{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XKLEXWKRWHVYX25TO57HJUSXY2","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":"47a327cac45c560a04a3cca5903ba03721f793da6b17ea812b9e030c34a139e4","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-20T16:30:22Z","title_canon_sha256":"f7e55affd246b149940fa33db4c2cfea8406eb44c774345d513cb823e338a31a"},"schema_version":"1.0","source":{"id":"1110.4573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4573","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4573v2","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4573","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"XKLEXWKRWHVY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XKLEXWKRWHVYX25T","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XKLEXWKR","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:71b1b9f72287a8af33802bdf5d3aedcf321f54e77e3f459aaef7ebbea492a29b","target":"graph","created_at":"2026-05-18T04:09:45Z","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":"Let G be a graph cellularly embedded in a surface S. Given two closed walks c and d in G, we take advantage of the RAM model to describe linear time algorithms to decide if c and d are homotopic in S, either freely or with fixed basepoint. We restrict S to be orientable for the free homotopy test, but allow non-orientable surfaces when the basepoint is fixed. After O(|G|) time preprocessing independent of c and d, our algorithms answer the homotopy test in O(|c|+|d|) time, where |G|, |c| and |d| are the respective numbers of edges of G, c and d. As a byproduct we obtain linear time algorithms ","authors_text":"Francis Lazarus, Julien Rivaud","cross_cats":["cs.DM","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-20T16:30:22Z","title":"On the homotopy test on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4573","kind":"arxiv","version":2},"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":"sha256:3dc90f44fb265ea420b7e5b818dca640c7ae987463e79a1a86ea2dd05aaaa506","target":"record","created_at":"2026-05-18T04:09:45Z","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":"47a327cac45c560a04a3cca5903ba03721f793da6b17ea812b9e030c34a139e4","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-20T16:30:22Z","title_canon_sha256":"f7e55affd246b149940fa33db4c2cfea8406eb44c774345d513cb823e338a31a"},"schema_version":"1.0","source":{"id":"1110.4573","kind":"arxiv","version":2}},"canonical_sha256":"ba964bd951b1eb8bebb3777e74d257c68042bea058ee801165cfd6645b85e5bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba964bd951b1eb8bebb3777e74d257c68042bea058ee801165cfd6645b85e5bd","first_computed_at":"2026-05-18T04:09:45.415502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:45.415502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ezrfNJ1YnlQr5ctIf3W/RHOl+qk5O1J7E+huoneKvvt1j5XDn3bvW0bvUGpXjL6ZXKln6y38RjyYI50TDETzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:45.415921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dc90f44fb265ea420b7e5b818dca640c7ae987463e79a1a86ea2dd05aaaa506","sha256:71b1b9f72287a8af33802bdf5d3aedcf321f54e77e3f459aaef7ebbea492a29b"],"state_sha256":"6601c092dc2d75ca421abe098edf5bd7249bfa04b61207e9c86e6b34e75c0545"}