{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6JW2I3NYHXKXCA2X6SGW5LSQL4","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":"2b7e5830aa7eb56ae421af4495d2aa46b1875aeabac5ce8ad521c52e8ff160c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-11T20:46:58Z","title_canon_sha256":"aed32b5ab84ddbb285d2ca5a0a6ddcc83cbaeb2d1df1142419a00d401c5f89b4"},"schema_version":"1.0","source":{"id":"1605.03616","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03616","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03616v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03616","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"6JW2I3NYHXKX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6JW2I3NYHXKXCA2X","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6JW2I3NY","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7e2aa8f11bb985a271390a7ff3c92ee47876d0d9863e800b8d806acab64d502a","target":"graph","created_at":"2026-05-18T00:46:49Z","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":"This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-rank approximations of the complementary low-rank matrix. A novel sweeping matrix compression technique further compresses the preliminary interpolative butterfly factorization via a sequence of structure-","authors_text":"Haizhao Yang, Yingzhou Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-11T20:46:58Z","title":"Interpolative Butterfly Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03616","kind":"arxiv","version":2},"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":"sha256:25733b3b3f281702ca3085c524cb93f3b49aecf38c8642e4e9979c63056e5b15","target":"record","created_at":"2026-05-18T00:46:49Z","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":"2b7e5830aa7eb56ae421af4495d2aa46b1875aeabac5ce8ad521c52e8ff160c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-11T20:46:58Z","title_canon_sha256":"aed32b5ab84ddbb285d2ca5a0a6ddcc83cbaeb2d1df1142419a00d401c5f89b4"},"schema_version":"1.0","source":{"id":"1605.03616","kind":"arxiv","version":2}},"canonical_sha256":"f26da46db83dd5710357f48d6eae505f2aadb79eeed3bec1aec6944b1d3ade83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f26da46db83dd5710357f48d6eae505f2aadb79eeed3bec1aec6944b1d3ade83","first_computed_at":"2026-05-18T00:46:49.451110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:49.451110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MuGMbLwRqOHj8lhRmQdtg19RbP2TlWW8UxfhsAFmrh2RZkg+cJ0dNbKgKVl5Htf26pUGrpoigadLorZ2y95OBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:49.451870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03616","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25733b3b3f281702ca3085c524cb93f3b49aecf38c8642e4e9979c63056e5b15","sha256:7e2aa8f11bb985a271390a7ff3c92ee47876d0d9863e800b8d806acab64d502a"],"state_sha256":"05b9aa2d9d011e98622f504cba3ecc0d73036151f168dced0c1bfa642cac9dc1"}