{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GFTTVSXG4AHTGUEQ5U7CKMQNLL","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":"be9d99536f7ce4cba7e1ccd2531fe12a45664b1d041e87924c77cff9c388bd19","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-09T17:01:39Z","title_canon_sha256":"5096e1587d410ad412f127d145dfca2c01b24332fb2897cf962f7e19367ea2e3"},"schema_version":"1.0","source":{"id":"0901.1275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1275","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1275v1","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1275","created_at":"2026-05-18T02:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"GFTTVSXG4AHT","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GFTTVSXG4AHTGUEQ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GFTTVSXG","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:1bbdfa2a63a3be31e9589ece9d29af708378c832b32dbe08450c5774008887ea","target":"graph","created_at":"2026-05-18T02:15:02Z","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":"We discuss the relevance to deformation quantization of Feichtinger's modulation spaces, especially of the weighted Sjoestrand classes. These function spaces are good classes of symbols of pseudo-differential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well adapted to the study of the Moyal star-product and of the star-exponential.","authors_text":"Franz Luef, Maurice de Gosson","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-09T17:01:39Z","title":"On the Usefulness of Modulation Spaces in Deformation Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1275","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":"sha256:4b86a2526f381826b4ff2945e96e3532c6c09902fc8a078cd62e250ae6ab9187","target":"record","created_at":"2026-05-18T02:15:02Z","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":"be9d99536f7ce4cba7e1ccd2531fe12a45664b1d041e87924c77cff9c388bd19","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-09T17:01:39Z","title_canon_sha256":"5096e1587d410ad412f127d145dfca2c01b24332fb2897cf962f7e19367ea2e3"},"schema_version":"1.0","source":{"id":"0901.1275","kind":"arxiv","version":1}},"canonical_sha256":"31673acae6e00f335090ed3e25320d5ae04d012295a8c68d353516b520a00a33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31673acae6e00f335090ed3e25320d5ae04d012295a8c68d353516b520a00a33","first_computed_at":"2026-05-18T02:15:02.760438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:02.760438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Btem0AidK5NQHPPd4p9XAgPgwKHR9yT86vVN8jX5zPZ+SaoHVl0zUZffsMCgFSGI13NpFXPhTuBe/pp1FXJaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:02.760870Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b86a2526f381826b4ff2945e96e3532c6c09902fc8a078cd62e250ae6ab9187","sha256:1bbdfa2a63a3be31e9589ece9d29af708378c832b32dbe08450c5774008887ea"],"state_sha256":"81704fdeeadb01c33ef9d13cd7bdfc76f198ed7abd0172f185a817dfd47de93d"}