{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MJHEAHLSS757J2YU7FFNVA6ZE3","short_pith_number":"pith:MJHEAHLS","canonical_record":{"source":{"id":"1809.05042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-13T16:21:11Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"214468963e08070d8da76e50c4b7a2bcb2987b924dd75ac28a1b8c5a6714b716","abstract_canon_sha256":"909eaa4af35bf02ff16aaf4056641ff79bbb367e5bf1fe28f58daf494fa61784"},"schema_version":"1.0"},"canonical_sha256":"624e401d7297fbf4eb14f94ada83d926e3e3adef11c1b20bcb94775655093e51","source":{"kind":"arxiv","id":"1809.05042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05042","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05042v1","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05042","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"MJHEAHLSS757","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MJHEAHLSS757J2YU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MJHEAHLS","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MJHEAHLSS757J2YU7FFNVA6ZE3","target":"record","payload":{"canonical_record":{"source":{"id":"1809.05042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-13T16:21:11Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"214468963e08070d8da76e50c4b7a2bcb2987b924dd75ac28a1b8c5a6714b716","abstract_canon_sha256":"909eaa4af35bf02ff16aaf4056641ff79bbb367e5bf1fe28f58daf494fa61784"},"schema_version":"1.0"},"canonical_sha256":"624e401d7297fbf4eb14f94ada83d926e3e3adef11c1b20bcb94775655093e51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:46.771325Z","signature_b64":"qy9ipGzZ/m8hN3HBElxQUL+9NpiR3tDSZe18HrkWMFChxkOYff67TGsOjCnNXGHp95vk172QEfK+bPZto7aVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"624e401d7297fbf4eb14f94ada83d926e3e3adef11c1b20bcb94775655093e51","last_reissued_at":"2026-05-18T00:05:46.770691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:46.770691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.05042","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":"2026-05-18T00:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kAGQrtroK3c72HpbWwP27hEKnKcH5ys5arLdiUilpEkJP/6nLhNV0MCtyxgW8mqzfVDCMP0f0T9ioBxAAi6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:45:56.556064Z"},"content_sha256":"01cb45045fe4f6c83c92fa06b5ff8d9fea0eeade55e8ac8ebd0177e18cb46487","schema_version":"1.0","event_id":"sha256:01cb45045fe4f6c83c92fa06b5ff8d9fea0eeade55e8ac8ebd0177e18cb46487"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MJHEAHLSS757J2YU7FFNVA6ZE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian Descent Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Arnaud Doucet, Brendan O'Donoghue, Chris J. Maddison, Daniel Paulin, Yee Whye Teh","submitted_at":"2018-09-13T16:21:11Z","abstract_excerpt":"We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger class includes functions whose second derivatives may be singular or unbounded at their minima. Our methods are discretizations of conformal Hamiltonian dynamics, which generalize the classical momentum method to model the motion of a particle with non-standard kinetic energy exposed to a dissipative force and the gradient field of the function of interest. They"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05042","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":"2026-05-18T00:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ekoSiRWZ5/L0HkdaVxFLUQq2inWUJrNW4xjQTR3P3+GxwCvD43TZg2eMiAA/etejpSLQULkxqNflD2znzHfCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:45:56.556729Z"},"content_sha256":"21d819b402e10da7e60ce72514aa4e7dbd0370e63341e62138305558f16949b7","schema_version":"1.0","event_id":"sha256:21d819b402e10da7e60ce72514aa4e7dbd0370e63341e62138305558f16949b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/bundle.json","state_url":"https://pith.science/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/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":"2026-05-26T00:45:56Z","links":{"resolver":"https://pith.science/pith/MJHEAHLSS757J2YU7FFNVA6ZE3","bundle":"https://pith.science/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/bundle.json","state":"https://pith.science/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJHEAHLSS757J2YU7FFNVA6ZE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MJHEAHLSS757J2YU7FFNVA6ZE3","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":"909eaa4af35bf02ff16aaf4056641ff79bbb367e5bf1fe28f58daf494fa61784","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-13T16:21:11Z","title_canon_sha256":"214468963e08070d8da76e50c4b7a2bcb2987b924dd75ac28a1b8c5a6714b716"},"schema_version":"1.0","source":{"id":"1809.05042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05042","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05042v1","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05042","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"MJHEAHLSS757","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MJHEAHLSS757J2YU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MJHEAHLS","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:21d819b402e10da7e60ce72514aa4e7dbd0370e63341e62138305558f16949b7","target":"graph","created_at":"2026-05-18T00:05:46Z","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 optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger class includes functions whose second derivatives may be singular or unbounded at their minima. Our methods are discretizations of conformal Hamiltonian dynamics, which generalize the classical momentum method to model the motion of a particle with non-standard kinetic energy exposed to a dissipative force and the gradient field of the function of interest. They","authors_text":"Arnaud Doucet, Brendan O'Donoghue, Chris J. Maddison, Daniel Paulin, Yee Whye Teh","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-13T16:21:11Z","title":"Hamiltonian Descent Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05042","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":"sha256:01cb45045fe4f6c83c92fa06b5ff8d9fea0eeade55e8ac8ebd0177e18cb46487","target":"record","created_at":"2026-05-18T00:05:46Z","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":"909eaa4af35bf02ff16aaf4056641ff79bbb367e5bf1fe28f58daf494fa61784","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-13T16:21:11Z","title_canon_sha256":"214468963e08070d8da76e50c4b7a2bcb2987b924dd75ac28a1b8c5a6714b716"},"schema_version":"1.0","source":{"id":"1809.05042","kind":"arxiv","version":1}},"canonical_sha256":"624e401d7297fbf4eb14f94ada83d926e3e3adef11c1b20bcb94775655093e51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"624e401d7297fbf4eb14f94ada83d926e3e3adef11c1b20bcb94775655093e51","first_computed_at":"2026-05-18T00:05:46.770691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:46.770691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qy9ipGzZ/m8hN3HBElxQUL+9NpiR3tDSZe18HrkWMFChxkOYff67TGsOjCnNXGHp95vk172QEfK+bPZto7aVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:46.771325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01cb45045fe4f6c83c92fa06b5ff8d9fea0eeade55e8ac8ebd0177e18cb46487","sha256:21d819b402e10da7e60ce72514aa4e7dbd0370e63341e62138305558f16949b7"],"state_sha256":"81a2a02a7a7caa9d06f70dd4dd42addb809071a8f0b485a0b0c644365ee49eb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"672AVYaJChqgjl4777LQGjZhFzH2dJWTPXCF8fADq9S+YIjCu46y4qNbFRQRxDn6hqGTCHurEVsaDUfq7rxJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:45:56.560346Z","bundle_sha256":"cb22856c42ade6a93330cb247358735048538cb6cc447c12e298007d57522358"}}