{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VE76KO3EE555FCUISXVPH2JEIJ","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":"2d59f22abfa01da9c3711a3ed4a87fa4743709d2d4f2b65ce82f09feab82309c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:46:48Z","title_canon_sha256":"023cf0a0654da5abae56e71cc057fcfb70321ebf1abb5755e14bd15dbd631be6"},"schema_version":"1.0","source":{"id":"1706.06171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06171","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06171v1","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06171","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"pith_short_12","alias_value":"VE76KO3EE555","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VE76KO3EE555FCUI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VE76KO3E","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:340d29c0fbf073fac4351d0303f21fb34881aa4ce2c41046df8aca935a07b090","target":"graph","created_at":"2026-05-18T00:42:04Z","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 characterization of positivity properties of Weyl operators is a notoriously difficult problem, and not much progress has been made since the pioneering work of Kastler, Loupias, and Miracle-Sole (KLM). In this paper we begin by reviewing and giving simpler proofs of some known results for trace-class Weyl operators; the latter play an essential role in quantum mechanics. We then apply time-frequency analysis techniques to prove a phase space version of the KLM condition; the main tools are Gabor frames and the Wigner formalism. Finally, discrete approximations of the KLM condition, which ","authors_text":"Elena Cordero, Fabio Nicola, Maurice de Gosson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:46:48Z","title":"On the Positivity of Trace Class Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06171","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":"sha256:0812c6004e8a5893c0067bcd1f7c0160fa92389324f1a4aaa372bff3a1843fd3","target":"record","created_at":"2026-05-18T00:42:04Z","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":"2d59f22abfa01da9c3711a3ed4a87fa4743709d2d4f2b65ce82f09feab82309c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:46:48Z","title_canon_sha256":"023cf0a0654da5abae56e71cc057fcfb70321ebf1abb5755e14bd15dbd631be6"},"schema_version":"1.0","source":{"id":"1706.06171","kind":"arxiv","version":1}},"canonical_sha256":"a93fe53b64277bd28a8895eaf3e92442709b2d7bcd2ab21cd98553ad8399c42e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a93fe53b64277bd28a8895eaf3e92442709b2d7bcd2ab21cd98553ad8399c42e","first_computed_at":"2026-05-18T00:42:04.077717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:04.077717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1GUDJpOTfSzKE62utn+OI3wnGUWqG/owt+RT13qed1Lp148HzNQRSWDICkxgrNLBoTEZvq5DrT/V6AQ6ONdnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:04.078425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0812c6004e8a5893c0067bcd1f7c0160fa92389324f1a4aaa372bff3a1843fd3","sha256:340d29c0fbf073fac4351d0303f21fb34881aa4ce2c41046df8aca935a07b090"],"state_sha256":"ffad77685fc20b6b15e8d69cea26a36d5ec2c5b18f5c629787cb97294ddfe74e"}