{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HZ44XI7U4VHEFOBSF3CDR4YFNY","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":"f30f1db647e50f9f1da1151428939c9352ea62883af441dc1883d5b3509bc74e","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-15T06:51:40Z","title_canon_sha256":"9018165e2ce9c98da512386393de01b0cc74f2530ad7ff403e97c2033dd6aa33"},"schema_version":"1.0","source":{"id":"1703.04969","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04969","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04969v3","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04969","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"pith_short_12","alias_value":"HZ44XI7U4VHE","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HZ44XI7U4VHEFOBS","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HZ44XI7U","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:0fd421eecb1714b132bf567bedd68bbbae44fee4051099576b8d19b41da404da","target":"graph","created_at":"2026-05-18T00:45:06Z","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 a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighted zeta function of a graph. Our main results determine explicitly all the right eigenvalues of the quaternionic Szegedy walk by using complex right eigenvalues of the corresponding doubly weighted matrix","authors_text":"Hideo Mitsuhashi, Iwao Sato, Kaname Matsue, Norio Konno","cross_cats":["math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-15T06:51:40Z","title":"Quaternionic quantum walks of Szegedy type and zeta functions of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04969","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:c7849d50adf55569d1304db0561b45db9debef7c295a85b175c5e1f19663de3b","target":"record","created_at":"2026-05-18T00:45:06Z","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":"f30f1db647e50f9f1da1151428939c9352ea62883af441dc1883d5b3509bc74e","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-15T06:51:40Z","title_canon_sha256":"9018165e2ce9c98da512386393de01b0cc74f2530ad7ff403e97c2033dd6aa33"},"schema_version":"1.0","source":{"id":"1703.04969","kind":"arxiv","version":3}},"canonical_sha256":"3e79cba3f4e54e42b8322ec438f3056e2d21b70e043c8ef60cd2ff2acf5a65df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e79cba3f4e54e42b8322ec438f3056e2d21b70e043c8ef60cd2ff2acf5a65df","first_computed_at":"2026-05-18T00:45:06.077588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:06.077588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i40lsdaGBG4tptXItYbfEOIZM/0Xu8c80nRnVq7Wckm8h+H9avAxWS78qacim+9judZApBO58dY0wdfKv5zKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:06.078005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04969","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7849d50adf55569d1304db0561b45db9debef7c295a85b175c5e1f19663de3b","sha256:0fd421eecb1714b132bf567bedd68bbbae44fee4051099576b8d19b41da404da"],"state_sha256":"80b89d93d12ca8834fa6552da8ad2c23f33d8a6eabc20e7941c5b9702ebcc4bf"}