{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EG5D2CY57NKB4UTKCHVUJM2WYX","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":"89164ca29171f21f098d643bd2ec5eba92e5f3486af18dbd54b8993b0d89ec6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-01-27T11:50:19Z","title_canon_sha256":"c3e74ba4ec7f0e8f2af080802dea181e9fc0401c8796a3f003a37071cf833c4c"},"schema_version":"1.0","source":{"id":"1801.09075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09075","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09075v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09075","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"EG5D2CY57NKB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EG5D2CY57NKB4UTK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EG5D2CY5","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:935412ea8d669347c52d1221d8f710e05ae68964ed2663ca0d9ac2b2162243b3","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described by a system of inequalities. Also, the relation between Yamada polynomial of graphs and the chain polynomial of edge-labelled graphs is obtained.","authors_text":"Andrei Vesnin, Fengchun Lei, Fengling Li, Miaowang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-01-27T11:50:19Z","title":"On Yamada polynomial of spatial graphs obtained by edge replacements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09075","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":"sha256:5fa6e9b42d774630a5d9908aa0cfbf487895f2d1d27e7237b53694c20b9e1137","target":"record","created_at":"2026-05-18T00:24:58Z","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":"89164ca29171f21f098d643bd2ec5eba92e5f3486af18dbd54b8993b0d89ec6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-01-27T11:50:19Z","title_canon_sha256":"c3e74ba4ec7f0e8f2af080802dea181e9fc0401c8796a3f003a37071cf833c4c"},"schema_version":"1.0","source":{"id":"1801.09075","kind":"arxiv","version":1}},"canonical_sha256":"21ba3d0b1dfb541e526a11eb44b356c5cb47222c07c109d488092a74c1a5dc75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21ba3d0b1dfb541e526a11eb44b356c5cb47222c07c109d488092a74c1a5dc75","first_computed_at":"2026-05-18T00:24:58.705401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.705401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfHvse40dibbmWMo1g35wvio2Vew+Y5wHQ2Gx5ayaCLIJtbFSGqZXKeYcgfhmh5ic8cR7Jlwr85XKkuDAEn5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.706164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa6e9b42d774630a5d9908aa0cfbf487895f2d1d27e7237b53694c20b9e1137","sha256:935412ea8d669347c52d1221d8f710e05ae68964ed2663ca0d9ac2b2162243b3"],"state_sha256":"64f61d55b96a2c9206dbf132e398c670e7b5916dc1ec4ebe6adad5203f27c3c7"}