{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6F6LHNGTAIUWYPVRQ2VI3AYPKF","short_pith_number":"pith:6F6LHNGT","canonical_record":{"source":{"id":"1703.00839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-02T15:53:52Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3defabf5777b80d1f1a1e1944bcb1707f4b790934dd80c7082ff256e6eed0f05","abstract_canon_sha256":"867f8f18dab8769d30c61c8d6eded2cee7df3408a79db6e3eaa829744a55079d"},"schema_version":"1.0"},"canonical_sha256":"f17cb3b4d302296c3eb186aa8d830f517c3abd4c6372437f0174fcfabbfdbf84","source":{"kind":"arxiv","id":"1703.00839","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00839","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00839v1","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00839","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"6F6LHNGTAIUW","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6F6LHNGTAIUWYPVR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6F6LHNGT","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6F6LHNGTAIUWYPVRQ2VI3AYPKF","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-02T15:53:52Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3defabf5777b80d1f1a1e1944bcb1707f4b790934dd80c7082ff256e6eed0f05","abstract_canon_sha256":"867f8f18dab8769d30c61c8d6eded2cee7df3408a79db6e3eaa829744a55079d"},"schema_version":"1.0"},"canonical_sha256":"f17cb3b4d302296c3eb186aa8d830f517c3abd4c6372437f0174fcfabbfdbf84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:40.644936Z","signature_b64":"r9VW0gnSzZ20mLxuaiY83HRoDd0lXfb0G/YOqRUwhz71qwLWm/quEgjqTlkTaem0Uk2lP0dNpqAANy3ItBBlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f17cb3b4d302296c3eb186aa8d830f517c3abd4c6372437f0174fcfabbfdbf84","last_reissued_at":"2026-05-18T00:49:40.644358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:40.644358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00839","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":"2026-05-18T00:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0dzGbHJ2K14TvBKxtjGFlFHLr/vIQx+CBc5jfR9qkN0DeQakSPMWjEEqZg9WCuymEL7PDXovxx/HOqGmGWpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:46:25.566699Z"},"content_sha256":"82ab081c22de09d596132a531637bd1fc2ce5f3c27c94da3acacf12a700b26d0","schema_version":"1.0","event_id":"sha256:82ab081c22de09d596132a531637bd1fc2ce5f3c27c94da3acacf12a700b26d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6F6LHNGTAIUWYPVRQ2VI3AYPKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Encrypted accelerated least squares regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Chris C. Holmes, Louis J. M. Aslett, Pedro M. Esperan\\c{c}a","submitted_at":"2017-03-02T15:53:52Z","abstract_excerpt":"Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradient descent is shown to dominate in terms of encrypted computational speed, and theoretical results are proven to give parameter bounds which ensure correctness of decryption. The characteristics of encr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00839","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":"2026-05-18T00:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFu7Tnn68xuQeSRFwy6+ngxP2Ch8RdDDCGmpJY26tfDnGczT6uLC57MfzWBQIiNqtKqeXzkkhwmcrNiu7NkMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:46:25.567048Z"},"content_sha256":"117331bcf8a154b4bc0c96e49d09bfdf83a79186c62ba054123f7bbef1599718","schema_version":"1.0","event_id":"sha256:117331bcf8a154b4bc0c96e49d09bfdf83a79186c62ba054123f7bbef1599718"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/bundle.json","state_url":"https://pith.science/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/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":"2026-06-21T21:46:25Z","links":{"resolver":"https://pith.science/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF","bundle":"https://pith.science/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/bundle.json","state":"https://pith.science/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6F6LHNGTAIUWYPVRQ2VI3AYPKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6F6LHNGTAIUWYPVRQ2VI3AYPKF","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":"867f8f18dab8769d30c61c8d6eded2cee7df3408a79db6e3eaa829744a55079d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-02T15:53:52Z","title_canon_sha256":"3defabf5777b80d1f1a1e1944bcb1707f4b790934dd80c7082ff256e6eed0f05"},"schema_version":"1.0","source":{"id":"1703.00839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00839","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00839v1","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00839","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"6F6LHNGTAIUW","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6F6LHNGTAIUWYPVR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6F6LHNGT","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:117331bcf8a154b4bc0c96e49d09bfdf83a79186c62ba054123f7bbef1599718","target":"graph","created_at":"2026-05-18T00:49:40Z","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":"Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradient descent is shown to dominate in terms of encrypted computational speed, and theoretical results are proven to give parameter bounds which ensure correctness of decryption. The characteristics of encr","authors_text":"Chris C. Holmes, Louis J. M. Aslett, Pedro M. Esperan\\c{c}a","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-02T15:53:52Z","title":"Encrypted accelerated least squares regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00839","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":"sha256:82ab081c22de09d596132a531637bd1fc2ce5f3c27c94da3acacf12a700b26d0","target":"record","created_at":"2026-05-18T00:49:40Z","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":"867f8f18dab8769d30c61c8d6eded2cee7df3408a79db6e3eaa829744a55079d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-03-02T15:53:52Z","title_canon_sha256":"3defabf5777b80d1f1a1e1944bcb1707f4b790934dd80c7082ff256e6eed0f05"},"schema_version":"1.0","source":{"id":"1703.00839","kind":"arxiv","version":1}},"canonical_sha256":"f17cb3b4d302296c3eb186aa8d830f517c3abd4c6372437f0174fcfabbfdbf84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f17cb3b4d302296c3eb186aa8d830f517c3abd4c6372437f0174fcfabbfdbf84","first_computed_at":"2026-05-18T00:49:40.644358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:40.644358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r9VW0gnSzZ20mLxuaiY83HRoDd0lXfb0G/YOqRUwhz71qwLWm/quEgjqTlkTaem0Uk2lP0dNpqAANy3ItBBlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:40.644936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82ab081c22de09d596132a531637bd1fc2ce5f3c27c94da3acacf12a700b26d0","sha256:117331bcf8a154b4bc0c96e49d09bfdf83a79186c62ba054123f7bbef1599718"],"state_sha256":"e0e1721c4f6fcf6bf104d45581db5b1a5fa4632939a86bfe60e92b1e212f51e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8g8afXf7WpUuiLhtGrpP9SPsn7DxOzempt6lTbmPDgDqqhx1aGA/jwmRYzwb57euwh/6a6wpbPfHDfAca+tBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:46:25.569002Z","bundle_sha256":"2d29353d24dae0346dfd80fab9d92114cd2992d54b79cd4c558cb8e84b4d49f6"}}