{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LUAG6KSD65G6FT6W4EDQXZCJZJ","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":"97f7301b35510bd40625e29e0692a6bd9d86d4b4acec48bc06abec02c629a32a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-19T12:44:19Z","title_canon_sha256":"d39ba48c0fc093b6b0ee2025222f0b382ec613846efd568d8aa3705f1961c268"},"schema_version":"1.0","source":{"id":"1202.4150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4150","created_at":"2026-05-18T04:02:00Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4150v1","created_at":"2026-05-18T04:02:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4150","created_at":"2026-05-18T04:02:00Z"},{"alias_kind":"pith_short_12","alias_value":"LUAG6KSD65G6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LUAG6KSD65G6FT6W","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LUAG6KSD","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1ba253253025c15819760b32e2313407e55a3c50d466624032de92ab250077d6","target":"graph","created_at":"2026-05-18T04:02:00Z","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 Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps.","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":"2012-02-19T12:44:19Z","title":"Contractible Hamiltonian Cycles in Polyhedral Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4150","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":"sha256:759b432c0507bff880ceb3ba5b6aa84c375593212ebc18aa7209534a6850c77e","target":"record","created_at":"2026-05-18T04:02:00Z","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":"97f7301b35510bd40625e29e0692a6bd9d86d4b4acec48bc06abec02c629a32a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-19T12:44:19Z","title_canon_sha256":"d39ba48c0fc093b6b0ee2025222f0b382ec613846efd568d8aa3705f1961c268"},"schema_version":"1.0","source":{"id":"1202.4150","kind":"arxiv","version":1}},"canonical_sha256":"5d006f2a43f74de2cfd6e1070be449ca582d8f804c9cfe7310df4b1f43aef744","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d006f2a43f74de2cfd6e1070be449ca582d8f804c9cfe7310df4b1f43aef744","first_computed_at":"2026-05-18T04:02:00.086618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:00.086618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i5JHSX66rM6asmvf3DNQQS6Gg8wskM1rjdZU/cEPpZ2qOPwG2VCugbVjYuA2fc9Vddg5tNMcFSDwTTjPVm1NDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:00.087485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:759b432c0507bff880ceb3ba5b6aa84c375593212ebc18aa7209534a6850c77e","sha256:1ba253253025c15819760b32e2313407e55a3c50d466624032de92ab250077d6"],"state_sha256":"4b6ed1b7db976232d35bd828abf751c62fa0179747bfb266eb21b8cdfff6c100"}