{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZNS62GSQ44LK3EYDO6TV67GBTP","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":"64fe978be59009fa7cf43748e758257d2d49b2e34b03d72b4b203c03549feb50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T17:13:21Z","title_canon_sha256":"c9840abe735a92a9deccd467d4b3f35c5f9feda3aed79638859b779c719c752d"},"schema_version":"1.0","source":{"id":"1905.09249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09249","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09249v1","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09249","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZNS62GSQ44LK","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZNS62GSQ44LK3EYD","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZNS62GSQ","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:d27502c64341706e51882a019c3865350c19d145044e8c8f5f213f667a51260a","target":"graph","created_at":"2026-05-17T23:45:21Z","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 purpose of this article is to prove that the anti-Wick symbol of an operator mapping $ {\\cal S}(\\R^n)$ into ${\\cal S}'(\\R^n)$, which is generally not a tempered distribution, can still be defined as a Gelfand-Shilov generalized function. This result relies on test function spaces embeddings involving the Schwartz and Gelfand-Shilov spaces. An additional embedding concerning Schwartz and Gevrey spaces is also given.","authors_text":"Jean Nourrigat, Laurent Amour, Nicolas Lerner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T17:13:21Z","title":"On the anti-Wick symbol as a Gelfand-Shilov generalized function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09249","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":"sha256:8afc091114749703031b791ef61b9530a114fd3057148baaf2b589cc9a4e9459","target":"record","created_at":"2026-05-17T23:45:21Z","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":"64fe978be59009fa7cf43748e758257d2d49b2e34b03d72b4b203c03549feb50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-22T17:13:21Z","title_canon_sha256":"c9840abe735a92a9deccd467d4b3f35c5f9feda3aed79638859b779c719c752d"},"schema_version":"1.0","source":{"id":"1905.09249","kind":"arxiv","version":1}},"canonical_sha256":"cb65ed1a50e716ad930377a75f7cc19bdd90eb9e9401dd28584fed82ea036653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb65ed1a50e716ad930377a75f7cc19bdd90eb9e9401dd28584fed82ea036653","first_computed_at":"2026-05-17T23:45:21.483149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:21.483149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oa9KlhmAWfTfCnNs2IYvLT/uMXzIVqnbpvZtfLgaXqav2Qvd2V/wrevRH0R/j9pO2v9341unIVfQF5Ozs+XFCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:21.483884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8afc091114749703031b791ef61b9530a114fd3057148baaf2b589cc9a4e9459","sha256:d27502c64341706e51882a019c3865350c19d145044e8c8f5f213f667a51260a"],"state_sha256":"5dd2432c7e087d1606c6b0acadd20c2acb085c2cf60bfa909dd9fa645d44c18e"}