{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:RJAJBOQY6GCKSKL72WAKAPCC7A","short_pith_number":"pith:RJAJBOQY","schema_version":"1.0","canonical_sha256":"8a4090ba18f184a9297fd580a03c42f80d92a48702eaa58f3e43cfdb5126a74a","source":{"kind":"arxiv","id":"1009.0150","version":2},"attestation_state":"computed","paper":{"title":"Phase Space Quantum Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Maciej Blaszak, Ziemowit Domanski","submitted_at":"2010-09-01T10:09:12Z","abstract_excerpt":"The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative $\\star$-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems.\n  The considered class of deformations and the corresponding"},"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":"1009.0150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-01T10:09:12Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"4e56e8eb70c62adffa3161146f73737a510a0440b333a179aad53ce5e647716f","abstract_canon_sha256":"a25a612b131404af8a7639e02a95375b842c9dc54cb31c962a50a610fb909916"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:21.178775Z","signature_b64":"natD+v9qx6NXEPWbHACupo4dXoOLusq8NEN12+tC++z3U+A6+zIE7zLgSt55kP5b7urvywJcuOaQZdjXzFk2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a4090ba18f184a9297fd580a03c42f80d92a48702eaa58f3e43cfdb5126a74a","last_reissued_at":"2026-05-18T04:12:21.178094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:21.178094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Space Quantum Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Maciej Blaszak, Ziemowit Domanski","submitted_at":"2010-09-01T10:09:12Z","abstract_excerpt":"The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative $\\star$-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems.\n  The considered class of deformations and the corresponding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0150","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":"1009.0150","created_at":"2026-05-18T04:12:21.178211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.0150v2","created_at":"2026-05-18T04:12:21.178211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0150","created_at":"2026-05-18T04:12:21.178211+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJAJBOQY6GCK","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJAJBOQY6GCKSKL7","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJAJBOQY","created_at":"2026-05-18T12:26:13.927090+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/RJAJBOQY6GCKSKL72WAKAPCC7A","json":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A.json","graph_json":"https://pith.science/api/pith-number/RJAJBOQY6GCKSKL72WAKAPCC7A/graph.json","events_json":"https://pith.science/api/pith-number/RJAJBOQY6GCKSKL72WAKAPCC7A/events.json","paper":"https://pith.science/paper/RJAJBOQY"},"agent_actions":{"view_html":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A","download_json":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A.json","view_paper":"https://pith.science/paper/RJAJBOQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.0150&json=true","fetch_graph":"https://pith.science/api/pith-number/RJAJBOQY6GCKSKL72WAKAPCC7A/graph.json","fetch_events":"https://pith.science/api/pith-number/RJAJBOQY6GCKSKL72WAKAPCC7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A/action/storage_attestation","attest_author":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A/action/author_attestation","sign_citation":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A/action/citation_signature","submit_replication":"https://pith.science/pith/RJAJBOQY6GCKSKL72WAKAPCC7A/action/replication_record"}},"created_at":"2026-05-18T04:12:21.178211+00:00","updated_at":"2026-05-18T04:12:21.178211+00:00"}