{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:YYX4AGHINGF4AB5C3AJBVAIII3","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":"07f72aa1f034810c3ad771d7576bfb373df81fae33ffd0f485c5bdf85338b328","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-05-16T06:51:20Z","title_canon_sha256":"db08808ccede553dae31370fb46ea63f152e1070ade1bf86b58f015e46d758a4"},"schema_version":"1.0","source":{"id":"0705.2284","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.2284","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"0705.2284v2","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2284","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"YYX4AGHINGF4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YYX4AGHINGF4AB5C","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YYX4AGHI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:03bbb59f5a5a662d0d6159082bb073f2cc49c08052a980b48c99a78129f42f4b","target":"graph","created_at":"2026-05-18T04:38:14Z","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":"The complexity of a graph can be obtained as a derivative of a variation of the zeta function or a partial derivative of its generalized characteristic polynomial evaluated at a point [\\textit{J. Combin. Theory Ser. B}, 74 (1998), pp. 408--410]. A similar result for the weighted complexity of weighted graphs was found using a determinant function [\\textit{J. Combin. Theory Ser. B}, 89 (2003), pp. 17--26]. In this paper, we consider the determinant function of two variables and discover a condition that the weighted complexity of a weighted graph is a partial derivative of the determinant funct","authors_text":"Dongseok Kim, Jaeun Lee, Young Soo Kwon","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-05-16T06:51:20Z","title":"The weighted complexity and the determinant functions of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2284","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:b1df480f0598d7075288d288650857df36945a5a3eb7620f3a1e6a2e3925874a","target":"record","created_at":"2026-05-18T04:38:14Z","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":"07f72aa1f034810c3ad771d7576bfb373df81fae33ffd0f485c5bdf85338b328","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-05-16T06:51:20Z","title_canon_sha256":"db08808ccede553dae31370fb46ea63f152e1070ade1bf86b58f015e46d758a4"},"schema_version":"1.0","source":{"id":"0705.2284","kind":"arxiv","version":2}},"canonical_sha256":"c62fc018e8698bc007a2d8121a810846c7b26c7cf21d563dfb50e37fa7167593","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c62fc018e8698bc007a2d8121a810846c7b26c7cf21d563dfb50e37fa7167593","first_computed_at":"2026-05-18T04:38:14.573832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:14.573832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sasMeIHdezwcQngCzMhWc1xN8h5lXDXBPwjYznUzG7FiQN3UYlRTsyrcEqsEqthzFR0Qh49XXVz/j8QQoEe6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:14.574372Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.2284","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1df480f0598d7075288d288650857df36945a5a3eb7620f3a1e6a2e3925874a","sha256:03bbb59f5a5a662d0d6159082bb073f2cc49c08052a980b48c99a78129f42f4b"],"state_sha256":"9a800df236b2b374c8622eb63b0e0732fe0bfad0598ecaa6ffadfc5f481a6e91"}