{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JISGPGJLSJDHRJVRZKTRJ5KOO7","short_pith_number":"pith:JISGPGJL","canonical_record":{"source":{"id":"1908.06793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-19T13:31:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0aff1ee90378cb2c40c5e9d4d0fd06170c21e164547aac41d84039240ca94b79","abstract_canon_sha256":"84c30535221fbe9853ea58d68bbb2d6f27c5f5a39d1d09b37ce243b643c8da77"},"schema_version":"1.0"},"canonical_sha256":"4a2467992b924678a6b1caa714f54e77c212ffc592d959a64feacde882ee69a4","source":{"kind":"arxiv","id":"1908.06793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06793","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06793v1","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06793","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"JISGPGJLSJDH","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_16","alias_value":"JISGPGJLSJDHRJVR","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_8","alias_value":"JISGPGJL","created_at":"2026-07-04T23:58:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JISGPGJLSJDHRJVRZKTRJ5KOO7","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-19T13:31:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0aff1ee90378cb2c40c5e9d4d0fd06170c21e164547aac41d84039240ca94b79","abstract_canon_sha256":"84c30535221fbe9853ea58d68bbb2d6f27c5f5a39d1d09b37ce243b643c8da77"},"schema_version":"1.0"},"canonical_sha256":"4a2467992b924678a6b1caa714f54e77c212ffc592d959a64feacde882ee69a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:19.416056Z","signature_b64":"HlR1nk8AwNKBkvxL3w//hbSBC0MFayPLQskrTF5/2yNSCGbJefjOW5cHUEMAFAMSJppOrMsrHFkcPHmzPWosCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a2467992b924678a6b1caa714f54e77c212ffc592d959a64feacde882ee69a4","last_reissued_at":"2026-07-04T23:58:19.415661Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:19.415661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06793","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":"2026-07-04T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t5QRG8CtkafKTDhSpDpD4s2iVV16dtxmYjr7HYAy876nb70yZ62USYBIq+ef4Fqzti0wDm43DwEjBKVA7eE4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:46:25.836090Z"},"content_sha256":"4e6a7c37783a9d48ae39a85da5d6e45adfa2e7a25a9feec25c901a3c8095c12f","schema_version":"1.0","event_id":"sha256:4e6a7c37783a9d48ae39a85da5d6e45adfa2e7a25a9feec25c901a3c8095c12f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JISGPGJLSJDHRJVRZKTRJ5KOO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On definition of quantum tomography via the Sobolev embedding theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"G.G. Amosov, Ya.A. Korennoy","submitted_at":"2019-08-19T13:31:07Z","abstract_excerpt":"We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06793","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/1908.06793/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":"2026-07-04T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hxo8SMHTLEkbUsVbppyf5df4hbW0mlm+uDdiSPhydI0BRWywtbIX+qYsNz2roVOvqB3d262FIlFePHqBGMi0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:46:25.836928Z"},"content_sha256":"386bf65aa8dbbf078b7f71a0c97496f0c6d031236595a3c9d6537ee1aee35ea2","schema_version":"1.0","event_id":"sha256:386bf65aa8dbbf078b7f71a0c97496f0c6d031236595a3c9d6537ee1aee35ea2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/bundle.json","state_url":"https://pith.science/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/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":"2026-08-16T04:46:25Z","links":{"resolver":"https://pith.science/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7","bundle":"https://pith.science/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/bundle.json","state":"https://pith.science/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JISGPGJLSJDHRJVRZKTRJ5KOO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JISGPGJLSJDHRJVRZKTRJ5KOO7","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":"84c30535221fbe9853ea58d68bbb2d6f27c5f5a39d1d09b37ce243b643c8da77","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-19T13:31:07Z","title_canon_sha256":"0aff1ee90378cb2c40c5e9d4d0fd06170c21e164547aac41d84039240ca94b79"},"schema_version":"1.0","source":{"id":"1908.06793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06793","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06793v1","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06793","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"JISGPGJLSJDH","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_16","alias_value":"JISGPGJLSJDHRJVR","created_at":"2026-07-04T23:58:19Z"},{"alias_kind":"pith_short_8","alias_value":"JISGPGJL","created_at":"2026-07-04T23:58:19Z"}],"graph_snapshots":[{"event_id":"sha256:386bf65aa8dbbf078b7f71a0c97496f0c6d031236595a3c9d6537ee1aee35ea2","target":"graph","created_at":"2026-07-04T23:58:19Z","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/1908.06793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework.","authors_text":"G.G. Amosov, Ya.A. Korennoy","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-19T13:31:07Z","title":"On definition of quantum tomography via the Sobolev embedding theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06793","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":"sha256:4e6a7c37783a9d48ae39a85da5d6e45adfa2e7a25a9feec25c901a3c8095c12f","target":"record","created_at":"2026-07-04T23:58:19Z","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":"84c30535221fbe9853ea58d68bbb2d6f27c5f5a39d1d09b37ce243b643c8da77","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-19T13:31:07Z","title_canon_sha256":"0aff1ee90378cb2c40c5e9d4d0fd06170c21e164547aac41d84039240ca94b79"},"schema_version":"1.0","source":{"id":"1908.06793","kind":"arxiv","version":1}},"canonical_sha256":"4a2467992b924678a6b1caa714f54e77c212ffc592d959a64feacde882ee69a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a2467992b924678a6b1caa714f54e77c212ffc592d959a64feacde882ee69a4","first_computed_at":"2026-07-04T23:58:19.415661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:19.415661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlR1nk8AwNKBkvxL3w//hbSBC0MFayPLQskrTF5/2yNSCGbJefjOW5cHUEMAFAMSJppOrMsrHFkcPHmzPWosCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:19.416056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e6a7c37783a9d48ae39a85da5d6e45adfa2e7a25a9feec25c901a3c8095c12f","sha256:386bf65aa8dbbf078b7f71a0c97496f0c6d031236595a3c9d6537ee1aee35ea2"],"state_sha256":"4623e992c2448295929393fbe67dbab1ac11a4321a9e668198236278ed4b420e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhMF7BiK+SDcCzN/WN6qFkHCknx+xgDD3+WLtitGUQSVzY+Cd/SFcW1x/RdlO9AGaXPk8ia2KgyiAgGcKov6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T04:46:25.842728Z","bundle_sha256":"7e9726d429d8c01dc0625d1b62d37e8567c0118c2f71a25f8a76c6602f973d64"}}