{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VZFJMBCTAO4IH6JKGXWKTY4AP5","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":"a7f41aa54b7e22d7d14900ad7680a30c7c1c2c7f9eb833e9b76169041ddc964a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-07T13:17:31Z","title_canon_sha256":"0840eeae6fdc91c2875d45e5f28b3270c0b618b46f9ea7ffb4bf282d3f05face"},"schema_version":"1.0","source":{"id":"1405.1599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1599","created_at":"2026-05-18T02:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1599v1","created_at":"2026-05-18T02:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1599","created_at":"2026-05-18T02:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"VZFJMBCTAO4I","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VZFJMBCTAO4IH6JK","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VZFJMBCT","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:7634f6451aa6704cddbf259091ddd33f5d04dfd4f8674c2618ae6f5cc79ab87a","target":"graph","created_at":"2026-05-18T02:52:24Z","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 a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an algorithm to construct such cycles whenever it exists.","authors_text":"Ashish Kumar Upadhyay, Dipendu Maity","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-07T13:17:31Z","title":"Hamiltonian Cycles in Polyhedral Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1599","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":"sha256:9550169a03af4258f676fda896738815ed3725827d8c82147b0dbac2e9393dfd","target":"record","created_at":"2026-05-18T02:52:24Z","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":"a7f41aa54b7e22d7d14900ad7680a30c7c1c2c7f9eb833e9b76169041ddc964a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-07T13:17:31Z","title_canon_sha256":"0840eeae6fdc91c2875d45e5f28b3270c0b618b46f9ea7ffb4bf282d3f05face"},"schema_version":"1.0","source":{"id":"1405.1599","kind":"arxiv","version":1}},"canonical_sha256":"ae4a96045303b883f92a35eca9e3807f5da16541f6dae369661e50bc27f5ad2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae4a96045303b883f92a35eca9e3807f5da16541f6dae369661e50bc27f5ad2b","first_computed_at":"2026-05-18T02:52:24.391959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:24.391959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rERIVQggDjwzHoFoglkh+MtxKcC4b1NZhkZXPnWzJowcOne8nmd5lvQ9p5wj9Mm/8S+iKgeEMxzRFbt/516uCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:24.392656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9550169a03af4258f676fda896738815ed3725827d8c82147b0dbac2e9393dfd","sha256:7634f6451aa6704cddbf259091ddd33f5d04dfd4f8674c2618ae6f5cc79ab87a"],"state_sha256":"753a041d89156af266fda5d5a8a43e0d69588b7bb1dcc144711a865251a5297f"}