{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PGOFRQXMG72RNGVBULXWEPVL6K","short_pith_number":"pith:PGOFRQXM","canonical_record":{"source":{"id":"2605.30017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T14:41:16Z","cross_cats_sorted":[],"title_canon_sha256":"8e75b4b5fcbfbbba7085f93e26e2cc873e65db968ab0175db2f4da3f37ba732f","abstract_canon_sha256":"ab87f95e81de4c53ef200cc43bb3e14f05bf88d8b32b40805077dbe71ab5a462"},"schema_version":"1.0"},"canonical_sha256":"799c58c2ec37f5169aa1a2ef623eabf2a878515c97e4b76d113f6729df3185fa","source":{"kind":"arxiv","id":"2605.30017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30017","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30017v1","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30017","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"PGOFRQXMG72R","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"PGOFRQXMG72RNGVB","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"PGOFRQXM","created_at":"2026-05-29T02:06:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PGOFRQXMG72RNGVBULXWEPVL6K","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T14:41:16Z","cross_cats_sorted":[],"title_canon_sha256":"8e75b4b5fcbfbbba7085f93e26e2cc873e65db968ab0175db2f4da3f37ba732f","abstract_canon_sha256":"ab87f95e81de4c53ef200cc43bb3e14f05bf88d8b32b40805077dbe71ab5a462"},"schema_version":"1.0"},"canonical_sha256":"799c58c2ec37f5169aa1a2ef623eabf2a878515c97e4b76d113f6729df3185fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:07.134149Z","signature_b64":"jhZwPHjQcNisni/XwI9h9OZ4bkBBgDzIWVNcVXhe0Ms5qYLuBjAEDrgF9cVI6AgaiJ6oGHysvO/xZCLsXoySBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"799c58c2ec37f5169aa1a2ef623eabf2a878515c97e4b76d113f6729df3185fa","last_reissued_at":"2026-05-29T02:06:07.133492Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:07.133492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30017","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOQZKPL1qBTgVmDLgLRzx7wD87llMTNH+mKvAkZPMkYPrJwbQOE5wOzJeIt3p9wvES04m/5+1r7OrwMv6pM8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:34:31.457512Z"},"content_sha256":"0139f2cc7aad57bf60ec37604da18bf92367362fc87b2662ac129854cc864d92","schema_version":"1.0","event_id":"sha256:0139f2cc7aad57bf60ec37604da18bf92367362fc87b2662ac129854cc864d92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PGOFRQXMG72RNGVBULXWEPVL6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional Probability Spaces and the Structure of Agreement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Brandenburger, Erya Yang","submitted_at":"2026-05-28T14:41:16Z","abstract_excerpt":"We use the machinery of a conditional probability space (R\\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a family of conditioning events that satisfies concentration and a chain rule. Using this apparatus, we derive an Agreement Theorem that dispenses with the traditional assumptions of a common prior, information partitions, positivity of measure, and knowledge operators. Our treatment can be viewed as ``deconstructing\" the classic Agreement Theorem, by showing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30017","kind":"arxiv","version":1},"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/2605.30017/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":"2026-05-29T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G73UimRLYb92FSlZKXtGc5IB05BcRYv7IcH37gOTaZhUTTcW7pEgmH1x961nZRKzqlQP+fljKlSXEfhZD9y4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:34:31.457888Z"},"content_sha256":"78aa422117d82559fc31b118ecd6e604cf6385c27f5bfa23a8bf008cd70df9cc","schema_version":"1.0","event_id":"sha256:78aa422117d82559fc31b118ecd6e604cf6385c27f5bfa23a8bf008cd70df9cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGOFRQXMG72RNGVBULXWEPVL6K/bundle.json","state_url":"https://pith.science/pith/PGOFRQXMG72RNGVBULXWEPVL6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGOFRQXMG72RNGVBULXWEPVL6K/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":"2026-06-24T08:34:31Z","links":{"resolver":"https://pith.science/pith/PGOFRQXMG72RNGVBULXWEPVL6K","bundle":"https://pith.science/pith/PGOFRQXMG72RNGVBULXWEPVL6K/bundle.json","state":"https://pith.science/pith/PGOFRQXMG72RNGVBULXWEPVL6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGOFRQXMG72RNGVBULXWEPVL6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PGOFRQXMG72RNGVBULXWEPVL6K","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":"ab87f95e81de4c53ef200cc43bb3e14f05bf88d8b32b40805077dbe71ab5a462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T14:41:16Z","title_canon_sha256":"8e75b4b5fcbfbbba7085f93e26e2cc873e65db968ab0175db2f4da3f37ba732f"},"schema_version":"1.0","source":{"id":"2605.30017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30017","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30017v1","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30017","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"PGOFRQXMG72R","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"PGOFRQXMG72RNGVB","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"PGOFRQXM","created_at":"2026-05-29T02:06:07Z"}],"graph_snapshots":[{"event_id":"sha256:78aa422117d82559fc31b118ecd6e604cf6385c27f5bfa23a8bf008cd70df9cc","target":"graph","created_at":"2026-05-29T02:06:07Z","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/2605.30017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the machinery of a conditional probability space (R\\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a family of conditioning events that satisfies concentration and a chain rule. Using this apparatus, we derive an Agreement Theorem that dispenses with the traditional assumptions of a common prior, information partitions, positivity of measure, and knowledge operators. Our treatment can be viewed as ``deconstructing\" the classic Agreement Theorem, by showing ","authors_text":"Adam Brandenburger, Erya Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T14:41:16Z","title":"Conditional Probability Spaces and the Structure of Agreement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30017","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":"sha256:0139f2cc7aad57bf60ec37604da18bf92367362fc87b2662ac129854cc864d92","target":"record","created_at":"2026-05-29T02:06:07Z","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":"ab87f95e81de4c53ef200cc43bb3e14f05bf88d8b32b40805077dbe71ab5a462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T14:41:16Z","title_canon_sha256":"8e75b4b5fcbfbbba7085f93e26e2cc873e65db968ab0175db2f4da3f37ba732f"},"schema_version":"1.0","source":{"id":"2605.30017","kind":"arxiv","version":1}},"canonical_sha256":"799c58c2ec37f5169aa1a2ef623eabf2a878515c97e4b76d113f6729df3185fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"799c58c2ec37f5169aa1a2ef623eabf2a878515c97e4b76d113f6729df3185fa","first_computed_at":"2026-05-29T02:06:07.133492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:06:07.133492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jhZwPHjQcNisni/XwI9h9OZ4bkBBgDzIWVNcVXhe0Ms5qYLuBjAEDrgF9cVI6AgaiJ6oGHysvO/xZCLsXoySBQ==","signature_status":"signed_v1","signed_at":"2026-05-29T02:06:07.134149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0139f2cc7aad57bf60ec37604da18bf92367362fc87b2662ac129854cc864d92","sha256:78aa422117d82559fc31b118ecd6e604cf6385c27f5bfa23a8bf008cd70df9cc"],"state_sha256":"9af99ede52ba0b8c8867a6c6791290c445476ea6b7ab0c42bf13440762b1a03e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhYhBXMN9iefYyYr3lrZ+0UrMpSPV7EjVZVo/kZlaZuT0TfNVObK3DHWd2RSY1VTKys6WbJdc3X9XmAUnBcTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:34:31.459957Z","bundle_sha256":"dca6f4438e215067c6f9939086e3c99aee6abdd7eedd6ee090f5c4fec5aaf445"}}