{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:T7KSWWCBSLJR6P5EYKQUQ5WD7A","short_pith_number":"pith:T7KSWWCB","canonical_record":{"source":{"id":"0908.2510","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-08-18T07:39:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5e3f512c468402024e28d5a66f3d71ad6ad0da40d04d9322831d136b1c7826a7","abstract_canon_sha256":"6a4dcc47adfd22c5c238577e9511690154da896cef1615d0f70f5d2153a706b0"},"schema_version":"1.0"},"canonical_sha256":"9fd52b584192d31f3fa4c2a14876c3f8248de18b7a7312f0bd33fc35d1128f0d","source":{"kind":"arxiv","id":"0908.2510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2510","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2510v2","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2510","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"pith_short_12","alias_value":"T7KSWWCBSLJR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T7KSWWCBSLJR6P5E","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T7KSWWCB","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:T7KSWWCBSLJR6P5EYKQUQ5WD7A","target":"record","payload":{"canonical_record":{"source":{"id":"0908.2510","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-08-18T07:39:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5e3f512c468402024e28d5a66f3d71ad6ad0da40d04d9322831d136b1c7826a7","abstract_canon_sha256":"6a4dcc47adfd22c5c238577e9511690154da896cef1615d0f70f5d2153a706b0"},"schema_version":"1.0"},"canonical_sha256":"9fd52b584192d31f3fa4c2a14876c3f8248de18b7a7312f0bd33fc35d1128f0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:05.841479Z","signature_b64":"j3Y1d7jpTpxqtxaSHo7dg8Hnexv4YPu98E+0OD+32xoTiHPdIA92Rp/4sqDA3nw9wbVge3TenVnNs3dRcX1mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fd52b584192d31f3fa4c2a14876c3f8248de18b7a7312f0bd33fc35d1128f0d","last_reissued_at":"2026-05-18T00:31:05.840969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:05.840969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.2510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KgT8X46Zyk5W1D07qBXOed0t5Vdgi53WgyNSDDoM1tCAwFDyzg5jh65wNh4n+kgUaxBXumhCFEwPBsHwoDToCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:14:27.323962Z"},"content_sha256":"5649e428d76df9495f4e95fc1d54d11488607b32c80e076c09be22b151447853","schema_version":"1.0","event_id":"sha256:5649e428d76df9495f4e95fc1d54d11488607b32c80e076c09be22b151447853"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:T7KSWWCBSLJR6P5EYKQUQ5WD7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy of Partitions on Sequential Effect Algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Cho Minhyung, Wang Jiamei, Wu Junde","submitted_at":"2009-08-18T07:39:44Z","abstract_excerpt":"By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2510","kind":"arxiv","version":2},"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":"2026-05-18T00:31:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyiIWcHSoYCHZr5Iou5gATJBU6BZRivDeyeB6zgihtsT6cywyNsO062kLg/K+Vok7C+wogUnwH1M/gQ9iyN3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:14:27.324343Z"},"content_sha256":"b747c760d42ed3828fd4c3d31b8c1ca1b080daaeb7f538dc8b04a34d56c27713","schema_version":"1.0","event_id":"sha256:b747c760d42ed3828fd4c3d31b8c1ca1b080daaeb7f538dc8b04a34d56c27713"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/bundle.json","state_url":"https://pith.science/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/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":"2026-06-27T17:14:27Z","links":{"resolver":"https://pith.science/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A","bundle":"https://pith.science/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/bundle.json","state":"https://pith.science/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7KSWWCBSLJR6P5EYKQUQ5WD7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:T7KSWWCBSLJR6P5EYKQUQ5WD7A","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":"6a4dcc47adfd22c5c238577e9511690154da896cef1615d0f70f5d2153a706b0","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-08-18T07:39:44Z","title_canon_sha256":"5e3f512c468402024e28d5a66f3d71ad6ad0da40d04d9322831d136b1c7826a7"},"schema_version":"1.0","source":{"id":"0908.2510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2510","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2510v2","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2510","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"pith_short_12","alias_value":"T7KSWWCBSLJR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T7KSWWCBSLJR6P5E","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T7KSWWCB","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:b747c760d42ed3828fd4c3d31b8c1ca1b080daaeb7f538dc8b04a34d56c27713","target":"graph","created_at":"2026-05-18T00:31:05Z","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":"By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.","authors_text":"Cho Minhyung, Wang Jiamei, Wu Junde","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-08-18T07:39:44Z","title":"Entropy of Partitions on Sequential Effect Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2510","kind":"arxiv","version":2},"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":"sha256:5649e428d76df9495f4e95fc1d54d11488607b32c80e076c09be22b151447853","target":"record","created_at":"2026-05-18T00:31:05Z","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":"6a4dcc47adfd22c5c238577e9511690154da896cef1615d0f70f5d2153a706b0","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-08-18T07:39:44Z","title_canon_sha256":"5e3f512c468402024e28d5a66f3d71ad6ad0da40d04d9322831d136b1c7826a7"},"schema_version":"1.0","source":{"id":"0908.2510","kind":"arxiv","version":2}},"canonical_sha256":"9fd52b584192d31f3fa4c2a14876c3f8248de18b7a7312f0bd33fc35d1128f0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fd52b584192d31f3fa4c2a14876c3f8248de18b7a7312f0bd33fc35d1128f0d","first_computed_at":"2026-05-18T00:31:05.840969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:05.840969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j3Y1d7jpTpxqtxaSHo7dg8Hnexv4YPu98E+0OD+32xoTiHPdIA92Rp/4sqDA3nw9wbVge3TenVnNs3dRcX1mCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:05.841479Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5649e428d76df9495f4e95fc1d54d11488607b32c80e076c09be22b151447853","sha256:b747c760d42ed3828fd4c3d31b8c1ca1b080daaeb7f538dc8b04a34d56c27713"],"state_sha256":"aeb51c8632d40e2fa35671937d5f8b780a75f0d51653b0edcfdea9708741ac8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcKUmfnlaU9WvU/n1tAg47lcmZqYP2IuR1E9p3Z2fVt7vFVXT6tHAZn0ckZYayd881KvjlxpiBYJOkYt6Xe9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:14:27.326681Z","bundle_sha256":"42337ee6e3f6e407eab61e2bc6078411c1ef97dbdab149b17a29688866a6ccae"}}