{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TAK6YTUSCSTA352BENN4T5H5KX","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":"53bd622ee1c2b0706c0fd6767d4e6640e4e5c9304ea6f0ef26ba5e359c4e4095","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-19T15:40:45Z","title_canon_sha256":"468f2203116656c3cb5bd29287b7aeb35d3f916918e0ae790b48213a1b09808a"},"schema_version":"1.0","source":{"id":"1807.07500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07500","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07500v1","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07500","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"TAK6YTUSCSTA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TAK6YTUSCSTA352B","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TAK6YTUS","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:d5dc2d80cd333237a4bb7fee815cc422ae90201799d3091f108f6aea56187533","target":"graph","created_at":"2026-05-18T00:10:20Z","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":"A k-valuation is a special type of edge k-colouring of a medial graph. Various graph polynomials, such as the Tutte, Penrose, Bollob\\'as-Riordan, and transition polynomials, admit combinatorial interpretations and evaluations as weighted counts of k-valuations. In this paper, we consider a multivariate generating function of k-valuations. We show that this is a polynomial in k and hence defines a graph polynomial. We then show that the resulting polynomial has several desirable properties, including a recursive deletion-contraction-type definition, and specialises to the graph polynomials ment","authors_text":"Iain Moffatt, Joanna A. Ellis-Monaghan, Louis H. Kauffman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-19T15:40:45Z","title":"Edge colourings and topological graph polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07500","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":"sha256:9f5242aee3b99d64ba10b4b44a0277d652084a6897c9f8242f27de4452e45090","target":"record","created_at":"2026-05-18T00:10:20Z","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":"53bd622ee1c2b0706c0fd6767d4e6640e4e5c9304ea6f0ef26ba5e359c4e4095","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-19T15:40:45Z","title_canon_sha256":"468f2203116656c3cb5bd29287b7aeb35d3f916918e0ae790b48213a1b09808a"},"schema_version":"1.0","source":{"id":"1807.07500","kind":"arxiv","version":1}},"canonical_sha256":"9815ec4e9214a60df741235bc9f4fd55e3f8b41099e0c575f6621e2b94848d5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9815ec4e9214a60df741235bc9f4fd55e3f8b41099e0c575f6621e2b94848d5c","first_computed_at":"2026-05-18T00:10:20.006890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:20.006890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HrVmab6Yjj3I7Ds9e/nB6AHwuS+c1LSxduXkcyTgtfbbLOFI7P7ebwvPymtoX/b0vj3ZvCD+E6FZxhzt47kRCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:20.007693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f5242aee3b99d64ba10b4b44a0277d652084a6897c9f8242f27de4452e45090","sha256:d5dc2d80cd333237a4bb7fee815cc422ae90201799d3091f108f6aea56187533"],"state_sha256":"dc4b7d8928549350858a4d1167110791fd1ae003e752828e9dc9d38e10d87f91"}