{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KWXIJJI5IZUWELU6FNYN7DSWNX","short_pith_number":"pith:KWXIJJI5","canonical_record":{"source":{"id":"1908.07111","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2019-08-19T23:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"938270cd596b030637016b45b1bd56d769803907c37f090d288c6dbc286e6d89","abstract_canon_sha256":"4029ae8910d676f1d7630cae0e5168f2ed535ce598b13ca90faecc6c80a567b0"},"schema_version":"1.0"},"canonical_sha256":"55ae84a51d4669622e9e2b70df8e566ddd3ab3b6317aadca9cace7df6dce1d0a","source":{"kind":"arxiv","id":"1908.07111","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07111","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07111v1","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07111","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"KWXIJJI5IZUW","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_16","alias_value":"KWXIJJI5IZUWELU6","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_8","alias_value":"KWXIJJI5","created_at":"2026-07-04T23:58:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KWXIJJI5IZUWELU6FNYN7DSWNX","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07111","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2019-08-19T23:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"938270cd596b030637016b45b1bd56d769803907c37f090d288c6dbc286e6d89","abstract_canon_sha256":"4029ae8910d676f1d7630cae0e5168f2ed535ce598b13ca90faecc6c80a567b0"},"schema_version":"1.0"},"canonical_sha256":"55ae84a51d4669622e9e2b70df8e566ddd3ab3b6317aadca9cace7df6dce1d0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:30.947585Z","signature_b64":"fx1cZwzN+saIzuEwlI0KxvMIrjlGWnflWTOOPdzMHWMJgc4mGvspKMex8H7+qvWnyB2+s5I4AXoKlLCNW2/TCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55ae84a51d4669622e9e2b70df8e566ddd3ab3b6317aadca9cace7df6dce1d0a","last_reissued_at":"2026-07-04T23:58:30.947246Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:30.947246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07111","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":"2026-07-04T23:58:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qkn2sFHn5EDNiPrltLPNovT3DplMUZ03Opkg0a9rnFS9xK6fa4GDTQ6ykBhDV5KYXKTCKUBYDVFO7r4ly1w2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:10:09.386069Z"},"content_sha256":"e847237b112e6256293ab66d146d5faaccd39f716985a609fb0e005959ce6194","schema_version":"1.0","event_id":"sha256:e847237b112e6256293ab66d146d5faaccd39f716985a609fb0e005959ce6194"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KWXIJJI5IZUWELU6FNYN7DSWNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the asymptotic convergence and acceleration of gradient methods","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hongchao Zhang, Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","submitted_at":"2019-08-19T23:54:45Z","abstract_excerpt":"We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two-dimensional strictly co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07111/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:58:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CwAT74uZuGp+XVjWdk6iUpF9Cc2lk0azO7X0Q4P7rn7qWtZVlhtAc6VCrj+OxXeVJfTMC+cAyLJfOQEDR1EqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:10:09.386555Z"},"content_sha256":"8b8b973d9dae9dd38486c75cc727784828c378ba490a8d718b82174a973f75d6","schema_version":"1.0","event_id":"sha256:8b8b973d9dae9dd38486c75cc727784828c378ba490a8d718b82174a973f75d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/bundle.json","state_url":"https://pith.science/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/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":"2026-08-16T07:10:09Z","links":{"resolver":"https://pith.science/pith/KWXIJJI5IZUWELU6FNYN7DSWNX","bundle":"https://pith.science/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/bundle.json","state":"https://pith.science/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWXIJJI5IZUWELU6FNYN7DSWNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KWXIJJI5IZUWELU6FNYN7DSWNX","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":"4029ae8910d676f1d7630cae0e5168f2ed535ce598b13ca90faecc6c80a567b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2019-08-19T23:54:45Z","title_canon_sha256":"938270cd596b030637016b45b1bd56d769803907c37f090d288c6dbc286e6d89"},"schema_version":"1.0","source":{"id":"1908.07111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07111","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07111v1","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07111","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"KWXIJJI5IZUW","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_16","alias_value":"KWXIJJI5IZUWELU6","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_8","alias_value":"KWXIJJI5","created_at":"2026-07-04T23:58:30Z"}],"graph_snapshots":[{"event_id":"sha256:8b8b973d9dae9dd38486c75cc727784828c378ba490a8d718b82174a973f75d6","target":"graph","created_at":"2026-07-04T23:58:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two-dimensional strictly co","authors_text":"Hongchao Zhang, Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2019-08-19T23:54:45Z","title":"On the asymptotic convergence and acceleration of gradient methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07111","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:e847237b112e6256293ab66d146d5faaccd39f716985a609fb0e005959ce6194","target":"record","created_at":"2026-07-04T23:58:30Z","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":"4029ae8910d676f1d7630cae0e5168f2ed535ce598b13ca90faecc6c80a567b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2019-08-19T23:54:45Z","title_canon_sha256":"938270cd596b030637016b45b1bd56d769803907c37f090d288c6dbc286e6d89"},"schema_version":"1.0","source":{"id":"1908.07111","kind":"arxiv","version":1}},"canonical_sha256":"55ae84a51d4669622e9e2b70df8e566ddd3ab3b6317aadca9cace7df6dce1d0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55ae84a51d4669622e9e2b70df8e566ddd3ab3b6317aadca9cace7df6dce1d0a","first_computed_at":"2026-07-04T23:58:30.947246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:30.947246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fx1cZwzN+saIzuEwlI0KxvMIrjlGWnflWTOOPdzMHWMJgc4mGvspKMex8H7+qvWnyB2+s5I4AXoKlLCNW2/TCw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:30.947585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e847237b112e6256293ab66d146d5faaccd39f716985a609fb0e005959ce6194","sha256:8b8b973d9dae9dd38486c75cc727784828c378ba490a8d718b82174a973f75d6"],"state_sha256":"cb59e31195e3f90435382784b4b92ab08834fdd5ce1d9fae67b9ed7dfddafff5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63VkijlDXhM0XEdeXJ8Gl/jB8XdOz/BNsMNxo5zPoomrzEyHy/+x8ojYYl8yphWASYY65nU96f2yRXNmbWyBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:10:09.390951Z","bundle_sha256":"751e02431fe53729917d6509ab92802f9cf647456d668db9cafddea080e1c012"}}