{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DTZ7HJYS4WHYEDX7K336F7XV3B","short_pith_number":"pith:DTZ7HJYS","canonical_record":{"source":{"id":"1602.07527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-24T14:35:31Z","cross_cats_sorted":["cs.MS"],"title_canon_sha256":"a69509b725f3e63f47cc6cf8cdf6c48dd4f47939566d79b0ff306f3a161a9556","abstract_canon_sha256":"1252d6d7e903f3ba608215f2008d159774454e4ebe50ba0656c5f1907eff400f"},"schema_version":"1.0"},"canonical_sha256":"1cf3f3a712e58f820eff56f7e2fef5d866cf2ae4f150501a5694482dbfbbd26c","source":{"kind":"arxiv","id":"1602.07527","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07527","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07527v1","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07527","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"DTZ7HJYS4WHY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTZ7HJYS4WHYEDX7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTZ7HJYS","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DTZ7HJYS4WHYEDX7K336F7XV3B","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-24T14:35:31Z","cross_cats_sorted":["cs.MS"],"title_canon_sha256":"a69509b725f3e63f47cc6cf8cdf6c48dd4f47939566d79b0ff306f3a161a9556","abstract_canon_sha256":"1252d6d7e903f3ba608215f2008d159774454e4ebe50ba0656c5f1907eff400f"},"schema_version":"1.0"},"canonical_sha256":"1cf3f3a712e58f820eff56f7e2fef5d866cf2ae4f150501a5694482dbfbbd26c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:02.780160Z","signature_b64":"FJ2/YJPGFu4SROOiy3VmCIoa/uhqewqL7T4nG1n/38aclYeDUvgGb/aObFWe2NYKdsfBjVGylF8N0oO7kdFKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cf3f3a712e58f820eff56f7e2fef5d866cf2ae4f150501a5694482dbfbbd26c","last_reissued_at":"2026-05-18T01:20:02.779517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:02.779517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07527","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":"2026-05-18T01:20:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8X24YpBWhOH885RcBV9d//hbJfyFyrRToSRglreKo+91pZw5J0pVsN3Ts7c18TjJed1DnNBTA1W6dVmN/dHtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:09:30.427200Z"},"content_sha256":"43257e92e616f1612ed3af50bf24ce454850ae358b3a8a17cdf73549af60a176","schema_version":"1.0","event_id":"sha256:43257e92e616f1612ed3af50bf24ce454850ae358b3a8a17cdf73549af60a176"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DTZ7HJYS4WHYEDX7K336F7XV3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiation of the Cholesky decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS"],"primary_cat":"stat.CO","authors_text":"Iain Murray","submitted_at":"2016-02-24T14:35:31Z","abstract_excerpt":"We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on differentiating the Cholesky algorithm DPOTRF in the LAPACK library, which uses `Level 3' matrix-matrix operations from BLAS, and so is cache-friendly and easy to parallelize. For large matrices, the resulting algorithms are the fastest way to compute Cholesky derivatives, and are an order of magnitude faster than the algorithms in common usage. In some computin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07527","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":"2026-05-18T01:20:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXPbAwGv2V9lwmD6G+SmCwrolLkIDHz9tgpxzHy4UFCwASzUReCORpYqB3cjXH8QRkMpt8LFaFpARy926KYDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:09:30.427629Z"},"content_sha256":"db5ecebea5caba59d2c893a61e90295ccb8ad0952f55c80433a5a915ea87d778","schema_version":"1.0","event_id":"sha256:db5ecebea5caba59d2c893a61e90295ccb8ad0952f55c80433a5a915ea87d778"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/bundle.json","state_url":"https://pith.science/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/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":"2026-05-26T16:09:30Z","links":{"resolver":"https://pith.science/pith/DTZ7HJYS4WHYEDX7K336F7XV3B","bundle":"https://pith.science/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/bundle.json","state":"https://pith.science/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTZ7HJYS4WHYEDX7K336F7XV3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DTZ7HJYS4WHYEDX7K336F7XV3B","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":"1252d6d7e903f3ba608215f2008d159774454e4ebe50ba0656c5f1907eff400f","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-24T14:35:31Z","title_canon_sha256":"a69509b725f3e63f47cc6cf8cdf6c48dd4f47939566d79b0ff306f3a161a9556"},"schema_version":"1.0","source":{"id":"1602.07527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07527","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07527v1","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07527","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"DTZ7HJYS4WHY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTZ7HJYS4WHYEDX7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTZ7HJYS","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:db5ecebea5caba59d2c893a61e90295ccb8ad0952f55c80433a5a915ea87d778","target":"graph","created_at":"2026-05-18T01:20:02Z","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 review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on differentiating the Cholesky algorithm DPOTRF in the LAPACK library, which uses `Level 3' matrix-matrix operations from BLAS, and so is cache-friendly and easy to parallelize. For large matrices, the resulting algorithms are the fastest way to compute Cholesky derivatives, and are an order of magnitude faster than the algorithms in common usage. In some computin","authors_text":"Iain Murray","cross_cats":["cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-24T14:35:31Z","title":"Differentiation of the Cholesky decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07527","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":"sha256:43257e92e616f1612ed3af50bf24ce454850ae358b3a8a17cdf73549af60a176","target":"record","created_at":"2026-05-18T01:20:02Z","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":"1252d6d7e903f3ba608215f2008d159774454e4ebe50ba0656c5f1907eff400f","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-24T14:35:31Z","title_canon_sha256":"a69509b725f3e63f47cc6cf8cdf6c48dd4f47939566d79b0ff306f3a161a9556"},"schema_version":"1.0","source":{"id":"1602.07527","kind":"arxiv","version":1}},"canonical_sha256":"1cf3f3a712e58f820eff56f7e2fef5d866cf2ae4f150501a5694482dbfbbd26c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cf3f3a712e58f820eff56f7e2fef5d866cf2ae4f150501a5694482dbfbbd26c","first_computed_at":"2026-05-18T01:20:02.779517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:02.779517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJ2/YJPGFu4SROOiy3VmCIoa/uhqewqL7T4nG1n/38aclYeDUvgGb/aObFWe2NYKdsfBjVGylF8N0oO7kdFKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:02.780160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43257e92e616f1612ed3af50bf24ce454850ae358b3a8a17cdf73549af60a176","sha256:db5ecebea5caba59d2c893a61e90295ccb8ad0952f55c80433a5a915ea87d778"],"state_sha256":"e19fa8110a6d0452da59df93282952e69cfb10f52dd8a6fb1485b3b750f031b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+G5asEbH7yg5FYIKT4VrsMNbFZhTtWEOzVRPcv6yHHj9KY4VN4qpPTNDQvUnowztRH0T09uZFcd9NehsczXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:09:30.430835Z","bundle_sha256":"dd9d29d676e596267002db3981747dfe175186d52a8da7f29ae0ad3edd2dcc9b"}}