{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GWTW4DMMYWXSUP6S3XMD3P74FV","short_pith_number":"pith:GWTW4DMM","schema_version":"1.0","canonical_sha256":"35a76e0d8cc5af2a3fd2ddd83dbffc2d6c34e688efc2d09a51050dddec6bae1c","source":{"kind":"arxiv","id":"1501.05496","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic boundary forms for tight Gabor frames and lattice localization domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H.G. Feichtinger, K. Nowak, M. Pap","submitted_at":"2015-01-22T13:47:53Z","abstract_excerpt":"We consider Gabor localization operators $G_{\\phi,\\Omega}$ defined by two parameters, the generating function $\\phi$ of a tight Gabor frame $\\{\\phi_\\lambda\\}_{\\lambda \\in \\Lambda}$, parametrized by the elements of a given lattice $\\Lambda \\subset \\Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\\Bbb{R}^2$, and a lattice localization domain $\\Omega \\subset \\Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\\Lambda$. We find an explicit formula for the boundary form $BF(\\phi,\\Omega)=\\text{A}_\\Lambda \\lim_{R\\rightarrow \\infty}\\frac{PF(G_{\\phi,R\\Omega})}{R}$, the norm"},"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":"1501.05496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-22T13:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"177b1867fdca1c61557e6c0a817c64e5f49b5dd0e9a688b72ad2374e6aec3b85","abstract_canon_sha256":"1a08cba9a14acd4137eacdf12b0126534236a4fbc473aed99d37d888f2c6edc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:54.539803Z","signature_b64":"oN26BlPa1OhqNDFxoJuJV7OIl6NIwjKsYxeUhSaQOTjd8VhygBmtYNshPllZ4n/JGkhvt4S9rU44PzrImfiqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35a76e0d8cc5af2a3fd2ddd83dbffc2d6c34e688efc2d09a51050dddec6bae1c","last_reissued_at":"2026-05-18T02:28:54.539453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:54.539453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic boundary forms for tight Gabor frames and lattice localization domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H.G. Feichtinger, K. Nowak, M. Pap","submitted_at":"2015-01-22T13:47:53Z","abstract_excerpt":"We consider Gabor localization operators $G_{\\phi,\\Omega}$ defined by two parameters, the generating function $\\phi$ of a tight Gabor frame $\\{\\phi_\\lambda\\}_{\\lambda \\in \\Lambda}$, parametrized by the elements of a given lattice $\\Lambda \\subset \\Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\\Bbb{R}^2$, and a lattice localization domain $\\Omega \\subset \\Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\\Lambda$. We find an explicit formula for the boundary form $BF(\\phi,\\Omega)=\\text{A}_\\Lambda \\lim_{R\\rightarrow \\infty}\\frac{PF(G_{\\phi,R\\Omega})}{R}$, the norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05496","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":""},"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":"1501.05496","created_at":"2026-05-18T02:28:54.539512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05496v1","created_at":"2026-05-18T02:28:54.539512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05496","created_at":"2026-05-18T02:28:54.539512+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWTW4DMMYWXS","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWTW4DMMYWXSUP6S","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWTW4DMM","created_at":"2026-05-18T12:29:22.688609+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/GWTW4DMMYWXSUP6S3XMD3P74FV","json":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV.json","graph_json":"https://pith.science/api/pith-number/GWTW4DMMYWXSUP6S3XMD3P74FV/graph.json","events_json":"https://pith.science/api/pith-number/GWTW4DMMYWXSUP6S3XMD3P74FV/events.json","paper":"https://pith.science/paper/GWTW4DMM"},"agent_actions":{"view_html":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV","download_json":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV.json","view_paper":"https://pith.science/paper/GWTW4DMM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05496&json=true","fetch_graph":"https://pith.science/api/pith-number/GWTW4DMMYWXSUP6S3XMD3P74FV/graph.json","fetch_events":"https://pith.science/api/pith-number/GWTW4DMMYWXSUP6S3XMD3P74FV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV/action/storage_attestation","attest_author":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV/action/author_attestation","sign_citation":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV/action/citation_signature","submit_replication":"https://pith.science/pith/GWTW4DMMYWXSUP6S3XMD3P74FV/action/replication_record"}},"created_at":"2026-05-18T02:28:54.539512+00:00","updated_at":"2026-05-18T02:28:54.539512+00:00"}