{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2CJZONJZZQHZDLZDM35C6QHKL3","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":"6ce724eb315fc3e1e508fdb84c3f5c3173c2e121e7121576d2217e0aa5bf9bd1","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-01T14:57:20Z","title_canon_sha256":"db09d9a3a35e4ebdcefbae9a1578420d5246687b83f2681fb2bbf72e4eaf8862"},"schema_version":"1.0","source":{"id":"1707.00164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00164","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00164v1","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00164","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"2CJZONJZZQHZ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2CJZONJZZQHZDLZD","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2CJZONJZ","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:c28868adfac440d4df20fa08ba7e2df476304d329f6dbd5ab2da7349adf10873","target":"graph","created_at":"2026-05-18T00:41:04Z","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":"We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, \"compression,\" of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \\log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \\log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sa","authors_text":"Chenhan D. Yu, George Biros, James Levitt, Severin Reiz","cross_cats":["cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-01T14:57:20Z","title":"Geometry-Oblivious FMM for Compressing Dense SPD Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00164","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:afa0d4bbf9cb8bec50c2a357b2b32a86d7dd905b7493b74dbdbf01b47508fde9","target":"record","created_at":"2026-05-18T00:41:04Z","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":"6ce724eb315fc3e1e508fdb84c3f5c3173c2e121e7121576d2217e0aa5bf9bd1","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-07-01T14:57:20Z","title_canon_sha256":"db09d9a3a35e4ebdcefbae9a1578420d5246687b83f2681fb2bbf72e4eaf8862"},"schema_version":"1.0","source":{"id":"1707.00164","kind":"arxiv","version":1}},"canonical_sha256":"d093973539cc0f91af2366fa2f40ea5eede6c1ba801262b9eaaab169ea72a29b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d093973539cc0f91af2366fa2f40ea5eede6c1ba801262b9eaaab169ea72a29b","first_computed_at":"2026-05-18T00:41:04.270406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:04.270406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pN0Mt7M+5GLfnZomb01wCeiFyc+jvOEi6ByhBzIG4UfudmUacHpNLAN17EoYmG2wy7v253eUnmCRiaGpHGRkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:04.270953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afa0d4bbf9cb8bec50c2a357b2b32a86d7dd905b7493b74dbdbf01b47508fde9","sha256:c28868adfac440d4df20fa08ba7e2df476304d329f6dbd5ab2da7349adf10873"],"state_sha256":"dd33a6d7f5a1dcc80d98f9bd188fb736067f17d27c7b7c9221baa992ad33820b"}