{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VPPOXIEHURKMG752RYWVZHOWT7","short_pith_number":"pith:VPPOXIEH","canonical_record":{"source":{"id":"1503.01892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-06T09:48:33Z","cross_cats_sorted":[],"title_canon_sha256":"c833fa7df3da87ac213c31a679a0a35f0522cfe3a6f3a709d10547e812bb896f","abstract_canon_sha256":"918bf65caecb7e20ff090ae1d4061ddd58d45f89ed06589d0f17445c1e799bb5"},"schema_version":"1.0"},"canonical_sha256":"abdeeba087a454c37fba8e2d5c9dd69fe0107bb85dd6182f3584de6da87dd6b0","source":{"kind":"arxiv","id":"1503.01892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01892","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01892v2","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01892","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"VPPOXIEHURKM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VPPOXIEHURKMG752","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VPPOXIEH","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VPPOXIEHURKMG752RYWVZHOWT7","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-06T09:48:33Z","cross_cats_sorted":[],"title_canon_sha256":"c833fa7df3da87ac213c31a679a0a35f0522cfe3a6f3a709d10547e812bb896f","abstract_canon_sha256":"918bf65caecb7e20ff090ae1d4061ddd58d45f89ed06589d0f17445c1e799bb5"},"schema_version":"1.0"},"canonical_sha256":"abdeeba087a454c37fba8e2d5c9dd69fe0107bb85dd6182f3584de6da87dd6b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:37.012785Z","signature_b64":"j/4GcCPZcRydHBLNMnReU34+uh5JdvwkhIsLGa+Two+rAETlJxR/MJvTp2nUhVUVXb/4GHcKgbZXlDo55EntAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abdeeba087a454c37fba8e2d5c9dd69fe0107bb85dd6182f3584de6da87dd6b0","last_reissued_at":"2026-05-18T00:37:37.012243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:37.012243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01892","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4AxE3y8h1aShkVD30FIhEPlRpiWlRewdccW8T13yz4L9QMT3hWvg42ObEEs/bj6aowEBlscqYF6ACibe9WKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:06.255485Z"},"content_sha256":"ba2e4a500c0cd7775e14edf5cade992c7156b100fe57992bbaaf9abb03f16cd6","schema_version":"1.0","event_id":"sha256:ba2e4a500c0cd7775e14edf5cade992c7156b100fe57992bbaaf9abb03f16cd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VPPOXIEHURKMG752RYWVZHOWT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On exact linesearch quasi-Newton methods for minimizing a quadratic function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anders Forsgren, Tove Odland","submitted_at":"2015-03-06T09:48:33Z","abstract_excerpt":"This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton method, necessary and sufficient conditions can be given for an exact linesearch quasi-Newton method to generate a search direction which is parallel to that of the method of conjugate gradients.\n  We also analyze update matrices and give a complete description of the rank-one update matrices that give search direction parallel to those of the method of conju"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01892","kind":"arxiv","version":2},"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":"2026-05-18T00:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zn9pVJ5xtXOu5+5+r4gEP6TiSntnHTusoxW4UUx2BhjEC0Fg6ZPLlKSVhaxV62VCuUhFSVHRpeTY/ssDSl1/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:06.255835Z"},"content_sha256":"41a8d9bf331e01463e6c9b75216c7fba7f086f813d4c0c752adae2914766b143","schema_version":"1.0","event_id":"sha256:41a8d9bf331e01463e6c9b75216c7fba7f086f813d4c0c752adae2914766b143"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPPOXIEHURKMG752RYWVZHOWT7/bundle.json","state_url":"https://pith.science/pith/VPPOXIEHURKMG752RYWVZHOWT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPPOXIEHURKMG752RYWVZHOWT7/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":"2026-06-20T03:01:06Z","links":{"resolver":"https://pith.science/pith/VPPOXIEHURKMG752RYWVZHOWT7","bundle":"https://pith.science/pith/VPPOXIEHURKMG752RYWVZHOWT7/bundle.json","state":"https://pith.science/pith/VPPOXIEHURKMG752RYWVZHOWT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPPOXIEHURKMG752RYWVZHOWT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VPPOXIEHURKMG752RYWVZHOWT7","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":"918bf65caecb7e20ff090ae1d4061ddd58d45f89ed06589d0f17445c1e799bb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-06T09:48:33Z","title_canon_sha256":"c833fa7df3da87ac213c31a679a0a35f0522cfe3a6f3a709d10547e812bb896f"},"schema_version":"1.0","source":{"id":"1503.01892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01892","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01892v2","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01892","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"VPPOXIEHURKM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VPPOXIEHURKMG752","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VPPOXIEH","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:41a8d9bf331e01463e6c9b75216c7fba7f086f813d4c0c752adae2914766b143","target":"graph","created_at":"2026-05-18T00:37:37Z","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 concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton method, necessary and sufficient conditions can be given for an exact linesearch quasi-Newton method to generate a search direction which is parallel to that of the method of conjugate gradients.\n  We also analyze update matrices and give a complete description of the rank-one update matrices that give search direction parallel to those of the method of conju","authors_text":"Anders Forsgren, Tove Odland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-06T09:48:33Z","title":"On exact linesearch quasi-Newton methods for minimizing a quadratic function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01892","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:ba2e4a500c0cd7775e14edf5cade992c7156b100fe57992bbaaf9abb03f16cd6","target":"record","created_at":"2026-05-18T00:37:37Z","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":"918bf65caecb7e20ff090ae1d4061ddd58d45f89ed06589d0f17445c1e799bb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-06T09:48:33Z","title_canon_sha256":"c833fa7df3da87ac213c31a679a0a35f0522cfe3a6f3a709d10547e812bb896f"},"schema_version":"1.0","source":{"id":"1503.01892","kind":"arxiv","version":2}},"canonical_sha256":"abdeeba087a454c37fba8e2d5c9dd69fe0107bb85dd6182f3584de6da87dd6b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abdeeba087a454c37fba8e2d5c9dd69fe0107bb85dd6182f3584de6da87dd6b0","first_computed_at":"2026-05-18T00:37:37.012243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:37.012243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j/4GcCPZcRydHBLNMnReU34+uh5JdvwkhIsLGa+Two+rAETlJxR/MJvTp2nUhVUVXb/4GHcKgbZXlDo55EntAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:37.012785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba2e4a500c0cd7775e14edf5cade992c7156b100fe57992bbaaf9abb03f16cd6","sha256:41a8d9bf331e01463e6c9b75216c7fba7f086f813d4c0c752adae2914766b143"],"state_sha256":"353e371898dd30a93b59e0587ca5d6748600c5a2156d9fc183edecd53b66d8df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnFaw+0iWYwU32eGnM51q6mTGpwGMwqgwHc6IPAsFXikSn7ETphIvyrlvAyueqa1O+OnoU9uYaag2s1ef/bmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:01:06.257734Z","bundle_sha256":"a89bdcaaa128b98b8787449593a54e12b58225b5102d16c01190fc291e7427a5"}}