{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QV2CPA3LDSXN4IJGWQ5NAUXQPX","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":"20d28d50867ed30b344ebae4dc02f1147af2315c95f0e6b6d33c2db706f3091a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-02T20:01:12Z","title_canon_sha256":"462b480c538716ff51521adff57359ddfd11a0dbc0a231be5f46dad8fd90f15c"},"schema_version":"1.0","source":{"id":"1406.0513","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0513","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0513v3","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0513","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"QV2CPA3LDSXN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QV2CPA3LDSXN4IJG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QV2CPA3L","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:a0f08796a4bb300214fa1441b7a9bf4003ee82514568e0e98f38efbd2b8dc660","target":"graph","created_at":"2026-05-18T02:30:15Z","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":"Since its appearing in 1996, the Stockwell transform (S-transform) has been applied to medical imaging, geophysics and signal processing in general. In this paper, we prove that the system of functions (so-called DOST basis) is indeed an orthonormal basis of L^2([0,1]), which is time-frequency localized, in the sense of Donoho-Stark Theorem (1989). Our approach provides a unified setting in which to study the Stockwell transform (associated to different admissible windows) and its orthogonal decomposition. Finally, we introduce a fast -- O(N log N) -- algorithm to compute the Stockwell coeffic","authors_text":"Luigi Riba, Ubertino Battisti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-02T20:01:12Z","title":"Window-Dependent Bases for Efficient Representations of the Stockwell Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0513","kind":"arxiv","version":3},"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:c9e5aa5c56d0e8250b98c83268355cc4d8c621d582174fd3467b6a341f460eb5","target":"record","created_at":"2026-05-18T02:30:15Z","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":"20d28d50867ed30b344ebae4dc02f1147af2315c95f0e6b6d33c2db706f3091a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-02T20:01:12Z","title_canon_sha256":"462b480c538716ff51521adff57359ddfd11a0dbc0a231be5f46dad8fd90f15c"},"schema_version":"1.0","source":{"id":"1406.0513","kind":"arxiv","version":3}},"canonical_sha256":"857427836b1caede2126b43ad052f07df5f2cfc2f84d790719eaf1009afb2333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"857427836b1caede2126b43ad052f07df5f2cfc2f84d790719eaf1009afb2333","first_computed_at":"2026-05-18T02:30:15.578878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.578878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uwvwm8uZ8VfNcFVe8YjZatQ4G9jF976n632LlvQ+6sssE6vKmU2r/4hmb48Bgd16Za/UpgZZSCtOFcwz26OlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.579293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0513","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e5aa5c56d0e8250b98c83268355cc4d8c621d582174fd3467b6a341f460eb5","sha256:a0f08796a4bb300214fa1441b7a9bf4003ee82514568e0e98f38efbd2b8dc660"],"state_sha256":"07a5756473dae4d17caa6cf0b12929c2b59cd77daa140b60f14864f4306ad11b"}