{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5CH6TJAICGR42EXKDTTV7SQU7P","short_pith_number":"pith:5CH6TJAI","canonical_record":{"source":{"id":"2303.12010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-03-21T16:47:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"66fb818fdb340d8004d55faaa0923e8ef3b4597d8da599d6541d400c30bd2188","abstract_canon_sha256":"7bf40b770afcee8b83e5ccda360bd58d10769806858512b5358c1ef95f7545ab"},"schema_version":"1.0"},"canonical_sha256":"e88fe9a40811a3cd12ea1ce75fca14fbdf5e282abd0934ade91f2d44d07d6310","source":{"kind":"arxiv","id":"2303.12010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12010","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12010v1","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12010","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"5CH6TJAICGR4","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_16","alias_value":"5CH6TJAICGR42EXK","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_8","alias_value":"5CH6TJAI","created_at":"2026-07-05T05:53:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5CH6TJAICGR42EXKDTTV7SQU7P","target":"record","payload":{"canonical_record":{"source":{"id":"2303.12010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-03-21T16:47:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"66fb818fdb340d8004d55faaa0923e8ef3b4597d8da599d6541d400c30bd2188","abstract_canon_sha256":"7bf40b770afcee8b83e5ccda360bd58d10769806858512b5358c1ef95f7545ab"},"schema_version":"1.0"},"canonical_sha256":"e88fe9a40811a3cd12ea1ce75fca14fbdf5e282abd0934ade91f2d44d07d6310","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:53:24.467900Z","signature_b64":"1qwc+mNDFrbLtwdsJQVoWxjxMqmBbDg8utNFp2IxiHBTKhh2qF20rp0rYC88YsnJmKmlcc5YqkBzX4sR8i2TBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e88fe9a40811a3cd12ea1ce75fca14fbdf5e282abd0934ade91f2d44d07d6310","last_reissued_at":"2026-07-05T05:53:24.467486Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:53:24.467486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.12010","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":"2026-07-05T05:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCVj9IoF+U1uONFYzFQjD224cF2JLwOGK21LU1oEc7xPg55LYGeqji04Q++tpiw/1JDkbhFxlrE0VJftiGxtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:43:17.305462Z"},"content_sha256":"7f41ce648eba3c845a6ce32906cbb2078a45c844c8b5951bafa6daadf0f978ed","schema_version":"1.0","event_id":"sha256:7f41ce648eba3c845a6ce32906cbb2078a45c844c8b5951bafa6daadf0f978ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5CH6TJAICGR42EXKDTTV7SQU7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A topological quantum field theory approach to graph coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Ben McCarty, Scott Baldridge","submitted_at":"2023-03-21T16:47:00Z","abstract_excerpt":"In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number of ways that each face of the CW complex can be colored with one of $n$ colors so that no two adjacent faces have the same color. We use these homologies to define new invariants of graphs, give new characterizations of well-known polynomial invariants of graphs, and rephrase and offer new approaches to famous conjectures about graph coloring. In particular,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12010","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/2303.12010/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":"2026-07-05T05:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+xwFGhkzUMpaUDcg4GTZPgXsZ17CImfEqQfwSl6vb8Co35UXn0lbk+wmudyN60U1ELuOUuU18JqXMh7e8HpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:43:17.306084Z"},"content_sha256":"6e8a0433669717c53958b9fe9a753871bbc4f379e0b9f79e4aef4ed663cf1eb7","schema_version":"1.0","event_id":"sha256:6e8a0433669717c53958b9fe9a753871bbc4f379e0b9f79e4aef4ed663cf1eb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CH6TJAICGR42EXKDTTV7SQU7P/bundle.json","state_url":"https://pith.science/pith/5CH6TJAICGR42EXKDTTV7SQU7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CH6TJAICGR42EXKDTTV7SQU7P/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":"2026-08-15T18:43:17Z","links":{"resolver":"https://pith.science/pith/5CH6TJAICGR42EXKDTTV7SQU7P","bundle":"https://pith.science/pith/5CH6TJAICGR42EXKDTTV7SQU7P/bundle.json","state":"https://pith.science/pith/5CH6TJAICGR42EXKDTTV7SQU7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CH6TJAICGR42EXKDTTV7SQU7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5CH6TJAICGR42EXKDTTV7SQU7P","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":"7bf40b770afcee8b83e5ccda360bd58d10769806858512b5358c1ef95f7545ab","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-03-21T16:47:00Z","title_canon_sha256":"66fb818fdb340d8004d55faaa0923e8ef3b4597d8da599d6541d400c30bd2188"},"schema_version":"1.0","source":{"id":"2303.12010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.12010","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"2303.12010v1","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12010","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"5CH6TJAICGR4","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_16","alias_value":"5CH6TJAICGR42EXK","created_at":"2026-07-05T05:53:24Z"},{"alias_kind":"pith_short_8","alias_value":"5CH6TJAI","created_at":"2026-07-05T05:53:24Z"}],"graph_snapshots":[{"event_id":"sha256:6e8a0433669717c53958b9fe9a753871bbc4f379e0b9f79e4aef4ed663cf1eb7","target":"graph","created_at":"2026-07-05T05:53:24Z","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/2303.12010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number of ways that each face of the CW complex can be colored with one of $n$ colors so that no two adjacent faces have the same color. We use these homologies to define new invariants of graphs, give new characterizations of well-known polynomial invariants of graphs, and rephrase and offer new approaches to famous conjectures about graph coloring. In particular,","authors_text":"Ben McCarty, Scott Baldridge","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-03-21T16:47:00Z","title":"A topological quantum field theory approach to graph coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12010","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":"sha256:7f41ce648eba3c845a6ce32906cbb2078a45c844c8b5951bafa6daadf0f978ed","target":"record","created_at":"2026-07-05T05:53:24Z","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":"7bf40b770afcee8b83e5ccda360bd58d10769806858512b5358c1ef95f7545ab","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-03-21T16:47:00Z","title_canon_sha256":"66fb818fdb340d8004d55faaa0923e8ef3b4597d8da599d6541d400c30bd2188"},"schema_version":"1.0","source":{"id":"2303.12010","kind":"arxiv","version":1}},"canonical_sha256":"e88fe9a40811a3cd12ea1ce75fca14fbdf5e282abd0934ade91f2d44d07d6310","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e88fe9a40811a3cd12ea1ce75fca14fbdf5e282abd0934ade91f2d44d07d6310","first_computed_at":"2026-07-05T05:53:24.467486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:53:24.467486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1qwc+mNDFrbLtwdsJQVoWxjxMqmBbDg8utNFp2IxiHBTKhh2qF20rp0rYC88YsnJmKmlcc5YqkBzX4sR8i2TBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:53:24.467900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.12010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f41ce648eba3c845a6ce32906cbb2078a45c844c8b5951bafa6daadf0f978ed","sha256:6e8a0433669717c53958b9fe9a753871bbc4f379e0b9f79e4aef4ed663cf1eb7"],"state_sha256":"48e90e186ad02e88bd8413bee1b7da8831d288aa4e6d8dca2207b1b29cc81db4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9X3vz46pQpQrq24FhAUVYgG2oWdAM8hTCLIMkmTaKy2I8VvpcDu0d3lSB8dEqFfKHelgiqeBdUJqsApzReaFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T18:43:17.310984Z","bundle_sha256":"1bf244049c1abbc9ca45d09b9f04db2391a08fb13807d4e4908aa7bb399925c5"}}