2YR2oc9tqXfBPUtTptmfhZOfZL50MJjWRfKy7HGLyz7+AzCp/tZkStS87o0ZPzMuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T03:15:39.704221Z","bundle_sha256":"70143a426050e863a90fbae5e707bef815b68c4142b1babfdc64324a553e5334"}}