{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:I6V7FP67PWVXIJR7O7KQPZENQB","short_pith_number":"pith:I6V7FP67","schema_version":"1.0","canonical_sha256":"47abf2bfdf7dab74263f77d507e48d805da64c2aa61480510a77d19c5c936517","source":{"kind":"arxiv","id":"1508.03688","version":1},"attestation_state":"computed","paper":{"title":"\\v{C}ech complexes for covers of small categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Kohei Tanaka","submitted_at":"2015-08-15T02:59:44Z","abstract_excerpt":"We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion principle for the Euler characteristic of a finite category."},"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":"1508.03688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-08-15T02:59:44Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"9316e9e2a87315d71d02974c3df95149de005392435ed58e624d7a8a03a38d41","abstract_canon_sha256":"c9bb4bd2a45a2f2a3d100a2e1698c7a7720cdcdc1c68c0ece850ce6bd7cb1a11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:15.428972Z","signature_b64":"15OxSINUN3YKwMEfEHeblUW+P7hiwBXlWHo/GhOxpBzqDKclappRSzg9niqnx8so+5ppJMPGsp55x9TD++PKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47abf2bfdf7dab74263f77d507e48d805da64c2aa61480510a77d19c5c936517","last_reissued_at":"2026-05-18T01:35:15.428564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:15.428564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"\\v{C}ech complexes for covers of small categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Kohei Tanaka","submitted_at":"2015-08-15T02:59:44Z","abstract_excerpt":"We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion principle for the Euler characteristic of a finite category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03688","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":"1508.03688","created_at":"2026-05-18T01:35:15.428619+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03688v1","created_at":"2026-05-18T01:35:15.428619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03688","created_at":"2026-05-18T01:35:15.428619+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6V7FP67PWVX","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6V7FP67PWVXIJR7","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6V7FP67","created_at":"2026-05-18T12:29:25.134429+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/I6V7FP67PWVXIJR7O7KQPZENQB","json":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB.json","graph_json":"https://pith.science/api/pith-number/I6V7FP67PWVXIJR7O7KQPZENQB/graph.json","events_json":"https://pith.science/api/pith-number/I6V7FP67PWVXIJR7O7KQPZENQB/events.json","paper":"https://pith.science/paper/I6V7FP67"},"agent_actions":{"view_html":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB","download_json":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB.json","view_paper":"https://pith.science/paper/I6V7FP67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03688&json=true","fetch_graph":"https://pith.science/api/pith-number/I6V7FP67PWVXIJR7O7KQPZENQB/graph.json","fetch_events":"https://pith.science/api/pith-number/I6V7FP67PWVXIJR7O7KQPZENQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB/action/storage_attestation","attest_author":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB/action/author_attestation","sign_citation":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB/action/citation_signature","submit_replication":"https://pith.science/pith/I6V7FP67PWVXIJR7O7KQPZENQB/action/replication_record"}},"created_at":"2026-05-18T01:35:15.428619+00:00","updated_at":"2026-05-18T01:35:15.428619+00:00"}