{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z2KNTLXRKTDECLKXRS26BR3YGY","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":"045154b81a1047fde85ffd4a65f892e6b87386dd769f185f41fbde7e7706ca2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-06T01:02:54Z","title_canon_sha256":"5647d8b59098683119ed889e0c9c88864c2bf451c6d2d11653763829352363e8"},"schema_version":"1.0","source":{"id":"1403.1307","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1307","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1307v5","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1307","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"Z2KNTLXRKTDE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2KNTLXRKTDECLKX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2KNTLXR","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:85c605cb6f8ae31c39be584d8b889b3b034e60f1ee839eb408102331c2618017","target":"graph","created_at":"2026-05-18T02:46:39Z","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":"Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years.\n  An early result by Morgenstern from 1973, provides an $\\Omega(n \\log n)$ lower bound for the unnormalized Fourier transform when the constants used in the computation are bounded. The proof uses a potential function related to a determinant. The result does not explain why the normalized Fourier transform (of unit determinant) should be difficult to compute in the same model. Hence, the result is not scale insensitive","authors_text":"Nir Ailon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-06T01:02:54Z","title":"An n\\log n Lower Bound for Fourier Transform Computation in the Well Conditioned Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1307","kind":"arxiv","version":5},"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:fd03b324874b3ac4d36c80b7b9a39cbbcb1e400214dcdbc631017e48f132e313","target":"record","created_at":"2026-05-18T02:46:39Z","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":"045154b81a1047fde85ffd4a65f892e6b87386dd769f185f41fbde7e7706ca2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-06T01:02:54Z","title_canon_sha256":"5647d8b59098683119ed889e0c9c88864c2bf451c6d2d11653763829352363e8"},"schema_version":"1.0","source":{"id":"1403.1307","kind":"arxiv","version":5}},"canonical_sha256":"ce94d9aef154c6412d578cb5e0c77836208249417143d72217f95b72710bb2b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce94d9aef154c6412d578cb5e0c77836208249417143d72217f95b72710bb2b2","first_computed_at":"2026-05-18T02:46:39.167376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:39.167376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IyqbXie6wXRjiKZKlyxdQjjD78spaWxPAGCNGl0+CUS8sfNxWixbohu0yTG3k2+rhR/YB4ROxCCgNgJb3a/nBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:39.168002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1307","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd03b324874b3ac4d36c80b7b9a39cbbcb1e400214dcdbc631017e48f132e313","sha256:85c605cb6f8ae31c39be584d8b889b3b034e60f1ee839eb408102331c2618017"],"state_sha256":"a1ee44458e3c22ab914c4e7e9e17e09d10dd563a05231c2d2a72d60c104c3885"}