{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GENGRQWSA3DMKV6OBDC65VOJ2Q","short_pith_number":"pith:GENGRQWS","canonical_record":{"source":{"id":"1703.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-02T18:37:35Z","cross_cats_sorted":["math-ph","math.MP","math.OA","math.PR"],"title_canon_sha256":"aba65b79eed502a66b3ce317479e99c5c9f7609fb4d494dbf2f21d56a41537e8","abstract_canon_sha256":"955a9f1fbd9e31542eb5c02c56816b982d94eb932d849181ec5ed4b50d5f060a"},"schema_version":"1.0"},"canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","source":{"kind":"arxiv","id":"1703.00889","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00889","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00889v2","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00889","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"GENGRQWSA3DM","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GENGRQWSA3DMKV6O","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GENGRQWS","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GENGRQWSA3DMKV6OBDC65VOJ2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-02T18:37:35Z","cross_cats_sorted":["math-ph","math.MP","math.OA","math.PR"],"title_canon_sha256":"aba65b79eed502a66b3ce317479e99c5c9f7609fb4d494dbf2f21d56a41537e8","abstract_canon_sha256":"955a9f1fbd9e31542eb5c02c56816b982d94eb932d849181ec5ed4b50d5f060a"},"schema_version":"1.0"},"canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:34.643822Z","signature_b64":"YBcPDS8mlrOF3jE605Ig3owIoRHahnOYvI5oCPsV6I6hz57Y65yn/OHDAN5t4gNslKeZicZT5AwG3HoCa7A2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","last_reissued_at":"2026-05-17T23:48:34.643268Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:34.643268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00889","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":"2026-05-17T23:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yX2MVjGl04Il4bQ+K/stE+W4NgicLjWcTIlijuQIbSTrzOXKgr3c0abJ+zE+FyooR26MmZvLaV+G0apw1je8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:25:28.921923Z"},"content_sha256":"a29440687f740b69b4530033637736ebef6da60ba3c5a906ac92b209d76f262c","schema_version":"1.0","event_id":"sha256:a29440687f740b69b4530033637736ebef6da60ba3c5a906ac92b209d76f262c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GENGRQWSA3DMKV6OBDC65VOJ2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Harmonic Analysis of the Density Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA","math.PR"],"primary_cat":"quant-ph","authors_text":"Maurice A. de Gosson","submitted_at":"2017-03-02T18:37:35Z","abstract_excerpt":"We will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00889","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":"2026-05-17T23:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oxIUH3lIkb45m/4oeoc0AD+ygOoygl1j7przQoXgJJajA9W6M/rLdSjvDHKgZrTEkYdCBVle5uE+zzQUyY+tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:25:28.922267Z"},"content_sha256":"a22960f5bdc80f3a828cbfb3ee3a7c3f284b6e3e1d0f9733e75d7156b551e7be","schema_version":"1.0","event_id":"sha256:a22960f5bdc80f3a828cbfb3ee3a7c3f284b6e3e1d0f9733e75d7156b551e7be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/bundle.json","state_url":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/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":"2026-06-01T11:25:28Z","links":{"resolver":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q","bundle":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/bundle.json","state":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GENGRQWSA3DMKV6OBDC65VOJ2Q","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":"955a9f1fbd9e31542eb5c02c56816b982d94eb932d849181ec5ed4b50d5f060a","cross_cats_sorted":["math-ph","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-02T18:37:35Z","title_canon_sha256":"aba65b79eed502a66b3ce317479e99c5c9f7609fb4d494dbf2f21d56a41537e8"},"schema_version":"1.0","source":{"id":"1703.00889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00889","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00889v2","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00889","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"GENGRQWSA3DM","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GENGRQWSA3DMKV6O","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GENGRQWS","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:a22960f5bdc80f3a828cbfb3ee3a7c3f284b6e3e1d0f9733e75d7156b551e7be","target":"graph","created_at":"2026-05-17T23:48:34Z","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 will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.","authors_text":"Maurice A. de Gosson","cross_cats":["math-ph","math.MP","math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-02T18:37:35Z","title":"Quantum Harmonic Analysis of the Density Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00889","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:a29440687f740b69b4530033637736ebef6da60ba3c5a906ac92b209d76f262c","target":"record","created_at":"2026-05-17T23:48:34Z","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":"955a9f1fbd9e31542eb5c02c56816b982d94eb932d849181ec5ed4b50d5f060a","cross_cats_sorted":["math-ph","math.MP","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-03-02T18:37:35Z","title_canon_sha256":"aba65b79eed502a66b3ce317479e99c5c9f7609fb4d494dbf2f21d56a41537e8"},"schema_version":"1.0","source":{"id":"1703.00889","kind":"arxiv","version":2}},"canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","first_computed_at":"2026-05-17T23:48:34.643268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:34.643268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBcPDS8mlrOF3jE605Ig3owIoRHahnOYvI5oCPsV6I6hz57Y65yn/OHDAN5t4gNslKeZicZT5AwG3HoCa7A2CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:34.643822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a29440687f740b69b4530033637736ebef6da60ba3c5a906ac92b209d76f262c","sha256:a22960f5bdc80f3a828cbfb3ee3a7c3f284b6e3e1d0f9733e75d7156b551e7be"],"state_sha256":"e91a0c0bdbb6ff579c3885436d219f6fbbea7da782d15a2b2321ed2f13cdc825"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQBxHuGytVnpWVY2p2XZRpphGqdXhzcxjelqlxYq/90eWkY8rCZqbMG0+pOSZYkj3Y/+laNeCTHi6rMmEVe1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:25:28.924399Z","bundle_sha256":"3cff3095cd5147ae06848fd4208c2ab60f321c93ee3bc0cddee1788d7c74f6e9"}}