{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MIOIGZZGUSENGOQ6CIA2CGTFIL","short_pith_number":"pith:MIOIGZZG","canonical_record":{"source":{"id":"2501.15238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-01-25T15:01:25Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"770babf3bc7d830aec35849aea9b96583660d0d2c76011e1648a15de2b655d38","abstract_canon_sha256":"95f5dbb89c7b625cb88b279b47bc330e2bc0858531e3f73bb6d5e30e3297b1aa"},"schema_version":"1.0"},"canonical_sha256":"621c836726a488d33a1e1201a11a6542f464a95728f45345ede874a521720dc0","source":{"kind":"arxiv","id":"2501.15238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15238","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15238v1","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15238","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"MIOIGZZGUSEN","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"MIOIGZZGUSENGOQ6","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"MIOIGZZG","created_at":"2026-07-05T10:05:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MIOIGZZGUSENGOQ6CIA2CGTFIL","target":"record","payload":{"canonical_record":{"source":{"id":"2501.15238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-01-25T15:01:25Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"770babf3bc7d830aec35849aea9b96583660d0d2c76011e1648a15de2b655d38","abstract_canon_sha256":"95f5dbb89c7b625cb88b279b47bc330e2bc0858531e3f73bb6d5e30e3297b1aa"},"schema_version":"1.0"},"canonical_sha256":"621c836726a488d33a1e1201a11a6542f464a95728f45345ede874a521720dc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:05:26.163027Z","signature_b64":"kdl+rx11DsICF0dHlGYqU/Q0GDOfxW85kVXzZ3vAyHjxGFElK70brnEi/TsH+0CMDFpz4W3oIXKEYwRnTfgQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621c836726a488d33a1e1201a11a6542f464a95728f45345ede874a521720dc0","last_reissued_at":"2026-07-05T10:05:26.162493Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:05:26.162493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.15238","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":"2026-07-05T10:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oEmLYyY1FBgusabKFqzbq7sU/cqiXUt915QBEw49LzhyJxQdvQlfN/n1MD3Zts07BSD75e7Z0xJmxE38mL9JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:39:20.429922Z"},"content_sha256":"47dfcc9b40fbcfa0bdcbdc83d0bbdbe96fbc29bf64d8b4460a295eca5a87e299","schema_version":"1.0","event_id":"sha256:47dfcc9b40fbcfa0bdcbdc83d0bbdbe96fbc29bf64d8b4460a295eca5a87e299"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MIOIGZZGUSENGOQ6CIA2CGTFIL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete Quantum Relational Hoare Logics from Optimal Transport Duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.LO","authors_text":"Gilles Barthe, Li Zhou, Minbo Gao, Theo Wang","submitted_at":"2025-01-25T15:01:25Z","abstract_excerpt":"We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded postconditions and almost surely terminating programs. Our completeness result is based on a quantum version of the duality theorem from optimal transport. We also define a complete embedding into our logic of a relational Hoare logic with projective assertions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15238","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/2501.15238/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":"2026-07-05T10:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3XROkEGDUPBIeqxDkCwNhGoTSyaqQcI7xqC95iWf6/C5loi+4IIXb76k8GywUhbrT8T+z+7cBkjrCpv1xGfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:39:20.430830Z"},"content_sha256":"0f0164fbd2ede9b914ceb8a8f20b13bf97927d778fc475fde1327af3766b2b70","schema_version":"1.0","event_id":"sha256:0f0164fbd2ede9b914ceb8a8f20b13bf97927d778fc475fde1327af3766b2b70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/bundle.json","state_url":"https://pith.science/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/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":"2026-08-11T12:39:20Z","links":{"resolver":"https://pith.science/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL","bundle":"https://pith.science/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/bundle.json","state":"https://pith.science/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIOIGZZGUSENGOQ6CIA2CGTFIL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MIOIGZZGUSENGOQ6CIA2CGTFIL","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":"95f5dbb89c7b625cb88b279b47bc330e2bc0858531e3f73bb6d5e30e3297b1aa","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-01-25T15:01:25Z","title_canon_sha256":"770babf3bc7d830aec35849aea9b96583660d0d2c76011e1648a15de2b655d38"},"schema_version":"1.0","source":{"id":"2501.15238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15238","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15238v1","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15238","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"MIOIGZZGUSEN","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"MIOIGZZGUSENGOQ6","created_at":"2026-07-05T10:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"MIOIGZZG","created_at":"2026-07-05T10:05:26Z"}],"graph_snapshots":[{"event_id":"sha256:0f0164fbd2ede9b914ceb8a8f20b13bf97927d778fc475fde1327af3766b2b70","target":"graph","created_at":"2026-07-05T10:05:26Z","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/2501.15238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded postconditions and almost surely terminating programs. Our completeness result is based on a quantum version of the duality theorem from optimal transport. We also define a complete embedding into our logic of a relational Hoare logic with projective assertions.","authors_text":"Gilles Barthe, Li Zhou, Minbo Gao, Theo Wang","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-01-25T15:01:25Z","title":"Complete Quantum Relational Hoare Logics from Optimal Transport Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15238","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":"sha256:47dfcc9b40fbcfa0bdcbdc83d0bbdbe96fbc29bf64d8b4460a295eca5a87e299","target":"record","created_at":"2026-07-05T10:05:26Z","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":"95f5dbb89c7b625cb88b279b47bc330e2bc0858531e3f73bb6d5e30e3297b1aa","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-01-25T15:01:25Z","title_canon_sha256":"770babf3bc7d830aec35849aea9b96583660d0d2c76011e1648a15de2b655d38"},"schema_version":"1.0","source":{"id":"2501.15238","kind":"arxiv","version":1}},"canonical_sha256":"621c836726a488d33a1e1201a11a6542f464a95728f45345ede874a521720dc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"621c836726a488d33a1e1201a11a6542f464a95728f45345ede874a521720dc0","first_computed_at":"2026-07-05T10:05:26.162493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:26.162493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kdl+rx11DsICF0dHlGYqU/Q0GDOfxW85kVXzZ3vAyHjxGFElK70brnEi/TsH+0CMDFpz4W3oIXKEYwRnTfgQCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:26.163027Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47dfcc9b40fbcfa0bdcbdc83d0bbdbe96fbc29bf64d8b4460a295eca5a87e299","sha256:0f0164fbd2ede9b914ceb8a8f20b13bf97927d778fc475fde1327af3766b2b70"],"state_sha256":"9d9084db21945f315e22f8c99d8866479ee88b47c8ec5e1baf5978891a9fc452"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+sqIHXgfv8oJhAOWQkjq498PiB27b8ijpJ2SnbII3TnFd3AxLWwqKc/9VGT9GYXMCwdLO2m4qlyu5PLzfPxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:39:20.442081Z","bundle_sha256":"12c79b06ed75ece08d794a012ea44171c29aeca31cfb655d1f351499b9b07216"}}