{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5BHCIRILQALY37DZUXDX4S6655","short_pith_number":"pith:5BHCIRIL","canonical_record":{"source":{"id":"0902.2537","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-02-15T11:41:55Z","cross_cats_sorted":["cs.CC","cs.DS","math.NA"],"title_canon_sha256":"5000fea93d05c252477148d1aa4ee79d52f69cc2f6f0b1df6fafedfb9afc8c18","abstract_canon_sha256":"455f6da963ba6fcb6c14b4ca74c6bae93c12808097d2327b20a7ea7474658421"},"schema_version":"1.0"},"canonical_sha256":"e84e24450b80178dfc79a5c77e4bdeef766d932717a52446dbc6ebea43ae1923","source":{"kind":"arxiv","id":"0902.2537","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2537","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2537v3","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2537","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"5BHCIRILQALY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5BHCIRILQALY37DZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5BHCIRIL","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5BHCIRILQALY37DZUXDX4S6655","target":"record","payload":{"canonical_record":{"source":{"id":"0902.2537","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-02-15T11:41:55Z","cross_cats_sorted":["cs.CC","cs.DS","math.NA"],"title_canon_sha256":"5000fea93d05c252477148d1aa4ee79d52f69cc2f6f0b1df6fafedfb9afc8c18","abstract_canon_sha256":"455f6da963ba6fcb6c14b4ca74c6bae93c12808097d2327b20a7ea7474658421"},"schema_version":"1.0"},"canonical_sha256":"e84e24450b80178dfc79a5c77e4bdeef766d932717a52446dbc6ebea43ae1923","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:14.749809Z","signature_b64":"dv9X+6xjNZQpB6isXkiHq5mm+jyBEYwt4EtfAMVPkVh8HnkGSD0CpNtqg0GgIzzux4dOKEMafLypIR64rmeHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e84e24450b80178dfc79a5c77e4bdeef766d932717a52446dbc6ebea43ae1923","last_reissued_at":"2026-05-18T04:30:14.749153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:14.749153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.2537","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrdGUMo4HzerDBZlqCGkHx61o/zJpwFqaO5ZBc7x8si2JfALOmb+l/plRTnf6X12HGk0s/syoS2q85xIwLxGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:08:21.160510Z"},"content_sha256":"535c277d4eecc9e7f88d7be1842c2d4d6b367abf505dd8eba9ca3ff5b7b8772f","schema_version":"1.0","event_id":"sha256:535c277d4eecc9e7f88d7be1842c2d4d6b367abf505dd8eba9ca3ff5b7b8772f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5BHCIRILQALY37DZUXDX4S6655","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Communication-optimal Parallel and Sequential Cholesky Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.NA"],"primary_cat":"cs.NA","authors_text":"Grey Ballard, James Demmel, Oded Schwartz, Olga Holtz","submitted_at":"2009-02-15T11:41:55Z","abstract_excerpt":"Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case). Communication costs often dominate arithmetic costs, so it is of interest to design algorithms minimizing communication. In this paper we first extend known lower bounds on the communication cost (both for bandwidth and for latency) of conventional (O(n^3)) matrix multiplication to Cholesky factorization, which is used for solving dense symmetric positive defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2537","kind":"arxiv","version":3},"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":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9JUyzPZkChOJQrk2hQMK7zxOSHZ9JEUiSDW2mJ9pyR7KOeJlsxAvVpRHJxkhWx/zJAA/77A1DGH4wRWOoHlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:08:21.161174Z"},"content_sha256":"48412a6119a79397fb7d64749f730298064e5e0a9d0b6c89d4181a232059a0e8","schema_version":"1.0","event_id":"sha256:48412a6119a79397fb7d64749f730298064e5e0a9d0b6c89d4181a232059a0e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BHCIRILQALY37DZUXDX4S6655/bundle.json","state_url":"https://pith.science/pith/5BHCIRILQALY37DZUXDX4S6655/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BHCIRILQALY37DZUXDX4S6655/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":"2026-05-31T05:08:21Z","links":{"resolver":"https://pith.science/pith/5BHCIRILQALY37DZUXDX4S6655","bundle":"https://pith.science/pith/5BHCIRILQALY37DZUXDX4S6655/bundle.json","state":"https://pith.science/pith/5BHCIRILQALY37DZUXDX4S6655/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BHCIRILQALY37DZUXDX4S6655/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5BHCIRILQALY37DZUXDX4S6655","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":"455f6da963ba6fcb6c14b4ca74c6bae93c12808097d2327b20a7ea7474658421","cross_cats_sorted":["cs.CC","cs.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-02-15T11:41:55Z","title_canon_sha256":"5000fea93d05c252477148d1aa4ee79d52f69cc2f6f0b1df6fafedfb9afc8c18"},"schema_version":"1.0","source":{"id":"0902.2537","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2537","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2537v3","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2537","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"5BHCIRILQALY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5BHCIRILQALY37DZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5BHCIRIL","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:48412a6119a79397fb7d64749f730298064e5e0a9d0b6c89d4181a232059a0e8","target":"graph","created_at":"2026-05-18T04:30:14Z","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":"Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case). Communication costs often dominate arithmetic costs, so it is of interest to design algorithms minimizing communication. In this paper we first extend known lower bounds on the communication cost (both for bandwidth and for latency) of conventional (O(n^3)) matrix multiplication to Cholesky factorization, which is used for solving dense symmetric positive defi","authors_text":"Grey Ballard, James Demmel, Oded Schwartz, Olga Holtz","cross_cats":["cs.CC","cs.DS","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-02-15T11:41:55Z","title":"Communication-optimal Parallel and Sequential Cholesky Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2537","kind":"arxiv","version":3},"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":"sha256:535c277d4eecc9e7f88d7be1842c2d4d6b367abf505dd8eba9ca3ff5b7b8772f","target":"record","created_at":"2026-05-18T04:30:14Z","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":"455f6da963ba6fcb6c14b4ca74c6bae93c12808097d2327b20a7ea7474658421","cross_cats_sorted":["cs.CC","cs.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-02-15T11:41:55Z","title_canon_sha256":"5000fea93d05c252477148d1aa4ee79d52f69cc2f6f0b1df6fafedfb9afc8c18"},"schema_version":"1.0","source":{"id":"0902.2537","kind":"arxiv","version":3}},"canonical_sha256":"e84e24450b80178dfc79a5c77e4bdeef766d932717a52446dbc6ebea43ae1923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e84e24450b80178dfc79a5c77e4bdeef766d932717a52446dbc6ebea43ae1923","first_computed_at":"2026-05-18T04:30:14.749153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:14.749153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dv9X+6xjNZQpB6isXkiHq5mm+jyBEYwt4EtfAMVPkVh8HnkGSD0CpNtqg0GgIzzux4dOKEMafLypIR64rmeHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:14.749809Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2537","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:535c277d4eecc9e7f88d7be1842c2d4d6b367abf505dd8eba9ca3ff5b7b8772f","sha256:48412a6119a79397fb7d64749f730298064e5e0a9d0b6c89d4181a232059a0e8"],"state_sha256":"6579452064b95118dc7a7ee8c6ec0a2056dc7b2f15de1bee68e9cf9361a1b312"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTuYlm28aCGbBezEoBqTmGvk3iEPFGkvwG8qlb5OrfkEeXrLYgmM5NrYPqR2+5h9XMbVYP6cFNtqp1o1H0seCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:08:21.164866Z","bundle_sha256":"dc92c137a54131e7b41c84169767fabbf6eb71a6d1d2c85213bb59681b56bf31"}}