{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RHKD5FO2CDTCKOLLQAUJD7POGD","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":"bb921a18cdf1afa391e3f756777b0b2991be12ed16ff3bdcab5f3dce7b65d952","cross_cats_sorted":["cs.LO","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-22T03:16:03Z","title_canon_sha256":"57b021e65ddf4f13f3d411eb51bb37157a7ea5677aeefb21b42d66315575ad08"},"schema_version":"1.0","source":{"id":"1907.09104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09104","created_at":"2026-05-17T23:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09104v1","created_at":"2026-05-17T23:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09104","created_at":"2026-05-17T23:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"RHKD5FO2CDTC","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RHKD5FO2CDTCKOLL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RHKD5FO2","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:c9722c3d93962a48aeefdfae59b0dd986ae80f8f771b4ac0bd3464b3e21b842b","target":"graph","created_at":"2026-05-17T23:40:00Z","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 studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. Implications are as follows. First, each posterior is uniquely determined. Second, qualitative belief reduces to fully introspective knowledge in a ","authors_text":"Bocconi University), IGIER, Satoshi Fukuda (Department of Decision Sciences","cross_cats":["cs.LO","cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-22T03:16:03Z","title":"On the Consistency among Prior, Posteriors, and Information Sets (Extended Abstract)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09104","kind":"arxiv","version":1},"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":"sha256:7434d3170f3c0136ea9f2fddac76ab2b91138b9d25392ecf91a8cdff4f3536cb","target":"record","created_at":"2026-05-17T23:40:00Z","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":"bb921a18cdf1afa391e3f756777b0b2991be12ed16ff3bdcab5f3dce7b65d952","cross_cats_sorted":["cs.LO","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-22T03:16:03Z","title_canon_sha256":"57b021e65ddf4f13f3d411eb51bb37157a7ea5677aeefb21b42d66315575ad08"},"schema_version":"1.0","source":{"id":"1907.09104","kind":"arxiv","version":1}},"canonical_sha256":"89d43e95da10e625396b802891fdee30fea45b04c9e4a0005cb03d33709cfd6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d43e95da10e625396b802891fdee30fea45b04c9e4a0005cb03d33709cfd6f","first_computed_at":"2026-05-17T23:40:00.141597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:00.141597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WRkWaY7f7wHVkLxStDfw7aB2UMNCDKUCUn3bkWnSrF34SIiJhPx6WwIo0jBAy1ZU1SZCtIcTJ2JnwHzQaJGSDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:00.142092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7434d3170f3c0136ea9f2fddac76ab2b91138b9d25392ecf91a8cdff4f3536cb","sha256:c9722c3d93962a48aeefdfae59b0dd986ae80f8f771b4ac0bd3464b3e21b842b"],"state_sha256":"0d26026ba549618360a0210a873471ebd437949d171baf07cab57000462524b5"}