{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C5WWCVXAAQMQMRTEIMZSCSCD5C","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":"f60c6888cd7b3be74c2311fa530f4d2cfa55fe133604bab8f7500ce3baea72fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T13:53:57Z","title_canon_sha256":"a42a734fde70ddf8c4c9c3ca505507bf0bcd73b9af5cd57fef38773f5e7e428f"},"schema_version":"1.0","source":{"id":"1601.07760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07760","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07760v2","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07760","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"C5WWCVXAAQMQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C5WWCVXAAQMQMRTE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C5WWCVXA","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:69f4e8afd05fb53b696a37516cbae0c4b47e12daa25ad46315375561189a3a18","target":"graph","created_at":"2026-05-18T01:17:59Z","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 establish a generalization of the second weighted zeta function of a graph to the case of quaternions. For an arc-weighted graph whose weights are quaternions, we define the second weighted zeta function by using the Study determinant that is a quaternionic determinant for quaternionic matrices defined by Study. This definition is regarded as a quaternionic analogue of the determinant expression of Hashimoto type for the Ihara zeta function of a graph. We derive the Study determinant expression of Bass type and the Euler product for the quaternionic second weighted zeta function.","authors_text":"Hideo Mitsuhashi, Iwao Sato, Norio Konno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T13:53:57Z","title":"The quaternionic second weighted zeta function of a graph and the Study determinant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07760","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":"sha256:7cdc43bdbef764210fc7addea92bbb046942f7cf7843d2930b9af2c0d1c30698","target":"record","created_at":"2026-05-18T01:17:59Z","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":"f60c6888cd7b3be74c2311fa530f4d2cfa55fe133604bab8f7500ce3baea72fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T13:53:57Z","title_canon_sha256":"a42a734fde70ddf8c4c9c3ca505507bf0bcd73b9af5cd57fef38773f5e7e428f"},"schema_version":"1.0","source":{"id":"1601.07760","kind":"arxiv","version":2}},"canonical_sha256":"176d6156e004190646644333214843e896c2b11d7477f6e3d00bc910518ad11a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"176d6156e004190646644333214843e896c2b11d7477f6e3d00bc910518ad11a","first_computed_at":"2026-05-18T01:17:59.296594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:59.296594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qaHKzj3txSQKFAb14PC4cRlYdbmybtRWOyhKfR95+QNmNNYam4vQJMy8UlPkbrXVTeU7gWhz91a6Hf7D/KRFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:59.297274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cdc43bdbef764210fc7addea92bbb046942f7cf7843d2930b9af2c0d1c30698","sha256:69f4e8afd05fb53b696a37516cbae0c4b47e12daa25ad46315375561189a3a18"],"state_sha256":"da81370ac5375f666ade73aec24333636eca98b24813b9db2aaf9727564eb4d1"}