{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LDPDG4WOQGVUQKG4KMWLJNMKHJ","short_pith_number":"pith:LDPDG4WO","schema_version":"1.0","canonical_sha256":"58de3372ce81ab4828dc532cb4b58a3a6a6a034a5a361dc4b4ef258d864679c0","source":{"kind":"arxiv","id":"2606.10691","version":1},"attestation_state":"computed","paper":{"title":"A Phase Space Criterion for Dynamical Amrein-Berthier Uncertainty","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego Fiorletta, Fabio Nicola, Piero D'Ancona","submitted_at":"2026-06-09T10:48:56Z","abstract_excerpt":"We prove a phase space criterion for dynamical Amrein-Berthier uncertainty principles. The abstract result says that, for a Fourier integral operator $A\\in FIO(\\chi)$ associated with a tame canonical transformation $\\chi$, the localized operator $\\mathbf{1}_E A\\mathbf{1}_F$ is compact on $L^2(\\mathbb {R}^d)$ whenever $\\chi$ satisfies a vertical non refocusing condition: high frequency covectors issued from a spatially localized region cannot return to a vertical direction over the observation region. In the linear symplectic case this condition is equivalent to the familiar nondegeneracy $\\det"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.10691","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T10:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"87f316cc233c581818db2c6c606fbef059f390267301282538360e3b04d2bc39","abstract_canon_sha256":"0fe4d71b4aca479c1e4c32b497e56f7c9b390c2ba8fecba169ae795aa89a53b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:34.496946Z","signature_b64":"cxc+dOIUDMZ7iUhiJEtjm1jsKhoDTI2xKWa7y4WFWGg0GdNro14AV6MP9LD+MAceLv3ZV1V6q/l0Lx877h9OAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58de3372ce81ab4828dc532cb4b58a3a6a6a034a5a361dc4b4ef258d864679c0","last_reissued_at":"2026-06-10T01:10:34.496076Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:34.496076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Phase Space Criterion for Dynamical Amrein-Berthier Uncertainty","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego Fiorletta, Fabio Nicola, Piero D'Ancona","submitted_at":"2026-06-09T10:48:56Z","abstract_excerpt":"We prove a phase space criterion for dynamical Amrein-Berthier uncertainty principles. The abstract result says that, for a Fourier integral operator $A\\in FIO(\\chi)$ associated with a tame canonical transformation $\\chi$, the localized operator $\\mathbf{1}_E A\\mathbf{1}_F$ is compact on $L^2(\\mathbb {R}^d)$ whenever $\\chi$ satisfies a vertical non refocusing condition: high frequency covectors issued from a spatially localized region cannot return to a vertical direction over the observation region. In the linear symplectic case this condition is equivalent to the familiar nondegeneracy $\\det"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10691","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.10691","created_at":"2026-06-10T01:10:34.496246+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10691v1","created_at":"2026-06-10T01:10:34.496246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10691","created_at":"2026-06-10T01:10:34.496246+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDPDG4WOQGVU","created_at":"2026-06-10T01:10:34.496246+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDPDG4WOQGVUQKG4","created_at":"2026-06-10T01:10:34.496246+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDPDG4WO","created_at":"2026-06-10T01:10:34.496246+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ","json":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ.json","graph_json":"https://pith.science/api/pith-number/LDPDG4WOQGVUQKG4KMWLJNMKHJ/graph.json","events_json":"https://pith.science/api/pith-number/LDPDG4WOQGVUQKG4KMWLJNMKHJ/events.json","paper":"https://pith.science/paper/LDPDG4WO"},"agent_actions":{"view_html":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ","download_json":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ.json","view_paper":"https://pith.science/paper/LDPDG4WO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10691&json=true","fetch_graph":"https://pith.science/api/pith-number/LDPDG4WOQGVUQKG4KMWLJNMKHJ/graph.json","fetch_events":"https://pith.science/api/pith-number/LDPDG4WOQGVUQKG4KMWLJNMKHJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ/action/storage_attestation","attest_author":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ/action/author_attestation","sign_citation":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ/action/citation_signature","submit_replication":"https://pith.science/pith/LDPDG4WOQGVUQKG4KMWLJNMKHJ/action/replication_record"}},"created_at":"2026-06-10T01:10:34.496246+00:00","updated_at":"2026-06-10T01:10:34.496246+00:00"}