{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7JAIKG647VRY2HBOZ6CJQLHE3T","short_pith_number":"pith:7JAIKG64","schema_version":"1.0","canonical_sha256":"fa40851bdcfd638d1c2ecf84982ce4dcfa61e91eb261147201175feb3e7df3b8","source":{"kind":"arxiv","id":"1810.01066","version":2},"attestation_state":"computed","paper":{"title":"PDE Acceleration: A convergence rate analysis and applications to obstacle problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.DS","math.OC"],"primary_cat":"math.NA","authors_text":"Anthony Yezzi, Jeff Calder","submitted_at":"2018-10-02T04:56:05Z","abstract_excerpt":"This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems. PDE acceleration grew out of a variational interpretation of momentum methods, such as Nesterov's accelerated gradient method and Polyak's heavy ball method, that views acceleration methods as equations of motion for a generalized Lagrangian action. Its application to convex variational problems yields equations of motion in the form of a damped nonlinear wave equ"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.01066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-02T04:56:05Z","cross_cats_sorted":["cs.NA","math.AP","math.DS","math.OC"],"title_canon_sha256":"4dadd0b60514bab5807c07a21f75b29638db9017aa27a132956cd81ad45e156f","abstract_canon_sha256":"f2f7f0d0523774f8efac46aa095b85b338113d4f76d402611f224d7e5b82252d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:50:12.833304Z","signature_b64":"xOXNa9VJdcWvy1TcF6GZelDAO9a5c6aTqwpVCHM5k0eJ2Qm4a6I8A/WsycFtIcxLgRSETHQ5fUCc1HViGkcDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa40851bdcfd638d1c2ecf84982ce4dcfa61e91eb261147201175feb3e7df3b8","last_reissued_at":"2026-07-04T23:50:12.832867Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:50:12.832867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PDE Acceleration: A convergence rate analysis and applications to obstacle problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.DS","math.OC"],"primary_cat":"math.NA","authors_text":"Anthony Yezzi, Jeff Calder","submitted_at":"2018-10-02T04:56:05Z","abstract_excerpt":"This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems. PDE acceleration grew out of a variational interpretation of momentum methods, such as Nesterov's accelerated gradient method and Polyak's heavy ball method, that views acceleration methods as equations of motion for a generalized Lagrangian action. Its application to convex variational problems yields equations of motion in the form of a damped nonlinear wave equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01066","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.01066/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.01066","created_at":"2026-07-04T23:50:12.832923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01066v2","created_at":"2026-07-04T23:50:12.832923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01066","created_at":"2026-07-04T23:50:12.832923+00:00"},{"alias_kind":"pith_short_12","alias_value":"7JAIKG647VRY","created_at":"2026-07-04T23:50:12.832923+00:00"},{"alias_kind":"pith_short_16","alias_value":"7JAIKG647VRY2HBO","created_at":"2026-07-04T23:50:12.832923+00:00"},{"alias_kind":"pith_short_8","alias_value":"7JAIKG64","created_at":"2026-07-04T23:50:12.832923+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T","json":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T.json","graph_json":"https://pith.science/api/pith-number/7JAIKG647VRY2HBOZ6CJQLHE3T/graph.json","events_json":"https://pith.science/api/pith-number/7JAIKG647VRY2HBOZ6CJQLHE3T/events.json","paper":"https://pith.science/paper/7JAIKG64"},"agent_actions":{"view_html":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T","download_json":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T.json","view_paper":"https://pith.science/paper/7JAIKG64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01066&json=true","fetch_graph":"https://pith.science/api/pith-number/7JAIKG647VRY2HBOZ6CJQLHE3T/graph.json","fetch_events":"https://pith.science/api/pith-number/7JAIKG647VRY2HBOZ6CJQLHE3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T/action/storage_attestation","attest_author":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T/action/author_attestation","sign_citation":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T/action/citation_signature","submit_replication":"https://pith.science/pith/7JAIKG647VRY2HBOZ6CJQLHE3T/action/replication_record"}},"created_at":"2026-07-04T23:50:12.832923+00:00","updated_at":"2026-07-04T23:50:12.832923+00:00"}