{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3Z6NZVLCMXRNBKVATLVL3H2UZJ","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":"c71376e52da364cd9655576a63a83d9e33b71a0c448f5925518da843f1c0d82d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-18T08:41:18Z","title_canon_sha256":"b5cc463f39e0b190c127634cefdc6a619073cbd7e21b62c15ee372e7f5a6ee38"},"schema_version":"1.0","source":{"id":"1412.5756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5756","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5756v2","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5756","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"pith_short_12","alias_value":"3Z6NZVLCMXRN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3Z6NZVLCMXRNBKVA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3Z6NZVLC","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:01ca24ec89fdf320d6a81d730a743da1d9237159f38e44c69f71b3243b2dbe0a","target":"graph","created_at":"2026-05-18T01:07:58Z","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":"This paper presents categorical structures on classical measure spaces and quantum measure spaces in order to deal with canonical maps associated with conditional measures as morphisms. We extend the Riesz-Markov-Kakutani representation theorem and the Gelfand duality theorem to an equivalence of categories between them. From this categorical viewpoint, we introduce a quantum version of conditional measures as a dual concept of the classical one.","authors_text":"Hitoshi Motoyama, Kohei Tanaka","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-18T08:41:18Z","title":"Classical and quantum conditional measures from a categorical viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5756","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:da3047f1072affb5e5d8035b2669d9802ef68c9a247681ca505701a92bd35fe5","target":"record","created_at":"2026-05-18T01:07:58Z","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":"c71376e52da364cd9655576a63a83d9e33b71a0c448f5925518da843f1c0d82d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-18T08:41:18Z","title_canon_sha256":"b5cc463f39e0b190c127634cefdc6a619073cbd7e21b62c15ee372e7f5a6ee38"},"schema_version":"1.0","source":{"id":"1412.5756","kind":"arxiv","version":2}},"canonical_sha256":"de7cdcd56265e2d0aaa09aeabd9f54ca59c17295a8f91478bfa69ef079e5d4b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de7cdcd56265e2d0aaa09aeabd9f54ca59c17295a8f91478bfa69ef079e5d4b4","first_computed_at":"2026-05-18T01:07:58.582244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:58.582244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4UkUDxa/Y7jw1GXBZFeU4NH+2xAC9ZgN9PJ080oFhp5cTcFZXlu6BlEZURHLa21RJNJc5Md+9zER3NvgHGTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:58.589357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da3047f1072affb5e5d8035b2669d9802ef68c9a247681ca505701a92bd35fe5","sha256:01ca24ec89fdf320d6a81d730a743da1d9237159f38e44c69f71b3243b2dbe0a"],"state_sha256":"ea57c9c83f1cbcce13ab1f5f537f70784d0019000b5f7d2db5c6847a8d79abff"}