{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6MGTQ3O3FJKBXH2TULQUDEBSCI","short_pith_number":"pith:6MGTQ3O3","canonical_record":{"source":{"id":"1204.3982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-18T05:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"eef6210fd5025634e7daff3651e33af3e2dc8266d0fe246874563858b3881ad7","abstract_canon_sha256":"cd0f0ae9f1fc2ab1a7c4af9ff47509f1cd978eb75dd8911e697f9e4604f0a492"},"schema_version":"1.0"},"canonical_sha256":"f30d386ddb2a541b9f53a2e1419032120fe21fc35ee1dd4514abdfe0c9945e8c","source":{"kind":"arxiv","id":"1204.3982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3982","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3982v1","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3982","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"6MGTQ3O3FJKB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MGTQ3O3FJKBXH2T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MGTQ3O3","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6MGTQ3O3FJKBXH2TULQUDEBSCI","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-18T05:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"eef6210fd5025634e7daff3651e33af3e2dc8266d0fe246874563858b3881ad7","abstract_canon_sha256":"cd0f0ae9f1fc2ab1a7c4af9ff47509f1cd978eb75dd8911e697f9e4604f0a492"},"schema_version":"1.0"},"canonical_sha256":"f30d386ddb2a541b9f53a2e1419032120fe21fc35ee1dd4514abdfe0c9945e8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:38.098987Z","signature_b64":"QZ+rZkEZr6omvjXM+U8tgVSiEqpsG5gF6gDAC6hDPmWsBvaTFwwPRWG1DFLjOCAggteZ39BkUF7VijsUVkutBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f30d386ddb2a541b9f53a2e1419032120fe21fc35ee1dd4514abdfe0c9945e8c","last_reissued_at":"2026-05-18T03:57:38.098376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:38.098376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3982","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NQ+0huMpGnEIsKtxWi0CWxaSw8T0uyg7KfXohJZrK9QIX8BF5h80OWc63L5STsoMW81uuRYEXMpWWhUizTvkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:46:24.174478Z"},"content_sha256":"c1e3cd0a3efb69cdbd697121098b5b28349c94323e5d2cfc3d75af66e67a053d","schema_version":"1.0","event_id":"sha256:c1e3cd0a3efb69cdbd697121098b5b28349c94323e5d2cfc3d75af66e67a053d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6MGTQ3O3FJKBXH2TULQUDEBSCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Restart for Accelerated Gradient Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brendan O'Donoghue, Emmanuel Candes","submitted_at":"2012-04-18T05:53:59Z","abstract_excerpt":"In this paper we demonstrate a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes. The analysis of the technique relies on the observation that these schemes exhibit two modes of behavior depending on how much momentum is applied. In what we refer to as the 'high momentum' regime the iterates generated by an accelerated gradient scheme exhibit a periodic behavior, where the period is proportional to the square root of the local condition number of the objective function. This suggests a restart technique whereby we res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3982","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9kD3mfsBMszbqJz7ZRGCOImEIjPtUR8+RaWCc6axpq51l+rrS/K482ZA0wQ9LNAXQIuAiyUjCz4ZLBWnHZWrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:46:24.174827Z"},"content_sha256":"975a6e6f8825f9886044d1797ea4b9085dd313094387d186b2d6ff5060670e0a","schema_version":"1.0","event_id":"sha256:975a6e6f8825f9886044d1797ea4b9085dd313094387d186b2d6ff5060670e0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/bundle.json","state_url":"https://pith.science/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/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":"2026-06-03T10:46:24Z","links":{"resolver":"https://pith.science/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI","bundle":"https://pith.science/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/bundle.json","state":"https://pith.science/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MGTQ3O3FJKBXH2TULQUDEBSCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6MGTQ3O3FJKBXH2TULQUDEBSCI","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":"cd0f0ae9f1fc2ab1a7c4af9ff47509f1cd978eb75dd8911e697f9e4604f0a492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-18T05:53:59Z","title_canon_sha256":"eef6210fd5025634e7daff3651e33af3e2dc8266d0fe246874563858b3881ad7"},"schema_version":"1.0","source":{"id":"1204.3982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3982","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3982v1","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3982","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"6MGTQ3O3FJKB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MGTQ3O3FJKBXH2T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MGTQ3O3","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:975a6e6f8825f9886044d1797ea4b9085dd313094387d186b2d6ff5060670e0a","target":"graph","created_at":"2026-05-18T03:57:38Z","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":"In this paper we demonstrate a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes. The analysis of the technique relies on the observation that these schemes exhibit two modes of behavior depending on how much momentum is applied. In what we refer to as the 'high momentum' regime the iterates generated by an accelerated gradient scheme exhibit a periodic behavior, where the period is proportional to the square root of the local condition number of the objective function. This suggests a restart technique whereby we res","authors_text":"Brendan O'Donoghue, Emmanuel Candes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-18T05:53:59Z","title":"Adaptive Restart for Accelerated Gradient Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3982","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:c1e3cd0a3efb69cdbd697121098b5b28349c94323e5d2cfc3d75af66e67a053d","target":"record","created_at":"2026-05-18T03:57:38Z","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":"cd0f0ae9f1fc2ab1a7c4af9ff47509f1cd978eb75dd8911e697f9e4604f0a492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-18T05:53:59Z","title_canon_sha256":"eef6210fd5025634e7daff3651e33af3e2dc8266d0fe246874563858b3881ad7"},"schema_version":"1.0","source":{"id":"1204.3982","kind":"arxiv","version":1}},"canonical_sha256":"f30d386ddb2a541b9f53a2e1419032120fe21fc35ee1dd4514abdfe0c9945e8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f30d386ddb2a541b9f53a2e1419032120fe21fc35ee1dd4514abdfe0c9945e8c","first_computed_at":"2026-05-18T03:57:38.098376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:38.098376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZ+rZkEZr6omvjXM+U8tgVSiEqpsG5gF6gDAC6hDPmWsBvaTFwwPRWG1DFLjOCAggteZ39BkUF7VijsUVkutBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:38.098987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e3cd0a3efb69cdbd697121098b5b28349c94323e5d2cfc3d75af66e67a053d","sha256:975a6e6f8825f9886044d1797ea4b9085dd313094387d186b2d6ff5060670e0a"],"state_sha256":"a33144f0b613de4064c9a0ebd6beb5ab42ab1e83316584f04c5b42722023d212"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"inKUCfh6hiuvKTudZ6/IB62CHE3xcak/sxMHeW4I5A/VnilJsrmMDzL8wjGROcj0OrK1qTNZtPO9vwrQgaYnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:46:24.177184Z","bundle_sha256":"b3c589106c016ae098aac96b55b8a015671c80666fe341ec46b6225bf908c917"}}