{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GENGRQWSA3DMKV6OBDC65VOJ2Q","short_pith_number":"pith:GENGRQWS","schema_version":"1.0","canonical_sha256":"311a68c2d206c6c557ce08c5eed5c9d4336f3ea1eb9db8236208a00c4a3d9b1e","source":{"kind":"arxiv","id":"1703.00889","version":2},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.00889","created_at":"2026-05-17T23:48:34.643395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.00889v2","created_at":"2026-05-17T23:48:34.643395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00889","created_at":"2026-05-17T23:48:34.643395+00:00"},{"alias_kind":"pith_short_12","alias_value":"GENGRQWSA3DM","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GENGRQWSA3DMKV6O","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GENGRQWS","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q","json":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q.json","graph_json":"https://pith.science/api/pith-number/GENGRQWSA3DMKV6OBDC65VOJ2Q/graph.json","events_json":"https://pith.science/api/pith-number/GENGRQWSA3DMKV6OBDC65VOJ2Q/events.json","paper":"https://pith.science/paper/GENGRQWS"},"agent_actions":{"view_html":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q","download_json":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q.json","view_paper":"https://pith.science/paper/GENGRQWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.00889&json=true","fetch_graph":"https://pith.science/api/pith-number/GENGRQWSA3DMKV6OBDC65VOJ2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/GENGRQWSA3DMKV6OBDC65VOJ2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/action/storage_attestation","attest_author":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/action/author_attestation","sign_citation":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/action/citation_signature","submit_replication":"https://pith.science/pith/GENGRQWSA3DMKV6OBDC65VOJ2Q/action/replication_record"}},"created_at":"2026-05-17T23:48:34.643395+00:00","updated_at":"2026-05-17T23:48:34.643395+00:00"}