{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2YKTFTHOXTIH5WYGD7AXHTHKQI","short_pith_number":"pith:2YKTFTHO","schema_version":"1.0","canonical_sha256":"d61532cceebcd07edb061fc173ccea822e3475a95ba2b7fb3db88d4c830c72c2","source":{"kind":"arxiv","id":"2510.18683","version":3},"attestation_state":"computed","paper":{"title":"On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The nonlinear Wigner concentration problem admits an optimizer for any finite-measure phase space set and every p less than infinity.","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Erling A. T. Svela, Federico Stra, S. Ivan Trapasso","submitted_at":"2025-10-21T14:40:34Z","abstract_excerpt":"We prove that, for any measurable phase space subset $\\Omega\\subset\\mathbb{R}^{2d}$ with $0<|\\Omega|<\\infty$ and any $1\\le p < \\infty$, the nonlinear concentration problem $$ \\sup_{f \\in L^2(\\mathbb{R}^d)\\setminus\\{0\\}}\\frac{\\|Wf\\|_{L^p(\\Omega)}}{\\|f\\|_{L^2}^2}$$ admits an optimizer, where $Wf$ is the Wigner distribution of $f$. The main obstruction is that $Wf$ is covariant (not invariant) under time-frequency shifts, which impedes weak upper semicontinuity, so the effects of constructive interference must be taken into account. We close this compactness gap via concentration compactness for "},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2510.18683","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-10-21T14:40:34Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"50cbf89cd6c46fbe84be09b1e8223fb8d4a3211d76a4e3cfbdeed873cc1417f6","abstract_canon_sha256":"97cc210e585e1883991fcb1f7f6e1c2b2fcfff2cb72be4acab399ca0a6ea0d41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:03.478345Z","signature_b64":"WJ9YHcAitImTuD+5Y36qXRj7Ri7JZjXZRFpLVDXuIN9yttTMN/HWcuX2MDizRw7jSk7JZ/dxJ2YyliBwwufdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d61532cceebcd07edb061fc173ccea822e3475a95ba2b7fb3db88d4c830c72c2","last_reissued_at":"2026-05-26T02:05:03.477560Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:03.477560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The nonlinear Wigner concentration problem admits an optimizer for any finite-measure phase space set and every p less than infinity.","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Erling A. T. Svela, Federico Stra, S. Ivan Trapasso","submitted_at":"2025-10-21T14:40:34Z","abstract_excerpt":"We prove that, for any measurable phase space subset $\\Omega\\subset\\mathbb{R}^{2d}$ with $0<|\\Omega|<\\infty$ and any $1\\le p < \\infty$, the nonlinear concentration problem $$ \\sup_{f \\in L^2(\\mathbb{R}^d)\\setminus\\{0\\}}\\frac{\\|Wf\\|_{L^p(\\Omega)}}{\\|f\\|_{L^2}^2}$$ admits an optimizer, where $Wf$ is the Wigner distribution of $f$. The main obstruction is that $Wf$ is covariant (not invariant) under time-frequency shifts, which impedes weak upper semicontinuity, so the effects of constructive interference must be taken into account. We close this compactness gap via concentration compactness for "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For any measurable Ω ⊂ ℝ^{2d} with 0 < |Ω| < ∞ and any 1 ≤ p < ∞, the nonlinear concentration problem sup (||Wf||_{L^p(Ω)} / ||f||_{L^2}^2) admits an optimizer.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The new asymptotic formula that quantifies the limiting contribution to concentration over Ω from asymptotically separated wave packets holds and can be combined with concentration compactness for Heisenberg-type dislocations to restore the necessary upper semicontinuity (abstract, section on main proof strategy).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence of optimizers is established for the Wigner-distribution concentration functional over finite-measure phase-space sets for 1 ≤ p < ∞, with sharp constant 2^d attained at p = ∞.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The nonlinear Wigner concentration problem admits an optimizer for any finite-measure phase space set and every p less than infinity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4124ad858f6d5abc30d50928e15da46757e1fb0ae3bd93c22ae029f3c426f4f0"},"source":{"id":"2510.18683","kind":"arxiv","version":3},"verdict":{"id":"3441beb2-be73-4699-ab57-58fd1a7fc119","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T05:00:48.900187Z","strongest_claim":"For any measurable Ω ⊂ ℝ^{2d} with 0 < |Ω| < ∞ and any 1 ≤ p < ∞, the nonlinear concentration problem sup (||Wf||_{L^p(Ω)} / ||f||_{L^2}^2) admits an optimizer.","one_line_summary":"Existence of optimizers is established for the Wigner-distribution concentration functional over finite-measure phase-space sets for 1 ≤ p < ∞, with sharp constant 2^d attained at p = ∞.