{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:O4U3IZS67BSHBWG2YZBYVZKV6N","short_pith_number":"pith:O4U3IZS6","canonical_record":{"source":{"id":"2403.18899","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T18:00:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"cf79e222ff299ede834912227ae32c6b02225a109e964ec144bdc66e8eb58fe4","abstract_canon_sha256":"e0e9b043ae60f156638a321548c72fe4ac5a405bc6b6e47a107a05ce059d0bf1"},"schema_version":"1.0"},"canonical_sha256":"7729b4665ef86470d8dac6438ae555f378d3f7e26fb6902b93e230d90b25b70a","source":{"kind":"arxiv","id":"2403.18899","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18899","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18899v2","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18899","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"O4U3IZS67BSH","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_16","alias_value":"O4U3IZS67BSHBWG2","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_8","alias_value":"O4U3IZS6","created_at":"2026-07-05T09:56:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:O4U3IZS67BSHBWG2YZBYVZKV6N","target":"record","payload":{"canonical_record":{"source":{"id":"2403.18899","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T18:00:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"cf79e222ff299ede834912227ae32c6b02225a109e964ec144bdc66e8eb58fe4","abstract_canon_sha256":"e0e9b043ae60f156638a321548c72fe4ac5a405bc6b6e47a107a05ce059d0bf1"},"schema_version":"1.0"},"canonical_sha256":"7729b4665ef86470d8dac6438ae555f378d3f7e26fb6902b93e230d90b25b70a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:35.193944Z","signature_b64":"7ohJ3HOUejqLHEiIdasPOJctGfZ9UxqUrTzzkY1mzpTSbSTSbG3bzADODvfKkfBl9HAscub9pK8P/mIfVe/WCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7729b4665ef86470d8dac6438ae555f378d3f7e26fb6902b93e230d90b25b70a","last_reissued_at":"2026-07-05T09:56:35.193451Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:35.193451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.18899","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":"2026-07-05T09:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfoTchvtV+waYNKmIqKUFlRmKWhf4dYu4k2NZF1Fc244JVuBHCsFI/pjsVEIpWp7sauyYhALYgY8lLIA7xXVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:31:47.394949Z"},"content_sha256":"a23ac6f6b5a8ac29d392a6bbd4958133a2bf31457d29af50c9bcc00ad501ddb5","schema_version":"1.0","event_id":"sha256:a23ac6f6b5a8ac29d392a6bbd4958133a2bf31457d29af50c9bcc00ad501ddb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:O4U3IZS67BSHBWG2YZBYVZKV6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties and Applications of the Kirkwood-Dirac Distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Andrew N. Jordan, Christopher Langrenez, David R. M. Arvidsson-Shukur, Jeff S. Lundeen, Justin Dressel, Matteo Lostaglio, Nicole Yunger Halpern, Stephan De Bievre, William F. Braasch Jr.","submitted_at":"2024-03-27T18:00:02Z","abstract_excerpt":"Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18899","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.18899/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":"2026-07-05T09:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9JQsaCwA+faTrUnm7gPzzENrmR2B32cB8NIwqwyn4UeRV2Ygixhsa7+9LRQYhvhylsy7v2iTzSE8K66fOSiMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:31:47.395572Z"},"content_sha256":"dcaaf76daeb61147ef93b563e4692a4f24d3936fe8a7f6a74f5aa335c42790b3","schema_version":"1.0","event_id":"sha256:dcaaf76daeb61147ef93b563e4692a4f24d3936fe8a7f6a74f5aa335c42790b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/bundle.json","state_url":"https://pith.science/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/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":"2026-08-14T09:31:47Z","links":{"resolver":"https://pith.science/pith/O4U3IZS67BSHBWG2YZBYVZKV6N","bundle":"https://pith.science/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/bundle.json","state":"https://pith.science/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4U3IZS67BSHBWG2YZBYVZKV6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:O4U3IZS67BSHBWG2YZBYVZKV6N","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":"e0e9b043ae60f156638a321548c72fe4ac5a405bc6b6e47a107a05ce059d0bf1","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T18:00:02Z","title_canon_sha256":"cf79e222ff299ede834912227ae32c6b02225a109e964ec144bdc66e8eb58fe4"},"schema_version":"1.0","source":{"id":"2403.18899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18899","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18899v2","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18899","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"O4U3IZS67BSH","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_16","alias_value":"O4U3IZS67BSHBWG2","created_at":"2026-07-05T09:56:35Z"},{"alias_kind":"pith_short_8","alias_value":"O4U3IZS6","created_at":"2026-07-05T09:56:35Z"}],"graph_snapshots":[{"event_id":"sha256:dcaaf76daeb61147ef93b563e4692a4f24d3936fe8a7f6a74f5aa335c42790b3","target":"graph","created_at":"2026-07-05T09:56:35Z","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/2403.18899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summ","authors_text":"Andrew N. Jordan, Christopher Langrenez, David R. M. Arvidsson-Shukur, Jeff S. Lundeen, Justin Dressel, Matteo Lostaglio, Nicole Yunger Halpern, Stephan De Bievre, William F. Braasch Jr.","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T18:00:02Z","title":"Properties and Applications of the Kirkwood-Dirac Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18899","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:a23ac6f6b5a8ac29d392a6bbd4958133a2bf31457d29af50c9bcc00ad501ddb5","target":"record","created_at":"2026-07-05T09:56:35Z","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":"e0e9b043ae60f156638a321548c72fe4ac5a405bc6b6e47a107a05ce059d0bf1","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T18:00:02Z","title_canon_sha256":"cf79e222ff299ede834912227ae32c6b02225a109e964ec144bdc66e8eb58fe4"},"schema_version":"1.0","source":{"id":"2403.18899","kind":"arxiv","version":2}},"canonical_sha256":"7729b4665ef86470d8dac6438ae555f378d3f7e26fb6902b93e230d90b25b70a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7729b4665ef86470d8dac6438ae555f378d3f7e26fb6902b93e230d90b25b70a","first_computed_at":"2026-07-05T09:56:35.193451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:35.193451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ohJ3HOUejqLHEiIdasPOJctGfZ9UxqUrTzzkY1mzpTSbSTSbG3bzADODvfKkfBl9HAscub9pK8P/mIfVe/WCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:35.193944Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.18899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a23ac6f6b5a8ac29d392a6bbd4958133a2bf31457d29af50c9bcc00ad501ddb5","sha256:dcaaf76daeb61147ef93b563e4692a4f24d3936fe8a7f6a74f5aa335c42790b3"],"state_sha256":"20c6cbffdcec152f3bb5741a00dfeca67a720e59c9adcce339b47776411d3ce1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"in7yWpAv80fQIPk5vZRg26b3RDYlwj9lVwXiAVz7Uepy2cq9gdFSnAncfzWlQCT+gZAjdumdZETZrd05eKnPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T09:31:47.402318Z","bundle_sha256":"9757c88f7ae88033c1994e96a0cd07d9c42d8a783108f7ae2cb1156a6dbecce2"}}