{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HQOLFD2IRCH32BHR5QNM74UR5N","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":"2c5bbd49af05f72624d6c7dd5aea0c5d70f78bd0c4ce1e98140f064e917809cf","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-05T15:52:52Z","title_canon_sha256":"f6419d1296ca414789d995769e44e945c96e81d34ac8e980bfcb98d44e1fc6d5"},"schema_version":"1.0","source":{"id":"1509.03276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03276","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03276v2","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03276","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"HQOLFD2IRCH3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HQOLFD2IRCH32BHR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HQOLFD2I","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:8bb4ae595e453c27631609d46ea0f419adcc6c32147b4fa16a8a0a7b33315ef7","target":"graph","created_at":"2026-05-18T01:12:34Z","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 obtain discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type. It is shown that the microlocal properties of an ultradistribution can be obtained by sampling the Fourier transforms of its localizations over a lattice in $\\mathbb{R}^{d}$. In particular, we prove the following discrete characterization of the analytic wave front set of a distribution $f\\in\\mathcal{D}'(\\Omega)$. Let $\\Lambda$ be a lattice in $\\mathbb{R}^{d}$ and let $U$ be an open convex neighborhood of the origin such that $U\\cap\\Lambda^{*}=\\{0\\}$. The analytic wave front set $WF_{A}(f)$ coin","authors_text":"Andreas Debrouwere, Jasson Vindas","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-05T15:52:52Z","title":"Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03276","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":"sha256:3ee0590658b97a51d17c6401615a99f465cc177efc942bdd55fb7c9b20526355","target":"record","created_at":"2026-05-18T01:12:34Z","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":"2c5bbd49af05f72624d6c7dd5aea0c5d70f78bd0c4ce1e98140f064e917809cf","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-05T15:52:52Z","title_canon_sha256":"f6419d1296ca414789d995769e44e945c96e81d34ac8e980bfcb98d44e1fc6d5"},"schema_version":"1.0","source":{"id":"1509.03276","kind":"arxiv","version":2}},"canonical_sha256":"3c1cb28f48888fbd04f1ec1acff291eb55f394f3d1bf2d8fe55392812f758d6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c1cb28f48888fbd04f1ec1acff291eb55f394f3d1bf2d8fe55392812f758d6f","first_computed_at":"2026-05-18T01:12:34.858375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:34.858375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ahk+DiWE/XpPNuvYBbp2I6Sk+kgpKJhZBYbm35tXgDlxJ/ahxt9IXV4Y8QuFHmo9O9GNsIcBVm3MRpvR9/D0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:34.858745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ee0590658b97a51d17c6401615a99f465cc177efc942bdd55fb7c9b20526355","sha256:8bb4ae595e453c27631609d46ea0f419adcc6c32147b4fa16a8a0a7b33315ef7"],"state_sha256":"e0a1671e5c57df36c04add60250636ac5390a889ad3ac27ed5609c5fc895c4ac"}