{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZJ63TR3EVVRMGKTWEMMGROFJ3P","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":"a779f5f70227da505ba5ec47340270127da0c511bc15fae9ed56b82459ee599e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-04T23:59:15Z","title_canon_sha256":"1761f9758e9229fdcade92008926653ec9348d8fe8db66ac94e8101ddb0c4b81"},"schema_version":"1.0","source":{"id":"1907.02624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02624","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02624v1","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02624","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ63TR3EVVRM","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ63TR3EVVRMGKTW","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ63TR3E","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:d3adc8fabdb74372bc68f8f03ed11891bf0d35b5e2c13cfd3cfa4927b9a87de7","target":"graph","created_at":"2026-05-17T23:41:23Z","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 summarize several results about the regular coverings and the fundamental groupoids of Alexandroff spaces. In particular, we show that the fundamental groupoid of an Alexandroff space $X$ is naturally isomorphic to the localization, at its set of morphisms, of the thin category associated to the set $X$ considered as a preordered set with the specialization preorder. We also show that the regular coverings of an Alexandroff space $X$ are represented by certain morphism-inverting functors with domain $X$, extending a result of E. Minian and J. Barmak about the regular coverings of locally fi","authors_text":"Nicol\\'as Cianci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-04T23:59:15Z","title":"Regular coverings and fundamental groupoids of Alexandroff spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02624","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":"sha256:104b078ed01eae2c9a5a2f634e13823bf0d2bdd54daabf5221224c9aaa33a31f","target":"record","created_at":"2026-05-17T23:41:23Z","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":"a779f5f70227da505ba5ec47340270127da0c511bc15fae9ed56b82459ee599e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-07-04T23:59:15Z","title_canon_sha256":"1761f9758e9229fdcade92008926653ec9348d8fe8db66ac94e8101ddb0c4b81"},"schema_version":"1.0","source":{"id":"1907.02624","kind":"arxiv","version":1}},"canonical_sha256":"ca7db9c764ad62c32a76231868b8a9dbe4fd1ff4e529ecf5cfb4c22d6fbce7c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7db9c764ad62c32a76231868b8a9dbe4fd1ff4e529ecf5cfb4c22d6fbce7c4","first_computed_at":"2026-05-17T23:41:23.726954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:23.726954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucKK3o39AgDDeoLvgiEiR32UsuRiyqd7L930GDH2CHqAPM8kEWBunFWmO4ZOjG9ySAow+P6HomFvysIwAkbgCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:23.727796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:104b078ed01eae2c9a5a2f634e13823bf0d2bdd54daabf5221224c9aaa33a31f","sha256:d3adc8fabdb74372bc68f8f03ed11891bf0d35b5e2c13cfd3cfa4927b9a87de7"],"state_sha256":"2b631b83d33403ae056adef3a642d150fd8c67a41e83afd2bfeb0b8300bf829c"}