{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3FDOQISFBBCTALEQSN32DBGHLA","short_pith_number":"pith:3FDOQISF","schema_version":"1.0","canonical_sha256":"d946e822450845302c909377a184c75804b145137ad0cd325d520a5639907568","source":{"kind":"arxiv","id":"1210.5678","version":1},"attestation_state":"computed","paper":{"title":"Coverings of small categories and nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Kazunori Noguchi","submitted_at":"2012-10-21T02:56:00Z","abstract_excerpt":"We prove a certain proposition which states a relationship between coverings of small categories and nerves. As its application, we prove that for a covering $\\map{P}{E}{B}$ of finite categories, the zeta function of $E$ is the zeta function of $B$ to the number of sheet of $P$. Moreover, we prove the formula $\\chi(E)=\\chi(F)\\chi(B)$ for Euler characteristic of categories and coverings."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.5678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-10-21T02:56:00Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"9b63caff6224fde57478f06fa7b820b59067b01293eb31c35582f0732cbd5059","abstract_canon_sha256":"f14c08e1a132a3bd622380330f4535f0653a0afcae16b66d70d76d2c2cebd58a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:43.342446Z","signature_b64":"ek7M1TieKCcG6XLhZjkofyT22NfgHvq2ZrWKKDx4T8N8/8c+qk0+r0eb85oHpuswyj7cWbwfpY2+gjO1qiviBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d946e822450845302c909377a184c75804b145137ad0cd325d520a5639907568","last_reissued_at":"2026-05-18T03:42:43.341912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:43.341912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coverings of small categories and nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Kazunori Noguchi","submitted_at":"2012-10-21T02:56:00Z","abstract_excerpt":"We prove a certain proposition which states a relationship between coverings of small categories and nerves. As its application, we prove that for a covering $\\map{P}{E}{B}$ of finite categories, the zeta function of $E$ is the zeta function of $B$ to the number of sheet of $P$. Moreover, we prove the formula $\\chi(E)=\\chi(F)\\chi(B)$ for Euler characteristic of categories and coverings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5678","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.5678","created_at":"2026-05-18T03:42:43.341994+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5678v1","created_at":"2026-05-18T03:42:43.341994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5678","created_at":"2026-05-18T03:42:43.341994+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FDOQISFBBCT","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FDOQISFBBCTALEQ","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FDOQISF","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA","json":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA.json","graph_json":"https://pith.science/api/pith-number/3FDOQISFBBCTALEQSN32DBGHLA/graph.json","events_json":"https://pith.science/api/pith-number/3FDOQISFBBCTALEQSN32DBGHLA/events.json","paper":"https://pith.science/paper/3FDOQISF"},"agent_actions":{"view_html":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA","download_json":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA.json","view_paper":"https://pith.science/paper/3FDOQISF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5678&json=true","fetch_graph":"https://pith.science/api/pith-number/3FDOQISFBBCTALEQSN32DBGHLA/graph.json","fetch_events":"https://pith.science/api/pith-number/3FDOQISFBBCTALEQSN32DBGHLA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA/action/storage_attestation","attest_author":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA/action/author_attestation","sign_citation":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA/action/citation_signature","submit_replication":"https://pith.science/pith/3FDOQISFBBCTALEQSN32DBGHLA/action/replication_record"}},"created_at":"2026-05-18T03:42:43.341994+00:00","updated_at":"2026-05-18T03:42:43.341994+00:00"}