{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HJZRQCFNL5XD2PFFR6TJEP7OUC","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":"92c16a1a9a6184ab0ccf051b4ce101fda9dbfa96aa30df6f8849c0976b77b04b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-24T20:09:52Z","title_canon_sha256":"8069b5c5551b8f9e5a077d433eb6181a6679cd9268fdd0df902fb9482ec9b929"},"schema_version":"1.0","source":{"id":"1212.5961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5961","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5961v1","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5961","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"HJZRQCFNL5XD","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HJZRQCFNL5XD2PFF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HJZRQCFN","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:968b486a70c1cdd227629063961a79cb360aa4ecdd4a381fac1b05f61cee8773","target":"graph","created_at":"2026-05-18T03:07:44Z","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 Bollobas-Riordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial and its contraction/deletion rule for ordinary graphs to ribbon graphs. Given a ribbon graph $\\cG$, the related polynomial should be computable from the knowledge of the terminal forms of $\\cG$ namely specific induced graphs for which the contraction/deletion procedure becomes more involved. We consider some classes of terminal forms as rosette ribbon graphs with $N\\ge 1$ petals and solve their associate Bollobas-Riordan polynomial. This work therefore enlarges the list of terminal forms for ribbon graphs ","authors_text":"Etera R. Livine, Joseph Ben Geloun, Remi C. Avohou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-24T20:09:52Z","title":"On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5961","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:ee4fd3227cbbe519da0cf650171fad30f50407bcfa2fdf4ca229248fa2ab8463","target":"record","created_at":"2026-05-18T03:07:44Z","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":"92c16a1a9a6184ab0ccf051b4ce101fda9dbfa96aa30df6f8849c0976b77b04b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-24T20:09:52Z","title_canon_sha256":"8069b5c5551b8f9e5a077d433eb6181a6679cd9268fdd0df902fb9482ec9b929"},"schema_version":"1.0","source":{"id":"1212.5961","kind":"arxiv","version":1}},"canonical_sha256":"3a731808ad5f6e3d3ca58fa6923feea0a5211466a08a17bbed7ea520cf19fdaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a731808ad5f6e3d3ca58fa6923feea0a5211466a08a17bbed7ea520cf19fdaf","first_computed_at":"2026-05-18T03:07:44.494576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:44.494576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/L2vdCJ/GbdvrDneA6yFGtG+aM+SNAn6j4wbq7iH7xNgSAJtOw0MXxlJGI86UgMsAjsqM6y2zEVMgGlwq3lXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:44.495133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee4fd3227cbbe519da0cf650171fad30f50407bcfa2fdf4ca229248fa2ab8463","sha256:968b486a70c1cdd227629063961a79cb360aa4ecdd4a381fac1b05f61cee8773"],"state_sha256":"86f2d3f601b9701e86a57a8e55244083c2abcea71ea3db0bd7782130a2bc26ca"}