{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4TS2RCMQQGMLNUN4YDBA5W5FMO","short_pith_number":"pith:4TS2RCMQ","schema_version":"1.0","canonical_sha256":"e4e5a889908198b6d1bcc0c20edba563ba006d0309fd470774d0c23972787b99","source":{"kind":"arxiv","id":"1205.1488","version":3},"attestation_state":"computed","paper":{"title":"A categorical foundation for Bayesian probability","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CT","authors_text":"Jared Culbertson, Kirk Sturtz","submitted_at":"2012-05-07T19:35:39Z","abstract_excerpt":"Given two measurable spaces $H$ and $D$ with countably generated $\\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \\rightarrow D$, there is a corresponding inference map $I: D \\rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\\mu: 1 \\rightarrow D$, a posterior probability $\\widehat{P_H}= I \\circ \\mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additio"},"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":"1205.1488","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CT","submitted_at":"2012-05-07T19:35:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"99bfebfe4d14340744e189154415f822db29f252d6fb7aa5eecab2bbc828d64e","abstract_canon_sha256":"440a4a505950916641d6a38dde6cb9f3fa10f68a468316a365f20509d48fa205"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.587790Z","signature_b64":"TkElf9EmQPJv70J34pVb6p8aiRXqllJ9w5j+u/lQoO/GtggWJHte9Hr3EgFLPItyP4UuMu1n0tAGPaSHk9KEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4e5a889908198b6d1bcc0c20edba563ba006d0309fd470774d0c23972787b99","last_reissued_at":"2026-05-18T00:08:05.587350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.587350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A categorical foundation for Bayesian probability","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CT","authors_text":"Jared Culbertson, Kirk Sturtz","submitted_at":"2012-05-07T19:35:39Z","abstract_excerpt":"Given two measurable spaces $H$ and $D$ with countably generated $\\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \\rightarrow D$, there is a corresponding inference map $I: D \\rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\\mu: 1 \\rightarrow D$, a posterior probability $\\widehat{P_H}= I \\circ \\mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1488","kind":"arxiv","version":3},"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":"1205.1488","created_at":"2026-05-18T00:08:05.587437+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1488v3","created_at":"2026-05-18T00:08:05.587437+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1488","created_at":"2026-05-18T00:08:05.587437+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TS2RCMQQGML","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TS2RCMQQGMLNUN4","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TS2RCMQ","created_at":"2026-05-18T12:26:53.410803+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/4TS2RCMQQGMLNUN4YDBA5W5FMO","json":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO.json","graph_json":"https://pith.science/api/pith-number/4TS2RCMQQGMLNUN4YDBA5W5FMO/graph.json","events_json":"https://pith.science/api/pith-number/4TS2RCMQQGMLNUN4YDBA5W5FMO/events.json","paper":"https://pith.science/paper/4TS2RCMQ"},"agent_actions":{"view_html":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO","download_json":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO.json","view_paper":"https://pith.science/paper/4TS2RCMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1488&json=true","fetch_graph":"https://pith.science/api/pith-number/4TS2RCMQQGMLNUN4YDBA5W5FMO/graph.json","fetch_events":"https://pith.science/api/pith-number/4TS2RCMQQGMLNUN4YDBA5W5FMO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO/action/storage_attestation","attest_author":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO/action/author_attestation","sign_citation":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO/action/citation_signature","submit_replication":"https://pith.science/pith/4TS2RCMQQGMLNUN4YDBA5W5FMO/action/replication_record"}},"created_at":"2026-05-18T00:08:05.587437+00:00","updated_at":"2026-05-18T00:08:05.587437+00:00"}