{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JEAVYEYDZQF4P2IZMHGXSDZ4KD","short_pith_number":"pith:JEAVYEYD","canonical_record":{"source":{"id":"1408.1485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-07T06:26:15Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"1003faaaacd28a0e72b0f880980f0574cbfad339d89637316f1f99ea916cf64b","abstract_canon_sha256":"83b8b117fe26fe94b2b89d70364d0303513a1974200d45d20d2dda241c7eae82"},"schema_version":"1.0"},"canonical_sha256":"49015c1303cc0bc7e91961cd790f3c50ca330ae9ebb7b26de99d84a37a9d9a1c","source":{"kind":"arxiv","id":"1408.1485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1485","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1485v1","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1485","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"JEAVYEYDZQF4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JEAVYEYDZQF4P2IZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JEAVYEYD","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JEAVYEYDZQF4P2IZMHGXSDZ4KD","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-07T06:26:15Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"1003faaaacd28a0e72b0f880980f0574cbfad339d89637316f1f99ea916cf64b","abstract_canon_sha256":"83b8b117fe26fe94b2b89d70364d0303513a1974200d45d20d2dda241c7eae82"},"schema_version":"1.0"},"canonical_sha256":"49015c1303cc0bc7e91961cd790f3c50ca330ae9ebb7b26de99d84a37a9d9a1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:40.368833Z","signature_b64":"RAGmxOy9N8E7nSadsQoVNvw4UdLXXdMkpQvHJyN0CSRPnsu+wAN7G3V6tY0IDzC1XNjc2PG4tl+Kl0BpkRYHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49015c1303cc0bc7e91961cd790f3c50ca330ae9ebb7b26de99d84a37a9d9a1c","last_reissued_at":"2026-05-18T02:45:40.368235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:40.368235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1485","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":"2026-05-18T02:45:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVhqWxjA9sjkTGYewwT3HaU4iEJNfgOwK9hQdlwc5agQtjZv3ngHjApE7GV4FQXk6vnV9ixy65BokKNYuKAODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:14:01.202674Z"},"content_sha256":"7929e95d7355c7b30b4aa63f3633b5f1b119bb6ce69f6203074d7bc35229c7ee","schema_version":"1.0","event_id":"sha256:7929e95d7355c7b30b4aa63f3633b5f1b119bb6ce69f6203074d7bc35229c7ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JEAVYEYDZQF4P2IZMHGXSDZ4KD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Logic for Reasoning about Upper Probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.AI","authors_text":"Joseph Y. Halpern, Riccardo Pucella","submitted_at":"2014-08-07T06:26:15Z","abstract_excerpt":"We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show  that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1485","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":""},"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":"2026-05-18T02:45:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7zfGGHkuFnZYECTVb87TTqzdr/Tvlk9YkaOWz1aPQSYXjMuxFjwyxQ9kpY3TcG87jyQ5fSAawV0vC0H8FHMmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:14:01.203327Z"},"content_sha256":"66bbe03c0240a0a08b92f768c0f6359d5169da697e27921048abd8bba2c3fff4","schema_version":"1.0","event_id":"sha256:66bbe03c0240a0a08b92f768c0f6359d5169da697e27921048abd8bba2c3fff4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/bundle.json","state_url":"https://pith.science/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/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":"2026-05-24T07:14:01Z","links":{"resolver":"https://pith.science/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD","bundle":"https://pith.science/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/bundle.json","state":"https://pith.science/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEAVYEYDZQF4P2IZMHGXSDZ4KD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JEAVYEYDZQF4P2IZMHGXSDZ4KD","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":"83b8b117fe26fe94b2b89d70364d0303513a1974200d45d20d2dda241c7eae82","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-07T06:26:15Z","title_canon_sha256":"1003faaaacd28a0e72b0f880980f0574cbfad339d89637316f1f99ea916cf64b"},"schema_version":"1.0","source":{"id":"1408.1485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1485","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1485v1","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1485","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"JEAVYEYDZQF4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JEAVYEYDZQF4P2IZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JEAVYEYD","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:66bbe03c0240a0a08b92f768c0f6359d5169da697e27921048abd8bba2c3fff4","target":"graph","created_at":"2026-05-18T02:45:40Z","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":"We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show  that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.","authors_text":"Joseph Y. Halpern, Riccardo Pucella","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-07T06:26:15Z","title":"A Logic for Reasoning about Upper Probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1485","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":"sha256:7929e95d7355c7b30b4aa63f3633b5f1b119bb6ce69f6203074d7bc35229c7ee","target":"record","created_at":"2026-05-18T02:45:40Z","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":"83b8b117fe26fe94b2b89d70364d0303513a1974200d45d20d2dda241c7eae82","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-08-07T06:26:15Z","title_canon_sha256":"1003faaaacd28a0e72b0f880980f0574cbfad339d89637316f1f99ea916cf64b"},"schema_version":"1.0","source":{"id":"1408.1485","kind":"arxiv","version":1}},"canonical_sha256":"49015c1303cc0bc7e91961cd790f3c50ca330ae9ebb7b26de99d84a37a9d9a1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49015c1303cc0bc7e91961cd790f3c50ca330ae9ebb7b26de99d84a37a9d9a1c","first_computed_at":"2026-05-18T02:45:40.368235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:40.368235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RAGmxOy9N8E7nSadsQoVNvw4UdLXXdMkpQvHJyN0CSRPnsu+wAN7G3V6tY0IDzC1XNjc2PG4tl+Kl0BpkRYHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:40.368833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7929e95d7355c7b30b4aa63f3633b5f1b119bb6ce69f6203074d7bc35229c7ee","sha256:66bbe03c0240a0a08b92f768c0f6359d5169da697e27921048abd8bba2c3fff4"],"state_sha256":"213144f127152820d7f31c3e93c3bdfb7e337b96ece42793209131532eeeea68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awK5QVJ9Gy6U6hylEPQ1CnvTK1az8rc6bjC6dplRyRNV4YpmWqgu5RNhwmY2/ndfvLfYu+OqF4hqA4he1S8rAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T07:14:01.206606Z","bundle_sha256":"a6bcec4dc5d730cd170f3b51a6d3bd6a6be99ee380fd38a3d84ca5a802987b97"}}