{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MY5EOTF2HHC35SM4LRFWMOI6XU","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":"6dd88a3d4839da3f098172befc35d1328ef8afdda07036238947cd179e6b0797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-15T12:17:05Z","title_canon_sha256":"82c3b1d40364ef8db2853a31368eb5f95a297b95b4c5847f2bce88b8ab4247c7"},"schema_version":"1.0","source":{"id":"1402.3682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3682","created_at":"2026-05-18T02:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3682v1","created_at":"2026-05-18T02:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3682","created_at":"2026-05-18T02:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"MY5EOTF2HHC3","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MY5EOTF2HHC35SM4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MY5EOTF2","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:0ba4c889986a8c6a73595f379ceb4aa5a46aa7fdcd5e176c8a3ca787b153b3dc","target":"graph","created_at":"2026-05-18T02:58:55Z","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":"Grafakos and Sansing \\cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\\mr^n)$ based on Gabor systems in $\\ltr;$ the key tool is the \"ridge idea,\" which lifts a function of one variable to a function of several variables. We generalize their result by showing that similar results hold starting with general frames for $L^2(\\mr),$ both in the setting of discrete frames and continuous frames. This allows to apply the theory for several other classes of frames, e.g., wavelet frames and shift-invariant systems. We will consider applications to the Meye","authors_text":"Brigitte Forster, Ole Christensen, Peter Massopust","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-15T12:17:05Z","title":"Directional time frequency analysis via continuous frame"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3682","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":"sha256:1095b6edf1b0730eab70df894c33d10363d95b0109575d1f3c5b8b0b6d42a976","target":"record","created_at":"2026-05-18T02:58:55Z","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":"6dd88a3d4839da3f098172befc35d1328ef8afdda07036238947cd179e6b0797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-15T12:17:05Z","title_canon_sha256":"82c3b1d40364ef8db2853a31368eb5f95a297b95b4c5847f2bce88b8ab4247c7"},"schema_version":"1.0","source":{"id":"1402.3682","kind":"arxiv","version":1}},"canonical_sha256":"663a474cba39c5bec99c5c4b66391ebd010e2a0449616354e8ad2e5ff1f49ea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"663a474cba39c5bec99c5c4b66391ebd010e2a0449616354e8ad2e5ff1f49ea8","first_computed_at":"2026-05-18T02:58:55.831748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:55.831748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XEARD/mfLRkp6eDY0AnW+RFuHt/krOeRT/xmy73W+xyMmE3yhQZP3xkmqh0VIdEz9g8YfNbtTIsYTq5J7cPjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:55.832613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1095b6edf1b0730eab70df894c33d10363d95b0109575d1f3c5b8b0b6d42a976","sha256:0ba4c889986a8c6a73595f379ceb4aa5a46aa7fdcd5e176c8a3ca787b153b3dc"],"state_sha256":"8d7fac9e114f900d475630d23984bbbd44b097e0232ee4a4e9f5271bf5b61160"}