{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:25FCGMZHVTD37YJLG7C5AAUSVV","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":"4783b086ddbabbe96a417fa971f84d7b3a434d95b33f155a7dba586629b19b96","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-12-07T16:50:53Z","title_canon_sha256":"7011e929ab3af4859d42f28e6d222239cafe626cbf8d7dd4d3e0b4ec917c7365"},"schema_version":"1.0","source":{"id":"0812.1364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.1364","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"0812.1364v1","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.1364","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"25FCGMZHVTD3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"25FCGMZHVTD37YJL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"25FCGMZH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:dc0ecd9cc01e5a85c32a528e818e52c33c4054c0b8f83307a7395c3e8476e4ce","target":"graph","created_at":"2026-05-18T03:13:58Z","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":"Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.","authors_text":"Benny Godlin, Emilia Katz, Johann A. Makowsky","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-12-07T16:50:53Z","title":"Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1364","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:e0e7b74f2b0d50acc2c663fa1cb799f4270f2f7cf6cf8986060c73390b980e3b","target":"record","created_at":"2026-05-18T03:13:58Z","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":"4783b086ddbabbe96a417fa971f84d7b3a434d95b33f155a7dba586629b19b96","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-12-07T16:50:53Z","title_canon_sha256":"7011e929ab3af4859d42f28e6d222239cafe626cbf8d7dd4d3e0b4ec917c7365"},"schema_version":"1.0","source":{"id":"0812.1364","kind":"arxiv","version":1}},"canonical_sha256":"d74a233327acc7bfe12b37c5d00292ad6a3626e6c12eb0c52ed08699fc093130","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d74a233327acc7bfe12b37c5d00292ad6a3626e6c12eb0c52ed08699fc093130","first_computed_at":"2026-05-18T03:13:58.666400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:58.666400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhRz/DAuMCdA70fir9oPLWcbP+Pj8t0RZXheM+54SiVlGe914WJOR2neauHM6YQHjKVLI8c8VIM7UnSbi8tRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:58.666959Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.1364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0e7b74f2b0d50acc2c663fa1cb799f4270f2f7cf6cf8986060c73390b980e3b","sha256:dc0ecd9cc01e5a85c32a528e818e52c33c4054c0b8f83307a7395c3e8476e4ce"],"state_sha256":"8e5885004096357020b1de89eb590841a30be8964f25d6da917c08ba231ad725"}