{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:32YYQ4FXKAO6ZHWMPZWKD5DL3Z","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":"26bfd12a670b516e8b18fc28d0a0a1f7199017962e98440a4409250c524ec691","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-24T19:29:47Z","title_canon_sha256":"9234ff6b6e25b837a833388ac73c0f8d33af467df6e828ffcd70646ac2907a38"},"schema_version":"1.0","source":{"id":"1606.07796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07796","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07796v1","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07796","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"32YYQ4FXKAO6","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"32YYQ4FXKAO6ZHWM","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"32YYQ4FX","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:55b6160f6976e8a98a396ef08675a52315745bf999ded3aae303b7df0e726b37","target":"graph","created_at":"2026-05-18T00:20:27Z","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":"Quantization procedures play an essential role in microlocal analysis, time-frequency analysis and, of course, in quantum mechanics. Roughly speaking the basic idea, due to Dirac, is to associate to any symbol, or observable, $a(x,\\xi)$ an operator $\\mathrm{Op}(a)$, according to some axioms dictated by physical considerations. This led to the introduction of a variety of quantizations. They all agree when the symbol $a(x,\\xi)=f(x)$ depends only on $x$ or $a(x,\\xi)=g(\\xi)$ depends only on $\\xi$: \\[ \\mathrm{Op}(f\\otimes1)u=fu,\\quad\\mathrm{Op}(1\\otimes g)u=\\mathcal{F}% ^{-1}(g\\mathcal{F}u) \\] whe","authors_text":"Fabio Nicola, Maurice de Gosson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-24T19:29:47Z","title":"Born-Jordan Pseudodifferential Operators and the Dirac Correspondence: Beyond the Groenewold-van Hove Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07796","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:d1b3d35b08781e2957f707c5f748e5016e154f49571f7e5101246d60e6553670","target":"record","created_at":"2026-05-18T00:20:27Z","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":"26bfd12a670b516e8b18fc28d0a0a1f7199017962e98440a4409250c524ec691","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-24T19:29:47Z","title_canon_sha256":"9234ff6b6e25b837a833388ac73c0f8d33af467df6e828ffcd70646ac2907a38"},"schema_version":"1.0","source":{"id":"1606.07796","kind":"arxiv","version":1}},"canonical_sha256":"deb18870b7501dec9ecc7e6ca1f46bde4f883dca59b020dec5da436044e89f36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deb18870b7501dec9ecc7e6ca1f46bde4f883dca59b020dec5da436044e89f36","first_computed_at":"2026-05-18T00:20:27.755149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:27.755149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmQXk9bK5Ug9Onw/DW3QrO3qnjVI5OgFDyfr5pKp8/pVp0yqgovLvVnymC2sFXL5tY5UjehS/8eovWX19jnWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:27.755603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1b3d35b08781e2957f707c5f748e5016e154f49571f7e5101246d60e6553670","sha256:55b6160f6976e8a98a396ef08675a52315745bf999ded3aae303b7df0e726b37"],"state_sha256":"4c65a36fae826791af28f536cfa2425ce5cf18ffcea60bf15799a1311f46a72f"}