{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KXA2X5X53LLEJ6624KVDMPJAGN","short_pith_number":"pith:KXA2X5X5","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"},"canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","source":{"kind":"arxiv","id":"1605.08691","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08691","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08691v1","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08691","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"KXA2X5X53LLE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXA2X5X53LLEJ662","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXA2X5X5","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KXA2X5X53LLEJ6624KVDMPJAGN","target":"record","payload":{"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"},"canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","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"},"source_kind":"arxiv","source_id":"1605.08691","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eiNQqyacN5thyAp8iAMCAzAJNYpjQBryNDINl/I4B6XVyVBugcxnmVKd9hFJFtSBJE7eI3VarNFmx+8LfCkNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:47:03.247034Z"},"content_sha256":"316e401b9092e352d68f3e3eedf6ea41f4f55939fd2dd3b117ac887235e4504f","schema_version":"1.0","event_id":"sha256:316e401b9092e352d68f3e3eedf6ea41f4f55939fd2dd3b117ac887235e4504f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KXA2X5X53LLEJ6624KVDMPJAGN","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEgz9r2amQkBMgl4/5xuKrKAeuOSt7sO+3CNxK9VRTuqvd8RmYofAiVdTvhrTVl8xhmlGny9xyHQ3RTZQfyJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:47:03.247387Z"},"content_sha256":"db112ecaa843e543fbf6083eab583e8d51254f6b5db04fa4972e82d92db2d5e6","schema_version":"1.0","event_id":"sha256:db112ecaa843e543fbf6083eab583e8d51254f6b5db04fa4972e82d92db2d5e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/bundle.json","state_url":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXA2X5X53LLEJ6624KVDMPJAGN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T19:47:03Z","links":{"resolver":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN","bundle":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/bundle.json","state":"https://pith.science/pith/KXA2X5X53LLEJ6624KVDMPJAGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXA2X5X53LLEJ6624KVDMPJAGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KXA2X5X53LLEJ6624KVDMPJAGN","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":"51747513a1b7e8e964cdc97ae2944a6912783b6e5527a7a8fa4ecd543ab247c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-27T15:37:21Z","title_canon_sha256":"cb2b0c434c0ef1fe7989d27b85b5d3ca847b27efd8d1793580d74f32d1d2b7c5"},"schema_version":"1.0","source":{"id":"1605.08691","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08691","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08691v1","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08691","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"KXA2X5X53LLE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXA2X5X53LLEJ662","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXA2X5X5","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:db112ecaa843e543fbf6083eab583e8d51254f6b5db04fa4972e82d92db2d5e6","target":"graph","created_at":"2026-05-18T01:13:29Z","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 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.","authors_text":"Anita Tabacco, Michele Berra, Ubertino Battisti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-27T15:37:21Z","title":"Stockwell-Like Frames for Sobolev Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08691","kind":"arxiv","version":1},"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":"sha256:316e401b9092e352d68f3e3eedf6ea41f4f55939fd2dd3b117ac887235e4504f","target":"record","created_at":"2026-05-18T01:13:29Z","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":"51747513a1b7e8e964cdc97ae2944a6912783b6e5527a7a8fa4ecd543ab247c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-27T15:37:21Z","title_canon_sha256":"cb2b0c434c0ef1fe7989d27b85b5d3ca847b27efd8d1793580d74f32d1d2b7c5"},"schema_version":"1.0","source":{"id":"1605.08691","kind":"arxiv","version":1}},"canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55c1abf6fddad644fbdae2aa363d2033630fdfbbee20982813af1f06152cf6e8","first_computed_at":"2026-05-18T01:13:29.290540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:29.290540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4hVIrpcna6SfoIoCiTBg9Q94zFKaBUJIgDPXHg71a57O1uMZN1cC4SifKZdsJ8/7VP8HlX+/8CYvf4TFmCfVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:29.291056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08691","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:316e401b9092e352d68f3e3eedf6ea41f4f55939fd2dd3b117ac887235e4504f","sha256:db112ecaa843e543fbf6083eab583e8d51254f6b5db04fa4972e82d92db2d5e6"],"state_sha256":"db880bf8a1d30233ec3143866807dee0961443224eea774d1bf7083cfa2e8ac1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOW364dxZ3uK3e4L+ujGwCKXYcAo7wy1gXooXhK0ID5wZYmLJ3sKGCtQPKfHkR+j/h6elNVlmNGntTT+cEIUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:47:03.249271Z","bundle_sha256":"4eb72ff960d495256a9e09d69763bfaee6a4a238a10a6e61b1b70ad287afe426"}}