{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CDBOVNW7TMN2BQMZX5YCKNLHOU","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":"0bf97ed7597167c2dcea237a78441d5c1224e98044735612a884eff848ab05fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-02T01:15:49Z","title_canon_sha256":"20c98520858e72ba0c274d4c0d74c3c912090e6a84447e78987b7673c851b653"},"schema_version":"1.0","source":{"id":"1612.00532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00532","created_at":"2026-05-18T00:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00532v1","created_at":"2026-05-18T00:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00532","created_at":"2026-05-18T00:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"CDBOVNW7TMN2","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CDBOVNW7TMN2BQMZ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CDBOVNW7","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:0de196e5066227a05a63d695e6a0463c589b88d9e882d99567420c7a8a701a97","target":"graph","created_at":"2026-05-18T00:55:59Z","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 introduce the notion of the \"covering type\" of a space, which is more subtle that the notion of Lusternik Schnirelman category. It measures the complexity of a space which arises from coverings by contractible subspaces whose non-empty intersections are also contractible.","authors_text":"Charles Weibel, Max Karoubi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-02T01:15:49Z","title":"On the covering type of a space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00532","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:e194766f6177876c3d536eccf4b38aab798b9dc0055234957bd8b0620f0e154a","target":"record","created_at":"2026-05-18T00:55:59Z","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":"0bf97ed7597167c2dcea237a78441d5c1224e98044735612a884eff848ab05fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-02T01:15:49Z","title_canon_sha256":"20c98520858e72ba0c274d4c0d74c3c912090e6a84447e78987b7673c851b653"},"schema_version":"1.0","source":{"id":"1612.00532","kind":"arxiv","version":1}},"canonical_sha256":"10c2eab6df9b1ba0c199bf70253567753fc84bc4f49afc951a43f2291838ccc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10c2eab6df9b1ba0c199bf70253567753fc84bc4f49afc951a43f2291838ccc7","first_computed_at":"2026-05-18T00:55:59.754892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:59.754892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3sUEUD+VZh96lNkCcsPXZhePMPHifP0XGaO9554TeS3ZgHxI+wo8BzBmpcd7DWnfdda3yYE+j1NPjDYl0wRoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:59.755450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e194766f6177876c3d536eccf4b38aab798b9dc0055234957bd8b0620f0e154a","sha256:0de196e5066227a05a63d695e6a0463c589b88d9e882d99567420c7a8a701a97"],"state_sha256":"7484f96f0655e8b3426707b8e03036083898779038f74711ed9ffb3eaff56af1"}