{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7R5JEB2XWHLMGTT5I7I77SOZPU","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":"74028d571a3d9e6ed42695f47ad3c665210b2bb87ae27066b67985ebb2ba5fd6","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-01T21:48:00Z","title_canon_sha256":"b51b990780be97417b6f4bac2d478db05da85c11ab4c936de15d8efadb87d5bf"},"schema_version":"1.0","source":{"id":"1501.00320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00320","created_at":"2026-05-18T02:30:09Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00320v1","created_at":"2026-05-18T02:30:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00320","created_at":"2026-05-18T02:30:09Z"},{"alias_kind":"pith_short_12","alias_value":"7R5JEB2XWHLM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7R5JEB2XWHLMGTT5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7R5JEB2X","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:215e57849f389f5ee6b04ff69a722c66327471a2836407ee1b4019f89934c187","target":"graph","created_at":"2026-05-18T02:30:09Z","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":"The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k non-zero coefficients (where k < n), can we do better? In [1], we addressed this question and presented a novel FFAST (Fast Fourier Aliasing-based Sparse Transform) algorithm that cleverly induces sparse graph alias codes in the DFT domain, via a Chinese-Remainder-Theorem (CRT)-guided sub-sampling operation of the time-domain samples. The resulting sparse grap","authors_text":"Kannan Ramchandran, Sameer Pawar","cross_cats":["cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-01T21:48:00Z","title":"A robust sub-linear time R-FFAST algorithm for computing a sparse DFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00320","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":"sha256:3c3ec763e064bd09715a2abf7c05c05e1ceb54b5bbe9f3ff862972686eb479a5","target":"record","created_at":"2026-05-18T02:30:09Z","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":"74028d571a3d9e6ed42695f47ad3c665210b2bb87ae27066b67985ebb2ba5fd6","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-01T21:48:00Z","title_canon_sha256":"b51b990780be97417b6f4bac2d478db05da85c11ab4c936de15d8efadb87d5bf"},"schema_version":"1.0","source":{"id":"1501.00320","kind":"arxiv","version":1}},"canonical_sha256":"fc7a920757b1d6c34e7d47d1ffc9d97d28e69e0a1ceaf067242b6ff78fd29a5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc7a920757b1d6c34e7d47d1ffc9d97d28e69e0a1ceaf067242b6ff78fd29a5f","first_computed_at":"2026-05-18T02:30:09.580753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:09.580753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Io9+SZc94UCq1c7NyuCptxlNkkUy79qWv7ypkYvFNGsebllHMdd00zwc2MUPM6KfXOt6ET1APzOIuc5xhB/CDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:09.581502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c3ec763e064bd09715a2abf7c05c05e1ceb54b5bbe9f3ff862972686eb479a5","sha256:215e57849f389f5ee6b04ff69a722c66327471a2836407ee1b4019f89934c187"],"state_sha256":"9647ebf5adbfd42af0262ebbdc811c64f95ed1969419b2fff26f4bf354d81903"}