{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q5AX32CQPRPPNQQTAT4Y5OLCW3","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":"df0ca6cf2d5d742051f23686c1c6747b1917e6d697e526c6c336c2db9a51ac14","cross_cats_sorted":["math.CT","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-20T15:17:20Z","title_canon_sha256":"a5e422f6113d2a63b6e609bcace4897931c398059a2c4a9b0d82cd03fdf5a65f"},"schema_version":"1.0","source":{"id":"1508.05004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05004","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05004v1","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05004","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"pith_short_12","alias_value":"Q5AX32CQPRPP","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5AX32CQPRPPNQQT","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5AX32CQ","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:9e7d1e239f493dec6c2d55a444e18c425e91e93d0fcc47c78aa738a2293fef0b","target":"graph","created_at":"2026-05-18T01:32:09Z","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":"In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties. For each category $\\mathcal{C}$ of path-connected spaces having the unit disk as an object, we construct a category of $\\mathcal{C}$-coverings over a given space $X$ that embeds in the category of $\\pi_1(X,x_0)$-sets via the usual monodromy action on fibers. When $\\mathcal{C}$ is extended to its coreflective hull $\\mathscr{H}(\\mathcal{C})$, the resulting category of based $\\mathscr{H}(\\mathcal{C})$-co","authors_text":"Jeremy Brazas","cross_cats":["math.CT","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-20T15:17:20Z","title":"Generalized covering space theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05004","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":"sha256:3dad317b480933c49592f93df3a89a4fed0f7195a42afc540684629a7875f29a","target":"record","created_at":"2026-05-18T01:32:09Z","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":"df0ca6cf2d5d742051f23686c1c6747b1917e6d697e526c6c336c2db9a51ac14","cross_cats_sorted":["math.CT","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-20T15:17:20Z","title_canon_sha256":"a5e422f6113d2a63b6e609bcace4897931c398059a2c4a9b0d82cd03fdf5a65f"},"schema_version":"1.0","source":{"id":"1508.05004","kind":"arxiv","version":1}},"canonical_sha256":"87417de8507c5ef6c21304f98eb962b6e457b16393e7ecb9ee5a9929d28c4c0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87417de8507c5ef6c21304f98eb962b6e457b16393e7ecb9ee5a9929d28c4c0f","first_computed_at":"2026-05-18T01:32:09.977444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:09.977444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KPzYe4giyWbGSTQVJh7GjMmFQFARO+ZXgL2GbOwvfeNSCV03ZWyTXYj7F6IcWvGXWLxPzKlOKiOgd/0/bK6bBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:09.978203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dad317b480933c49592f93df3a89a4fed0f7195a42afc540684629a7875f29a","sha256:9e7d1e239f493dec6c2d55a444e18c425e91e93d0fcc47c78aa738a2293fef0b"],"state_sha256":"df43d50a52206e8f3e68a5d89f6bf9e1f350c9d79b479acc4ec1bae13c830eb5"}