{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SEAN7LM5I4MS7ANYNPQF3D4WHS","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":"7cf45cfd99fd1b67b998ae66602df84ae67e8ed9765f579a718ce56ebb530734","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-20T13:21:58Z","title_canon_sha256":"56f95c5ed6595c8418b2fec9171c91be1ab3002d2b2e781c45427339932c9e89"},"schema_version":"1.0","source":{"id":"1406.5376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5376","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5376v1","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5376","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"SEAN7LM5I4MS","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SEAN7LM5I4MS7ANY","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SEAN7LM5","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:e70a68cac52de1a7e1d4431a68853311fbe058806a3bdff78a983eaeaedc4c20","target":"graph","created_at":"2026-05-18T02:49:19Z","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":"Given a $c$-edge-coloured multigraph, a proper Hamiltonian path is a path that contains all the vertices of the multigraph such that no two adjacent edges have the same colour. In this work we establish sufficient conditions for an edge-coloured multigraph to guarantee the existence of a proper Hamiltonian path, involving various parameters as the number of edges, the number of colours, the rainbow degree and the connectivity.","authors_text":"Gervais Mendy, Leandro Montero, Marina Groshaus, Raquel \\'Agueda, Valentin Borozan, Yannis Manoussakis","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-20T13:21:58Z","title":"Proper Hamiltonian Paths in Edge-Coloured Multigraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5376","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:c02089272c997dd11cb4cfa7b5cc0bb02b13c35d1122b5821e2796cdd9eb33a7","target":"record","created_at":"2026-05-18T02:49:19Z","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":"7cf45cfd99fd1b67b998ae66602df84ae67e8ed9765f579a718ce56ebb530734","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-20T13:21:58Z","title_canon_sha256":"56f95c5ed6595c8418b2fec9171c91be1ab3002d2b2e781c45427339932c9e89"},"schema_version":"1.0","source":{"id":"1406.5376","kind":"arxiv","version":1}},"canonical_sha256":"9100dfad9d47192f81b86be05d8f963c906ba3058824d1a74b3e0ca22453e6fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9100dfad9d47192f81b86be05d8f963c906ba3058824d1a74b3e0ca22453e6fd","first_computed_at":"2026-05-18T02:49:19.240371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:19.240371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"08eh6kvc9Qz3dWC9mBICrydsgf33OGt/XgAabJN0lGMi5aJEYc7kZm65SCWXbtipe280bigWrPLlwW1bhF/zCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:19.240964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c02089272c997dd11cb4cfa7b5cc0bb02b13c35d1122b5821e2796cdd9eb33a7","sha256:e70a68cac52de1a7e1d4431a68853311fbe058806a3bdff78a983eaeaedc4c20"],"state_sha256":"5df54aa247d3f95645c3e8b20b895acbd2a42a6c407393282fc95f49d3668267"}