{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KXA2X5X53LLEJ6624KVDMPJAGN","short_pith_number":"pith:KXA2X5X5","schema_version":"1.0","canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","source":{"kind":"arxiv","id":"1605.08691","version":1},"attestation_state":"computed","paper":{"title":"Stockwell-Like Frames for Sobolev Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anita Tabacco, Michele Berra, Ubertino Battisti","submitted_at":"2016-05-27T15:37:21Z","abstract_excerpt":"We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space $H^s(\\mathbb{R}^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a time-frequency localized version of Fourier basis of $L^2([0,1])$. This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties."},"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":"1605.08691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-27T15:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"cb2b0c434c0ef1fe7989d27b85b5d3ca847b27efd8d1793580d74f32d1d2b7c5","abstract_canon_sha256":"51747513a1b7e8e964cdc97ae2944a6912783b6e5527a7a8fa4ecd543ab247c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:29.291056Z","signature_b64":"4hVIrpcna6SfoIoCiTBg9Q94zFKaBUJIgDPXHg71a57O1uMZN1cC4SifKZdsJ8/7VP8HlX+/8CYvf4TFmCfVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","last_reissued_at":"2026-05-18T01:13:29.290540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:29.290540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stockwell-Like Frames for Sobolev Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anita Tabacco, Michele Berra, Ubertino Battisti","submitted_at":"2016-05-27T15:37:21Z","abstract_excerpt":"We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space $H^s(\\mathbb{R}^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a time-frequency localized version of Fourier basis of $L^2([0,1])$. This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08691","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":"1605.08691","created_at":"2026-05-18T01:13:29.290609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08691v1","created_at":"2026-05-18T01:13:29.290609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08691","created_at":"2026-05-18T01:13:29.290609+00:00"},{"alias_kind":"pith_short_12","alias_value":"KXA2X5X53LLE","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"KXA2X5X53LLEJ662","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"KXA2X5X5","created_at":"2026-05-18T12:30:29.479603+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/KXA2X5X53LLEJ6624KVDMPJAGN","json":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN.json","graph_json":"https://pith.science/api/pith-number/KXA2X5X53LLEJ6624KVDMPJAGN/graph.json","events_json":"https://pith.science/api/pith-number/KXA2X5X53LLEJ6624KVDMPJAGN/events.json","paper":"https://pith.science/paper/KXA2X5X5"},"agent_actions":{"view_html":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN","download_json":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN.json","view_paper":"https://pith.science/paper/KXA2X5X5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08691&json=true","fetch_graph":"https://pith.science/api/pith-number/KXA2X5X53LLEJ6624KVDMPJAGN/graph.json","fetch_events":"https://pith.science/api/pith-number/KXA2X5X53LLEJ6624KVDMPJAGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/action/storage_attestation","attest_author":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/action/author_attestation","sign_citation":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/action/citation_signature","submit_replication":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/action/replication_record"}},"created_at":"2026-05-18T01:13:29.290609+00:00","updated_at":"2026-05-18T01:13:29.290609+00:00"}