{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PRWYJOBOIV7E35W7IUDPEOJQQK","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":"965db96a1dca7ff4c831aa257431960b3375d16c10696eb81f060f7ee78061f5","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T14:13:26Z","title_canon_sha256":"4d0e04fd5ecfc4e056c8dc8616d79ef42b30a02904aa97d847299bf1f9a3d183"},"schema_version":"1.0","source":{"id":"0902.0513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0513","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0513v2","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0513","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"PRWYJOBOIV7E","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PRWYJOBOIV7E35W7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PRWYJOBO","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:61ff2f794d0770a72e72d8ae15d29648631cf57b55de02127d929e85ce34e26e","target":"graph","created_at":"2026-05-18T03:28:43Z","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":"The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works. We prove criteria in terms of commutators for operators to be magnetic pseudo-differential operators of suitable symbol classes. The approach is completely intrinsic; neither the statements nor the proofs depend on a choice of a vector potential. We apply this criteria to inversion problems, functional calculus, affiliation results and to the study of the evolution group generated by a magnetic pseudo-differential operator.","authors_text":"Marius Mantoiu, Radu Purice, Viorel Iftimie","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T14:13:26Z","title":"Commutator Criteria for Magnetic Pseudodifferential Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0513","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":"sha256:131a612d0bc1d15b615254e538d0eaa8cc1bf20d9a83e1e2d5130f88f681aabf","target":"record","created_at":"2026-05-18T03:28:43Z","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":"965db96a1dca7ff4c831aa257431960b3375d16c10696eb81f060f7ee78061f5","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T14:13:26Z","title_canon_sha256":"4d0e04fd5ecfc4e056c8dc8616d79ef42b30a02904aa97d847299bf1f9a3d183"},"schema_version":"1.0","source":{"id":"0902.0513","kind":"arxiv","version":2}},"canonical_sha256":"7c6d84b82e457e4df6df4506f2393082a90db7a3c2b0832283ba3962d1b6c3ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c6d84b82e457e4df6df4506f2393082a90db7a3c2b0832283ba3962d1b6c3ef","first_computed_at":"2026-05-18T03:28:43.314644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.314644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVTs6da5eAIcmUMPndl6pViqHTPzvNvDL7qzSxV6sNaiTGbs2kmsoB+V8WH7eVsn6UmkA0DwHsHYRWOoT8/3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.315370Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:131a612d0bc1d15b615254e538d0eaa8cc1bf20d9a83e1e2d5130f88f681aabf","sha256:61ff2f794d0770a72e72d8ae15d29648631cf57b55de02127d929e85ce34e26e"],"state_sha256":"b6eefa1de0c0ab3bfe62f9535c9262f2bcf1b2c8878444cd982914c23f62adaa"}