{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LPB6ZRNTQVNBFSHNOYMQWG4WFW","short_pith_number":"pith:LPB6ZRNT","schema_version":"1.0","canonical_sha256":"5bc3ecc5b3855a12c8ed76190b1b962d913f88ac613bff60cc7d6add822072d2","source":{"kind":"arxiv","id":"1303.1209","version":1},"attestation_state":"computed","paper":{"title":"Sample-Optimal Average-Case Sparse Fourier Transform in Two Dimensions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Badih Ghazi, Dina Katabi, Eric Price, Haitham Hassanieh, Lixin Shi, Piotr Indyk","submitted_at":"2013-03-05T22:28:21Z","abstract_excerpt":"We present the first sample-optimal sublinear time algorithms for the sparse Discrete Fourier Transform over a two-dimensional sqrt{n} x sqrt{n} grid. Our algorithms are analyzed for /average case/ signals. For signals whose spectrum is exactly sparse, our algorithms use O(k) samples and run in O(k log k) time, where k is the expected sparsity of the signal. For signals whose spectrum is approximately sparse, our algorithm uses O(k log n) samples and runs in O(k log^2 n) time; the latter algorithm works for k=Theta(sqrt{n}). The number of samples used by our algorithms matches the known lower "},"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":"1303.1209","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2013-03-05T22:28:21Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"414cfbae7514912f2ffd9c1c676b1e2dbe3bd5ac8ea3c872db7be97e723bccd8","abstract_canon_sha256":"91725cc0953d79fff3654d4d1744e77d5fdc5f930a733519c534bbd7149710d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:44.185849Z","signature_b64":"nuHhRbkry9zAxnd8iJsyx8nM93a1nKnuabmNFQ0tyBVOENCHR4APS3LCIfj3V85dz4K6AI2ZmH0RME7n7sfuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bc3ecc5b3855a12c8ed76190b1b962d913f88ac613bff60cc7d6add822072d2","last_reissued_at":"2026-05-18T03:31:44.185246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:44.185246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sample-Optimal Average-Case Sparse Fourier Transform in Two Dimensions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Badih Ghazi, Dina Katabi, Eric Price, Haitham Hassanieh, Lixin Shi, Piotr Indyk","submitted_at":"2013-03-05T22:28:21Z","abstract_excerpt":"We present the first sample-optimal sublinear time algorithms for the sparse Discrete Fourier Transform over a two-dimensional sqrt{n} x sqrt{n} grid. Our algorithms are analyzed for /average case/ signals. For signals whose spectrum is exactly sparse, our algorithms use O(k) samples and run in O(k log k) time, where k is the expected sparsity of the signal. For signals whose spectrum is approximately sparse, our algorithm uses O(k log n) samples and runs in O(k log^2 n) time; the latter algorithm works for k=Theta(sqrt{n}). The number of samples used by our algorithms matches the known lower "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1209","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":"1303.1209","created_at":"2026-05-18T03:31:44.185362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1209v1","created_at":"2026-05-18T03:31:44.185362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1209","created_at":"2026-05-18T03:31:44.185362+00:00"},{"alias_kind":"pith_short_12","alias_value":"LPB6ZRNTQVNB","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LPB6ZRNTQVNBFSHN","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LPB6ZRNT","created_at":"2026-05-18T12:27:51.066281+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/LPB6ZRNTQVNBFSHNOYMQWG4WFW","json":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW.json","graph_json":"https://pith.science/api/pith-number/LPB6ZRNTQVNBFSHNOYMQWG4WFW/graph.json","events_json":"https://pith.science/api/pith-number/LPB6ZRNTQVNBFSHNOYMQWG4WFW/events.json","paper":"https://pith.science/paper/LPB6ZRNT"},"agent_actions":{"view_html":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW","download_json":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW.json","view_paper":"https://pith.science/paper/LPB6ZRNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1209&json=true","fetch_graph":"https://pith.science/api/pith-number/LPB6ZRNTQVNBFSHNOYMQWG4WFW/graph.json","fetch_events":"https://pith.science/api/pith-number/LPB6ZRNTQVNBFSHNOYMQWG4WFW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW/action/storage_attestation","attest_author":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW/action/author_attestation","sign_citation":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW/action/citation_signature","submit_replication":"https://pith.science/pith/LPB6ZRNTQVNBFSHNOYMQWG4WFW/action/replication_record"}},"created_at":"2026-05-18T03:31:44.185362+00:00","updated_at":"2026-05-18T03:31:44.185362+00:00"}