{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MWQG3XDGLXXY36WJSXMJ7JZDWM","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":"5b00612320b7a1ac4a89c11204b95dcd4d703d003217ad768ce47d28f38a655f","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-06-14T06:29:50Z","title_canon_sha256":"11511911a09ba70279bdd0b05dc8472f5487c9a1b810e37d027e471e5029730d"},"schema_version":"1.0","source":{"id":"1806.05383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05383","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05383v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05383","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"MWQG3XDGLXXY","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MWQG3XDGLXXY36WJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MWQG3XDG","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:dbecae24284770f67e069c94ef8bd2f9a934162afc1242b1b4b506448506a691","target":"graph","created_at":"2026-05-18T00:13:16Z","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":"A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\\text{\\reflectbox{\\text{p}}}\\mkern-3mu\\text{p}\\left(q,p\\right)$ which might be computed from the position-space wave function $\\psi\\left(q\\right)$ with a transformation related to the Gabor transformation. The equation of motion for conservative systems can be written in the form of the Schr\\\"{o}dinger equation with a $4D$-dimensional Hamiltonian with classical terms on the diagonal and complex off-diagonal couplings. The Hamiltonian does not contain any differential operators and the quanti","authors_text":"Tomas Zimmermann","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-06-14T06:29:50Z","title":"Integral formulation of the quantum mechanics in the phase space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05383","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":"sha256:7a88286f67aac92361c372d02f78312d67fd09eefdc657dfd4d7482738944c88","target":"record","created_at":"2026-05-18T00:13:16Z","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":"5b00612320b7a1ac4a89c11204b95dcd4d703d003217ad768ce47d28f38a655f","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-06-14T06:29:50Z","title_canon_sha256":"11511911a09ba70279bdd0b05dc8472f5487c9a1b810e37d027e471e5029730d"},"schema_version":"1.0","source":{"id":"1806.05383","kind":"arxiv","version":1}},"canonical_sha256":"65a06ddc665def8dfac995d89fa723b32f2510546b58497d6a00eba650a1119e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a06ddc665def8dfac995d89fa723b32f2510546b58497d6a00eba650a1119e","first_computed_at":"2026-05-18T00:13:16.160423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:16.160423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDCnGMAlQpm4iDIjNJQOyFSj3ndVz5pyBiZIosQw9CW9PZ53EhCfo3s81RrmhJ/y93EC3wngd7MQm/9inVARCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:16.161385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a88286f67aac92361c372d02f78312d67fd09eefdc657dfd4d7482738944c88","sha256:dbecae24284770f67e069c94ef8bd2f9a934162afc1242b1b4b506448506a691"],"state_sha256":"d69afc65fe8a1f615f392e8861afdb2667dba6d68511e217c48b7dda3dcf00d0"}