{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OA3EEIPLOEBEV77F2FIE4ITEEQ","short_pith_number":"pith:OA3EEIPL","canonical_record":{"source":{"id":"1812.02974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-07T10:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"d8bdc58742f3fefbb33fc8d542e07d3749156bed34fd026bc7f49ace6b5181ca","abstract_canon_sha256":"863abee9bce4ab1dcf859ccf528afc8f56ae7c1f4362aba9cad175191e205bc8"},"schema_version":"1.0"},"canonical_sha256":"70364221eb71024affe5d1504e2264243c5bcfc38b1f194e74708716c4ac11b9","source":{"kind":"arxiv","id":"1812.02974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02974","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02974v1","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02974","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"OA3EEIPLOEBE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OA3EEIPLOEBEV77F","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OA3EEIPL","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OA3EEIPLOEBEV77F2FIE4ITEEQ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-07T10:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"d8bdc58742f3fefbb33fc8d542e07d3749156bed34fd026bc7f49ace6b5181ca","abstract_canon_sha256":"863abee9bce4ab1dcf859ccf528afc8f56ae7c1f4362aba9cad175191e205bc8"},"schema_version":"1.0"},"canonical_sha256":"70364221eb71024affe5d1504e2264243c5bcfc38b1f194e74708716c4ac11b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:51.241819Z","signature_b64":"XytmiT8o0X12S+y3NyPPDHyxwCce18m08F5S3hWePsJXoa6Un21e2pSV+Y3VfHe+vB2Y+Nxa6v+AQUTGyjI7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70364221eb71024affe5d1504e2264243c5bcfc38b1f194e74708716c4ac11b9","last_reissued_at":"2026-05-17T23:58:51.241397Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:51.241397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02974","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":"2026-05-17T23:58:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NsAZO7wXRPgzeeRIl6T3mwZotLUhNMZHf58plh1kAlahMrQJUgQAMnJ1tr5EGQq01MEgSLYkngb+4TCVBNymBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:43:31.158556Z"},"content_sha256":"6d1a536e8517e455a0c0086f2ef397528b59e2e4375168f0efa0222385256850","schema_version":"1.0","event_id":"sha256:6d1a536e8517e455a0c0086f2ef397528b59e2e4375168f0efa0222385256850"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OA3EEIPLOEBEV77F2FIE4ITEEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of spectral gradient methods for optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","submitted_at":"2018-12-07T10:51:51Z","abstract_excerpt":"We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is $R$-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is $R$-linearly convergent in the any-dimensional case. Numerical results of the family with different setting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02974","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":"2026-05-17T23:58:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"su21rqKFpOmt+w4DDti0XhU7QubFcSZQDyMYHBxhT5OV1kw8uSXx0iAlUQQRYewnsBWxAO+1TpwJsxgDXVFSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:43:31.159211Z"},"content_sha256":"35b0ed0cb6de4d321639652eec0770ceb5e4f97f3fcae44a79c3e754eb0193ed","schema_version":"1.0","event_id":"sha256:35b0ed0cb6de4d321639652eec0770ceb5e4f97f3fcae44a79c3e754eb0193ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/bundle.json","state_url":"https://pith.science/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/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":"2026-06-06T23:43:31Z","links":{"resolver":"https://pith.science/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ","bundle":"https://pith.science/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/bundle.json","state":"https://pith.science/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OA3EEIPLOEBEV77F2FIE4ITEEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OA3EEIPLOEBEV77F2FIE4ITEEQ","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":"863abee9bce4ab1dcf859ccf528afc8f56ae7c1f4362aba9cad175191e205bc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-07T10:51:51Z","title_canon_sha256":"d8bdc58742f3fefbb33fc8d542e07d3749156bed34fd026bc7f49ace6b5181ca"},"schema_version":"1.0","source":{"id":"1812.02974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02974","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02974v1","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02974","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"OA3EEIPLOEBE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OA3EEIPLOEBEV77F","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OA3EEIPL","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:35b0ed0cb6de4d321639652eec0770ceb5e4f97f3fcae44a79c3e754eb0193ed","target":"graph","created_at":"2026-05-17T23:58:51Z","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 propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is $R$-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is $R$-linearly convergent in the any-dimensional case. Numerical results of the family with different setting","authors_text":"Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-07T10:51:51Z","title":"A family of spectral gradient methods for optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02974","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":"sha256:6d1a536e8517e455a0c0086f2ef397528b59e2e4375168f0efa0222385256850","target":"record","created_at":"2026-05-17T23:58:51Z","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":"863abee9bce4ab1dcf859ccf528afc8f56ae7c1f4362aba9cad175191e205bc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-07T10:51:51Z","title_canon_sha256":"d8bdc58742f3fefbb33fc8d542e07d3749156bed34fd026bc7f49ace6b5181ca"},"schema_version":"1.0","source":{"id":"1812.02974","kind":"arxiv","version":1}},"canonical_sha256":"70364221eb71024affe5d1504e2264243c5bcfc38b1f194e74708716c4ac11b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70364221eb71024affe5d1504e2264243c5bcfc38b1f194e74708716c4ac11b9","first_computed_at":"2026-05-17T23:58:51.241397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:51.241397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XytmiT8o0X12S+y3NyPPDHyxwCce18m08F5S3hWePsJXoa6Un21e2pSV+Y3VfHe+vB2Y+Nxa6v+AQUTGyjI7Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:51.241819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d1a536e8517e455a0c0086f2ef397528b59e2e4375168f0efa0222385256850","sha256:35b0ed0cb6de4d321639652eec0770ceb5e4f97f3fcae44a79c3e754eb0193ed"],"state_sha256":"2d6830505a18dd49490b3f11603cded48d77cd1adc49f71f08537400d2c17719"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/wYpW833T92H9nSDK9H4UfkbKWEnQkK2/gS/hmnSJmBG7qQyx/4E95A4htvQ8HQoejqTgvn1f1k3FGGE5zUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:43:31.163141Z","bundle_sha256":"914532c53e9d8835002ecc7bf28a6d4c598d3a8a73f26312eda390d80a9b269c"}}