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The new asymptotic formula that quantifies the limiting contribution to concentration over Ω from asymptotically separated wave packets holds and can be combined with concentration compactness for Heisenberg-type dislocations to restore the necessary upper semicontinuity (abstract, section on main proof strategy).","pith_extraction_headline":"The nonlinear Wigner concentration problem admits an optimizer for any finite-measure phase space set and every p less than infinity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.18683/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":32,"sample":[{"doi":"","year":2010,"title":"P. Boggiatto, G. De Donno, and A. Oliaro. Time-frequency representations of Wigner type and pseudo-differential operators.Trans. Amer. Math. Soc., 362(9), 2010","work_id":"dfd296cb-4486-47ed-9298-a7a000ea1ed7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"A. J. Bracken, H.-D. Doebner, and J. G. Wood. Bounds on integrals of the wigner function.Phys. Rev. Lett., 83, 1999","work_id":"c4e854f5-0abb-4b7e-83bc-95b7af6391da","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Cohen.Time-frequency analysis","work_id":"8a54297e-793f-431f-9240-029afb2be1f9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"L. Cohen. Uncertainty principles of the short-time fourier transform. InAdvanced Signal Processing Algorithms, volume 2563, pages 80–90. SPIE, 1995","work_id":"e75d9ad6-f771-45b9-98c1-a278d32b8165","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"E. Cordero, M. de Gosson, and F. Nicola. On the reduction of the interferences in the Born-Jordan distribution.Appl. Comput. Harmon. Anal., 44(2), 2018","work_id":"4cae2b28-3d2d-4bc9-a3b8-1642c1c664d1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"a1d628225e0de4183680a62a8e9844d5b16e46051ac8f6f6732da876da6df026","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ac965098c8efd055c591752ad55feafc5bc5a72dc9b5ad2f4f8cd4100ca8452d"},"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":"2510.18683","created_at":"2026-05-26T02:05:03.477679+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.18683v3","created_at":"2026-05-26T02:05:03.477679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.18683","created_at":"2026-05-26T02:05:03.477679+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YKTFTHOXTIH","created_at":"2026-05-26T02:05:03.477679+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YKTFTHOXTIH5WYG","created_at":"2026-05-26T02:05:03.477679+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YKTFTHO","created_at":"2026-05-26T02:05:03.477679+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI","json":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI.json","graph_json":"https://pith.science/api/pith-number/2YKTFTHOXTIH5WYGD7AXHTHKQI/graph.json","events_json":"https://pith.science/api/pith-number/2YKTFTHOXTIH5WYGD7AXHTHKQI/events.json","paper":"https://pith.science/paper/2YKTFTHO"},"agent_actions":{"view_html":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI","download_json":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI.json","view_paper":"https://pith.science/paper/2YKTFTHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.18683&json=true","fetch_graph":"https://pith.science/api/pith-number/2YKTFTHOXTIH5WYGD7AXHTHKQI/graph.json","fetch_events":"https://pith.science/api/pith-number/2YKTFTHOXTIH5WYGD7AXHTHKQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI/action/storage_attestation","attest_author":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI/action/author_attestation","sign_citation":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI/action/citation_signature","submit_replication":"https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI/action/replication_record"}},"created_at":"2026-05-26T02:05:03.477679+00:00","updated_at":"2026-05-26T02:05:03.477679+00:00"}