{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F25QFJA46TWYVD6GZW7XTMHYUY","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":"b4e2473c6e78a4d838b406fed8d74a75d68fa2f5d73e2ac71c2eb615180bff98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-28T07:23:37Z","title_canon_sha256":"46f30a9268fb97f5954f1083c56c28e2f246d6a10e03e6874271f83d7fdc9c00"},"schema_version":"1.0","source":{"id":"1508.07110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07110","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07110v2","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07110","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"F25QFJA46TWY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F25QFJA46TWYVD6G","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F25QFJA4","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:e05eafbf0a38732856a12b2fceb76f5372980082028bbe10e8387e7dd23abf93","target":"graph","created_at":"2026-05-18T00:09:10Z","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 the present paper, we define a notion of good coverings of Alexandrov spaces with curvature bounded below, and prove that every Alexandrov space admits such a good covering and that it has the same homotopy type as the nerve of the good covering. We also prove the stability of the isomorphism classes of the nerves of good coverings in the non-collapsing case. In the proof, we need a version of Perelman's fibration theorem, which is also proved in this paper.","authors_text":"Ayato Mitsuishi, Takao Yamaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-28T07:23:37Z","title":"Good coverings of Alexandrov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07110","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:c63d1cde53b1e2ef17acea41c340fd7567e72d16b148a062872fdfc92ff87909","target":"record","created_at":"2026-05-18T00:09:10Z","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":"b4e2473c6e78a4d838b406fed8d74a75d68fa2f5d73e2ac71c2eb615180bff98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-28T07:23:37Z","title_canon_sha256":"46f30a9268fb97f5954f1083c56c28e2f246d6a10e03e6874271f83d7fdc9c00"},"schema_version":"1.0","source":{"id":"1508.07110","kind":"arxiv","version":2}},"canonical_sha256":"2ebb02a41cf4ed8a8fc6cdbf79b0f8a616393cef3fec5773f3e39a02426de12e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ebb02a41cf4ed8a8fc6cdbf79b0f8a616393cef3fec5773f3e39a02426de12e","first_computed_at":"2026-05-18T00:09:10.504924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:10.504924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TzVSLh1R8K7xQBoP+s7zGBS5RKQGJAHsv7PLIOct8Ir9sTPGCYPqvbDzE3DWaIIzexD5ObGuLWIVgb4+5CaFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:10.505578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c63d1cde53b1e2ef17acea41c340fd7567e72d16b148a062872fdfc92ff87909","sha256:e05eafbf0a38732856a12b2fceb76f5372980082028bbe10e8387e7dd23abf93"],"state_sha256":"1320177ab4b4c0aa0f93862da357678d45aba75cafeb16192b703541dbac7891"}