{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HMIXPUH5GE5TH4EYOXUTQKW22E","short_pith_number":"pith:HMIXPUH5","canonical_record":{"source":{"id":"2504.16240","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2025-04-22T20:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"4fd8004c389bf9b2b68869149076bbff8570bde7f0847b8f41134fe925e6a19f","abstract_canon_sha256":"dd9fb398e01b7d36d4dfc7f2966c03b604e869075ce24acac4b73daaf2678287"},"schema_version":"1.0"},"canonical_sha256":"3b1177d0fd313b33f09875e9382adad1137023991a610944483bbb6f54c86ba5","source":{"kind":"arxiv","id":"2504.16240","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16240","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16240v3","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16240","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_12","alias_value":"HMIXPUH5GE5T","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_16","alias_value":"HMIXPUH5GE5TH4EY","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_8","alias_value":"HMIXPUH5","created_at":"2026-06-19T16:12:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HMIXPUH5GE5TH4EYOXUTQKW22E","target":"record","payload":{"canonical_record":{"source":{"id":"2504.16240","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2025-04-22T20:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"4fd8004c389bf9b2b68869149076bbff8570bde7f0847b8f41134fe925e6a19f","abstract_canon_sha256":"dd9fb398e01b7d36d4dfc7f2966c03b604e869075ce24acac4b73daaf2678287"},"schema_version":"1.0"},"canonical_sha256":"3b1177d0fd313b33f09875e9382adad1137023991a610944483bbb6f54c86ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:03.488988Z","signature_b64":"xzmupLSBLIuTIFJ8E1zqMdfZNruu425r/IyXG3ugLkXfqpLuh8KALpWXito+dXbsE8H5DsgiWkfvMtqUzJvBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b1177d0fd313b33f09875e9382adad1137023991a610944483bbb6f54c86ba5","last_reissued_at":"2026-06-19T16:12:03.488498Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:03.488498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.16240","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m/L9ou2URBS9k8yf6dOyIn8D6SUhwuIAb5jKoVmMFWh3SMss4DUMO3J5qFJ7VELLJXrE3GRQPXCLPAJqfbLhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:19:16.670303Z"},"content_sha256":"82fbe306ea77c55d504627bb62a544d6ebd63b0f08d6536de956b5995bda9f66","schema_version":"1.0","event_id":"sha256:82fbe306ea77c55d504627bb62a544d6ebd63b0f08d6536de956b5995bda9f66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HMIXPUH5GE5TH4EYOXUTQKW22E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of Bayesian Equilibria in Incomplete Information Games without Common Priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"Denis Kojevnikov, Kyungchul Song","submitted_at":"2025-04-22T20:12:06Z","abstract_excerpt":"This paper focuses on finite-player incomplete information games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolute continuity of information in Milgrom and Weber (1985), and prove that Bayesian equilibria exist in a broad class of games, including those with discontinuous payoffs. Examples illustrate the scope and implications of our findings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16240","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16240/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVgVYpShFVvMa8bbgvuSFKgk9ClFpc1bDZFkDKWMmW0GToszxwQ6IrorBV6MdRxQ48o1P3gXjATMxmyBNm/DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:19:16.670964Z"},"content_sha256":"d81352b7506deedddba672c7052ef51b57e2e7eafea045585884dd746c2cf3ea","schema_version":"1.0","event_id":"sha256:d81352b7506deedddba672c7052ef51b57e2e7eafea045585884dd746c2cf3ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/bundle.json","state_url":"https://pith.science/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T08:19:16Z","links":{"resolver":"https://pith.science/pith/HMIXPUH5GE5TH4EYOXUTQKW22E","bundle":"https://pith.science/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/bundle.json","state":"https://pith.science/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMIXPUH5GE5TH4EYOXUTQKW22E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HMIXPUH5GE5TH4EYOXUTQKW22E","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":"dd9fb398e01b7d36d4dfc7f2966c03b604e869075ce24acac4b73daaf2678287","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2025-04-22T20:12:06Z","title_canon_sha256":"4fd8004c389bf9b2b68869149076bbff8570bde7f0847b8f41134fe925e6a19f"},"schema_version":"1.0","source":{"id":"2504.16240","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16240","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16240v3","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16240","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_12","alias_value":"HMIXPUH5GE5T","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_16","alias_value":"HMIXPUH5GE5TH4EY","created_at":"2026-06-19T16:12:03Z"},{"alias_kind":"pith_short_8","alias_value":"HMIXPUH5","created_at":"2026-06-19T16:12:03Z"}],"graph_snapshots":[{"event_id":"sha256:d81352b7506deedddba672c7052ef51b57e2e7eafea045585884dd746c2cf3ea","target":"graph","created_at":"2026-06-19T16:12:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.16240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper focuses on finite-player incomplete information games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolute continuity of information in Milgrom and Weber (1985), and prove that Bayesian equilibria exist in a broad class of games, including those with discontinuous payoffs. Examples illustrate the scope and implications of our findings.","authors_text":"Denis Kojevnikov, Kyungchul Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2025-04-22T20:12:06Z","title":"Existence of Bayesian Equilibria in Incomplete Information Games without Common Priors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16240","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":"sha256:82fbe306ea77c55d504627bb62a544d6ebd63b0f08d6536de956b5995bda9f66","target":"record","created_at":"2026-06-19T16:12:03Z","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":"dd9fb398e01b7d36d4dfc7f2966c03b604e869075ce24acac4b73daaf2678287","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2025-04-22T20:12:06Z","title_canon_sha256":"4fd8004c389bf9b2b68869149076bbff8570bde7f0847b8f41134fe925e6a19f"},"schema_version":"1.0","source":{"id":"2504.16240","kind":"arxiv","version":3}},"canonical_sha256":"3b1177d0fd313b33f09875e9382adad1137023991a610944483bbb6f54c86ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b1177d0fd313b33f09875e9382adad1137023991a610944483bbb6f54c86ba5","first_computed_at":"2026-06-19T16:12:03.488498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:03.488498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzmupLSBLIuTIFJ8E1zqMdfZNruu425r/IyXG3ugLkXfqpLuh8KALpWXito+dXbsE8H5DsgiWkfvMtqUzJvBBw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:03.488988Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16240","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82fbe306ea77c55d504627bb62a544d6ebd63b0f08d6536de956b5995bda9f66","sha256:d81352b7506deedddba672c7052ef51b57e2e7eafea045585884dd746c2cf3ea"],"state_sha256":"12f34c5e64dbf2e935ea8b5c454b11c12f372efee59ae371db132692f89d8858"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ywZ7hjva+lqRKkcdQ08C8vkJXHvPobWBLOPsMgHk7vDAeNnC1NdpxzodgMknq1rvzUJ8t2eiPmy0y8QUw6OBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:19:16.675096Z","bundle_sha256":"df5123f85b6f9741b275d87b7ed3637b16d5ebf26da2c0026132f9ecf029f8bf"}}