{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LTZ4JG4JZ76TS5GFCC54I2RKJP","short_pith_number":"pith:LTZ4JG4J","canonical_record":{"source":{"id":"1008.2972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-17T21:03:30Z","cross_cats_sorted":["math.IT","math.RA"],"title_canon_sha256":"86e8c58adfd47f60327b9236109b5bb332ec3674f4280a738ff46d64298a4816","abstract_canon_sha256":"371706a08a309f554368b82f991d907d289935b0ce2ab43a0068e4e006582f71"},"schema_version":"1.0"},"canonical_sha256":"5cf3c49b89cffd3974c510bbc46a2a4bc34ba41e4bd7647bf7c8f2ef1bdad53c","source":{"kind":"arxiv","id":"1008.2972","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2972","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2972v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2972","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"LTZ4JG4JZ76T","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LTZ4JG4JZ76TS5GF","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LTZ4JG4J","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LTZ4JG4JZ76TS5GFCC54I2RKJP","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-17T21:03:30Z","cross_cats_sorted":["math.IT","math.RA"],"title_canon_sha256":"86e8c58adfd47f60327b9236109b5bb332ec3674f4280a738ff46d64298a4816","abstract_canon_sha256":"371706a08a309f554368b82f991d907d289935b0ce2ab43a0068e4e006582f71"},"schema_version":"1.0"},"canonical_sha256":"5cf3c49b89cffd3974c510bbc46a2a4bc34ba41e4bd7647bf7c8f2ef1bdad53c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:23.471580Z","signature_b64":"rGJw31RU9GX6z2KFPcASHqmxKK6bg+xHbevmsAfQ2SlQA3pjv4tTtfiaps60ZQGs6OnyQf/QRB7zFYpy/K62BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cf3c49b89cffd3974c510bbc46a2a4bc34ba41e4bd7647bf7c8f2ef1bdad53c","last_reissued_at":"2026-05-18T04:18:23.470990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:23.470990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2972","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7mlx/Xtyw8YPLCxNAq14tSCVGCAK/6/o3ByAQS1OSPQo0KUKuX3zUrHmn13q7bQCfSyH+g1mI04foTV8JXFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:37:42.568061Z"},"content_sha256":"457b0f202dee2d915e4d2810a8f3b569eb73bb1cc1b8fa671dd2ae7cdbaa2415","schema_version":"1.0","event_id":"sha256:457b0f202dee2d915e4d2810a8f3b569eb73bb1cc1b8fa671dd2ae7cdbaa2415"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LTZ4JG4JZ76TS5GFCC54I2RKJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.RA"],"primary_cat":"cs.IT","authors_text":"Aliaksei Sandryhaila, Jelena Kovacevic, Markus Pueschel","submitted_at":"2010-08-17T21:03:30Z","abstract_excerpt":"A polynomial transform is the multiplication of an input vector $x\\in\\C^n$ by a matrix $\\PT_{b,\\alpha}\\in\\C^{n\\times n},$ whose $(k,\\ell)$-th element is defined as $p_\\ell(\\alpha_k)$ for polynomials $p_\\ell(x)\\in\\C[x]$ from a list $b=\\{p_0(x),\\dots,p_{n-1}(x)\\}$ and sample points $\\alpha_k\\in\\C$ from a list $\\alpha=\\{\\alpha_0,\\dots,\\alpha_{n-1}\\}$. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique to derive fast alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2972","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnXwrLDU2E7DAbWIXHJHgUXOFucEPLxh9e5Aab2u/SmP2dWupbv0YZTn548MpxQNfYOiOdDihDSN43fylntIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:37:42.568452Z"},"content_sha256":"7f1170845f6b29fc9725b6f1821b21a53c863869aae4efe7b327281b2f8112e3","schema_version":"1.0","event_id":"sha256:7f1170845f6b29fc9725b6f1821b21a53c863869aae4efe7b327281b2f8112e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/bundle.json","state_url":"https://pith.science/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T21:37:42Z","links":{"resolver":"https://pith.science/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP","bundle":"https://pith.science/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/bundle.json","state":"https://pith.science/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTZ4JG4JZ76TS5GFCC54I2RKJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LTZ4JG4JZ76TS5GFCC54I2RKJP","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":"371706a08a309f554368b82f991d907d289935b0ce2ab43a0068e4e006582f71","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-17T21:03:30Z","title_canon_sha256":"86e8c58adfd47f60327b9236109b5bb332ec3674f4280a738ff46d64298a4816"},"schema_version":"1.0","source":{"id":"1008.2972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2972","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2972v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2972","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"LTZ4JG4JZ76T","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LTZ4JG4JZ76TS5GF","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LTZ4JG4J","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:7f1170845f6b29fc9725b6f1821b21a53c863869aae4efe7b327281b2f8112e3","target":"graph","created_at":"2026-05-18T04:18:23Z","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":"A polynomial transform is the multiplication of an input vector $x\\in\\C^n$ by a matrix $\\PT_{b,\\alpha}\\in\\C^{n\\times n},$ whose $(k,\\ell)$-th element is defined as $p_\\ell(\\alpha_k)$ for polynomials $p_\\ell(x)\\in\\C[x]$ from a list $b=\\{p_0(x),\\dots,p_{n-1}(x)\\}$ and sample points $\\alpha_k\\in\\C$ from a list $\\alpha=\\{\\alpha_0,\\dots,\\alpha_{n-1}\\}$. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique to derive fast alg","authors_text":"Aliaksei Sandryhaila, Jelena Kovacevic, Markus Pueschel","cross_cats":["math.IT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-17T21:03:30Z","title":"Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2972","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":"sha256:457b0f202dee2d915e4d2810a8f3b569eb73bb1cc1b8fa671dd2ae7cdbaa2415","target":"record","created_at":"2026-05-18T04:18:23Z","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":"371706a08a309f554368b82f991d907d289935b0ce2ab43a0068e4e006582f71","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-17T21:03:30Z","title_canon_sha256":"86e8c58adfd47f60327b9236109b5bb332ec3674f4280a738ff46d64298a4816"},"schema_version":"1.0","source":{"id":"1008.2972","kind":"arxiv","version":1}},"canonical_sha256":"5cf3c49b89cffd3974c510bbc46a2a4bc34ba41e4bd7647bf7c8f2ef1bdad53c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cf3c49b89cffd3974c510bbc46a2a4bc34ba41e4bd7647bf7c8f2ef1bdad53c","first_computed_at":"2026-05-18T04:18:23.470990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:23.470990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGJw31RU9GX6z2KFPcASHqmxKK6bg+xHbevmsAfQ2SlQA3pjv4tTtfiaps60ZQGs6OnyQf/QRB7zFYpy/K62BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:23.471580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:457b0f202dee2d915e4d2810a8f3b569eb73bb1cc1b8fa671dd2ae7cdbaa2415","sha256:7f1170845f6b29fc9725b6f1821b21a53c863869aae4efe7b327281b2f8112e3"],"state_sha256":"051b964432aebde226394ca2e597ae2134a546c9aa7c70a01fa9df4756a587ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWX6VzJqxnRtUgpefnq//bDuwN/PVC7WPbN+4Us6dyFPspYP5Ber60acbx4+nz3/EU32rYl3Zsdx6bCYP75KBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:37:42.572340Z","bundle_sha256":"9a5193424a9d0173dff23500b9cf727144ba2d9bb2a39bb6dd33a9243a6a7e73"}}