{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:POHWN6Q3ED4VBFMFDHLIQ5LQL7","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":"cd3c7d1e139caff0c4804f294b202a466551b8e86a1e15343a8066d49e2d0420","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-03-28T02:01:05Z","title_canon_sha256":"09ec76766268e6fcf4e38bc1500d4ace785d2788c37a51a0a7fe17f558180188"},"schema_version":"1.0","source":{"id":"1203.6133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6133","created_at":"2026-05-18T03:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6133v3","created_at":"2026-05-18T03:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6133","created_at":"2026-05-18T03:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"POHWN6Q3ED4V","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"POHWN6Q3ED4VBFMF","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"POHWN6Q3","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:0b041c738023604fcf0f621a7a5dcada784143917dfc1b759135acf91eb39de3","target":"graph","created_at":"2026-05-18T03:55:58Z","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 define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when categories are finite groupoids, finite acyclic categories, categories with 2-objects and finite categories satisfying certain condition.","authors_text":"Kazunori Noguchi","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-03-28T02:01:05Z","title":"The zeta function of a finite category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6133","kind":"arxiv","version":3},"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:e39b7e6f693a3767aa43ec81ffa359940cadce4e691f9c1f8fe25f95a929f305","target":"record","created_at":"2026-05-18T03:55:58Z","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":"cd3c7d1e139caff0c4804f294b202a466551b8e86a1e15343a8066d49e2d0420","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-03-28T02:01:05Z","title_canon_sha256":"09ec76766268e6fcf4e38bc1500d4ace785d2788c37a51a0a7fe17f558180188"},"schema_version":"1.0","source":{"id":"1203.6133","kind":"arxiv","version":3}},"canonical_sha256":"7b8f66fa1b20f950958519d68875705fe0c32637b3f73eef64eca8719471bdde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b8f66fa1b20f950958519d68875705fe0c32637b3f73eef64eca8719471bdde","first_computed_at":"2026-05-18T03:55:58.743669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:58.743669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sLkF8NiahqEC2Zr2y6B69A0cfcEMMOtvmsFPuVoqIMxdswr7lS7fJTrRJTSAEfcCsEyDqtFEtgFAHuoij1SKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:58.744342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e39b7e6f693a3767aa43ec81ffa359940cadce4e691f9c1f8fe25f95a929f305","sha256:0b041c738023604fcf0f621a7a5dcada784143917dfc1b759135acf91eb39de3"],"state_sha256":"9c0685352a5e96059f284d4cad698b469ee9fa9f3dba00efd9df15f58a2a2b45"}