{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QNJBCVUMBLM7VKXSULI6KC7CST","short_pith_number":"pith:QNJBCVUM","canonical_record":{"source":{"id":"1102.2213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-10T20:10:57Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"55653db0256cc28aa62a24f5d30dc288d340e7c23801adfb106a7d4c790d6b2d","abstract_canon_sha256":"3d4a8ff510098795b2a4fcbea8fe7ebef578657d552d2464157b4b918adc4cee"},"schema_version":"1.0"},"canonical_sha256":"835211568c0ad9faaaf2a2d1e50be294efe511c8ebae53a308da7c84a6f7c2aa","source":{"kind":"arxiv","id":"1102.2213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2213","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2213v1","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2213","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"QNJBCVUMBLM7","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNJBCVUMBLM7VKXS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNJBCVUM","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QNJBCVUMBLM7VKXSULI6KC7CST","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-10T20:10:57Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"55653db0256cc28aa62a24f5d30dc288d340e7c23801adfb106a7d4c790d6b2d","abstract_canon_sha256":"3d4a8ff510098795b2a4fcbea8fe7ebef578657d552d2464157b4b918adc4cee"},"schema_version":"1.0"},"canonical_sha256":"835211568c0ad9faaaf2a2d1e50be294efe511c8ebae53a308da7c84a6f7c2aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:28.725752Z","signature_b64":"jiaSii+55nYgL97tKtiJdNuhTpb/vo0CjEKffQsb5wU5pJy8DWEyD7p/N+5LFS6OROn0kmvkHNkfY20kWra0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"835211568c0ad9faaaf2a2d1e50be294efe511c8ebae53a308da7c84a6f7c2aa","last_reissued_at":"2026-05-18T03:05:28.725146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:28.725146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2213","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":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6V4sZmu6DJWux7Bcps+hiHVAHwdNyduXVObNOA7+BkiIJAESyqoU7LhCLNxoP1/sqnZ8bUhD82DDap04PNwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:28:23.907305Z"},"content_sha256":"8bc5a41e96e4e2fdb90591cc1fd8fc8ac0b0cb08f5f13f16599413c615d8e1fe","schema_version":"1.0","event_id":"sha256:8bc5a41e96e4e2fdb90591cc1fd8fc8ac0b0cb08f5f13f16599413c615d8e1fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QNJBCVUMBLM7VKXSULI6KC7CST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical and Quantum Probabilities as Truth Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Andreas Doering, Chris J. Isham","submitted_at":"2011-02-10T20:10:57Z","abstract_excerpt":"We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension of our existing work on a topos approach to quantum theory. Earlier results on the representation of arbitrary quantum states are complemented with a purely logical perspective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2213","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":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5EdZDjzb2ltnylfP66QAWeyBtlP3NLMuuI114/DnCphVT33OLuAVJbAoRo2Oz/Rc2OSyH2uSJaA/WXLVAncLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:28:23.907688Z"},"content_sha256":"3fb33583c7a13610f5d595ad77f662fd1ee8a7e11f4b162b32025c0bd7cb30b0","schema_version":"1.0","event_id":"sha256:3fb33583c7a13610f5d595ad77f662fd1ee8a7e11f4b162b32025c0bd7cb30b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNJBCVUMBLM7VKXSULI6KC7CST/bundle.json","state_url":"https://pith.science/pith/QNJBCVUMBLM7VKXSULI6KC7CST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNJBCVUMBLM7VKXSULI6KC7CST/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":"2026-05-30T08:28:23Z","links":{"resolver":"https://pith.science/pith/QNJBCVUMBLM7VKXSULI6KC7CST","bundle":"https://pith.science/pith/QNJBCVUMBLM7VKXSULI6KC7CST/bundle.json","state":"https://pith.science/pith/QNJBCVUMBLM7VKXSULI6KC7CST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNJBCVUMBLM7VKXSULI6KC7CST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QNJBCVUMBLM7VKXSULI6KC7CST","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":"3d4a8ff510098795b2a4fcbea8fe7ebef578657d552d2464157b4b918adc4cee","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-10T20:10:57Z","title_canon_sha256":"55653db0256cc28aa62a24f5d30dc288d340e7c23801adfb106a7d4c790d6b2d"},"schema_version":"1.0","source":{"id":"1102.2213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2213","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2213v1","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2213","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"QNJBCVUMBLM7","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNJBCVUMBLM7VKXS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNJBCVUM","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:3fb33583c7a13610f5d595ad77f662fd1ee8a7e11f4b162b32025c0bd7cb30b0","target":"graph","created_at":"2026-05-18T03:05:28Z","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 show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension of our existing work on a topos approach to quantum theory. Earlier results on the representation of arbitrary quantum states are complemented with a purely logical perspective.","authors_text":"Andreas Doering, Chris J. Isham","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-10T20:10:57Z","title":"Classical and Quantum Probabilities as Truth Values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2213","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":"sha256:8bc5a41e96e4e2fdb90591cc1fd8fc8ac0b0cb08f5f13f16599413c615d8e1fe","target":"record","created_at":"2026-05-18T03:05:28Z","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":"3d4a8ff510098795b2a4fcbea8fe7ebef578657d552d2464157b4b918adc4cee","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-10T20:10:57Z","title_canon_sha256":"55653db0256cc28aa62a24f5d30dc288d340e7c23801adfb106a7d4c790d6b2d"},"schema_version":"1.0","source":{"id":"1102.2213","kind":"arxiv","version":1}},"canonical_sha256":"835211568c0ad9faaaf2a2d1e50be294efe511c8ebae53a308da7c84a6f7c2aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"835211568c0ad9faaaf2a2d1e50be294efe511c8ebae53a308da7c84a6f7c2aa","first_computed_at":"2026-05-18T03:05:28.725146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.725146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jiaSii+55nYgL97tKtiJdNuhTpb/vo0CjEKffQsb5wU5pJy8DWEyD7p/N+5LFS6OROn0kmvkHNkfY20kWra0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.725752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bc5a41e96e4e2fdb90591cc1fd8fc8ac0b0cb08f5f13f16599413c615d8e1fe","sha256:3fb33583c7a13610f5d595ad77f662fd1ee8a7e11f4b162b32025c0bd7cb30b0"],"state_sha256":"ddb6a624ef46817f19770b31308c8ea3af88d907592760b124685c9a5a49dff2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97XuLJH0fbKAnzY8+aiyfUiOVC2NT6CJ7JFs4J5CxdCIhWUv3rEVt3STB+gmqVkMpdlr4jH6Pg9zrzfdVfIeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:28:23.909777Z","bundle_sha256":"78bc2053d1eed680102c6730ae0376918967612fe2ca3f2e909d24308141dd69"}}