{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SC6SW2NPEOJYCPCEYVWETWIW62","short_pith_number":"pith:SC6SW2NP","canonical_record":{"source":{"id":"2602.00334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T21:35:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6d4faea1306c1a32be5480fdd7806c37b54581456c2b57c6084bb9aed86abaed","abstract_canon_sha256":"69d3daeb09d62484b39536233930adbc29025df779cfb1210676e4b5b9267d24"},"schema_version":"1.0"},"canonical_sha256":"90bd2b69af2393813c44c56c49d916f684a9574597fcac8f57b4bf6a16f273cc","source":{"kind":"arxiv","id":"2602.00334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00334","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00334v2","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00334","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"SC6SW2NPEOJY","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"SC6SW2NPEOJYCPCE","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"SC6SW2NP","created_at":"2026-06-29T01:15:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SC6SW2NPEOJYCPCEYVWETWIW62","target":"record","payload":{"canonical_record":{"source":{"id":"2602.00334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T21:35:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6d4faea1306c1a32be5480fdd7806c37b54581456c2b57c6084bb9aed86abaed","abstract_canon_sha256":"69d3daeb09d62484b39536233930adbc29025df779cfb1210676e4b5b9267d24"},"schema_version":"1.0"},"canonical_sha256":"90bd2b69af2393813c44c56c49d916f684a9574597fcac8f57b4bf6a16f273cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:15:03.992094Z","signature_b64":"Sgpudz82412vX4GmlIVgDqDw5tcBebnUJv7tAHZ5BUUH0v3Hj4FVkt981q4Vi3DZI2cqoA8lDRMx5vW8PXVVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90bd2b69af2393813c44c56c49d916f684a9574597fcac8f57b4bf6a16f273cc","last_reissued_at":"2026-06-29T01:15:03.991612Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:15:03.991612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.00334","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-29T01:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpJrqXockHLRr6s85lqGOwr02IIY/KhzaHmib5OAPZq1pX3iGiR0CFNqyEXJKXs+C8j/mdGn9+r6gHaSqYoyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:19:17.098224Z"},"content_sha256":"21da134d4256baeebdd7c4c89a70c16a7055a3db8e92911547e342ed0d8dcd7e","schema_version":"1.0","event_id":"sha256:21da134d4256baeebdd7c4c89a70c16a7055a3db8e92911547e342ed0d8dcd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SC6SW2NPEOJYCPCEYVWETWIW62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Momentum and Nonlinear Damping for Neural Network Training","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Aikaterini Karoni, Benedict Leimkuhler, Gabriel Stoltz, Rajit Rajpal","submitted_at":"2026-01-30T21:35:55Z","abstract_excerpt":"Momentum Stochastic Gradient Descent (mSGD) relies on a fixed momentum coefficient shared across all parameters, failing to account for the heterogeneous structure of modern loss landscapes. In this work, we adopt a continuous-time formulation to introduce individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This mechanism automatically adjusts to evolving training dynamics to maintain stability without sacrificing convergence speed. We demonstrate that this adaptive friction is inextricably linked to cubic damping, a suppression mechanism from st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00334","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/2602.00334/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":"2026-06-29T01:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uw5rrJnmV5yjFXBpI9bsh0C+uVRo2hHiAv6aQxPZJhrxwewOSwkojaODrVBIipLEqucZgHZV4wjCzoTLtVRFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:19:17.098614Z"},"content_sha256":"c1c81ade1b69e12845f1287845fc410c735566f9111c0d6ceba7550482373cc0","schema_version":"1.0","event_id":"sha256:c1c81ade1b69e12845f1287845fc410c735566f9111c0d6ceba7550482373cc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SC6SW2NPEOJYCPCEYVWETWIW62/bundle.json","state_url":"https://pith.science/pith/SC6SW2NPEOJYCPCEYVWETWIW62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SC6SW2NPEOJYCPCEYVWETWIW62/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":"2026-08-04T03:19:17Z","links":{"resolver":"https://pith.science/pith/SC6SW2NPEOJYCPCEYVWETWIW62","bundle":"https://pith.science/pith/SC6SW2NPEOJYCPCEYVWETWIW62/bundle.json","state":"https://pith.science/pith/SC6SW2NPEOJYCPCEYVWETWIW62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SC6SW2NPEOJYCPCEYVWETWIW62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SC6SW2NPEOJYCPCEYVWETWIW62","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":"69d3daeb09d62484b39536233930adbc29025df779cfb1210676e4b5b9267d24","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T21:35:55Z","title_canon_sha256":"6d4faea1306c1a32be5480fdd7806c37b54581456c2b57c6084bb9aed86abaed"},"schema_version":"1.0","source":{"id":"2602.00334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00334","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00334v2","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00334","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"SC6SW2NPEOJY","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"SC6SW2NPEOJYCPCE","created_at":"2026-06-29T01:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"SC6SW2NP","created_at":"2026-06-29T01:15:03Z"}],"graph_snapshots":[{"event_id":"sha256:c1c81ade1b69e12845f1287845fc410c735566f9111c0d6ceba7550482373cc0","target":"graph","created_at":"2026-06-29T01:15:03Z","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/2602.00334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Momentum Stochastic Gradient Descent (mSGD) relies on a fixed momentum coefficient shared across all parameters, failing to account for the heterogeneous structure of modern loss landscapes. In this work, we adopt a continuous-time formulation to introduce individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This mechanism automatically adjusts to evolving training dynamics to maintain stability without sacrificing convergence speed. We demonstrate that this adaptive friction is inextricably linked to cubic damping, a suppression mechanism from st","authors_text":"Aikaterini Karoni, Benedict Leimkuhler, Gabriel Stoltz, Rajit Rajpal","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T21:35:55Z","title":"Adaptive Momentum and Nonlinear Damping for Neural Network Training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00334","kind":"arxiv","version":2},"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":"sha256:21da134d4256baeebdd7c4c89a70c16a7055a3db8e92911547e342ed0d8dcd7e","target":"record","created_at":"2026-06-29T01:15:03Z","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":"69d3daeb09d62484b39536233930adbc29025df779cfb1210676e4b5b9267d24","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T21:35:55Z","title_canon_sha256":"6d4faea1306c1a32be5480fdd7806c37b54581456c2b57c6084bb9aed86abaed"},"schema_version":"1.0","source":{"id":"2602.00334","kind":"arxiv","version":2}},"canonical_sha256":"90bd2b69af2393813c44c56c49d916f684a9574597fcac8f57b4bf6a16f273cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90bd2b69af2393813c44c56c49d916f684a9574597fcac8f57b4bf6a16f273cc","first_computed_at":"2026-06-29T01:15:03.991612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:15:03.991612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sgpudz82412vX4GmlIVgDqDw5tcBebnUJv7tAHZ5BUUH0v3Hj4FVkt981q4Vi3DZI2cqoA8lDRMx5vW8PXVVAQ==","signature_status":"signed_v1","signed_at":"2026-06-29T01:15:03.992094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.00334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21da134d4256baeebdd7c4c89a70c16a7055a3db8e92911547e342ed0d8dcd7e","sha256:c1c81ade1b69e12845f1287845fc410c735566f9111c0d6ceba7550482373cc0"],"state_sha256":"49a640fb4c06419b0898841562aed588c8af9c20a0f8d1bb6dddfd6a774e2455"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4xo18ntzyDN7dnBA66uDX/0EZ1C+dYLHfIJ9fsX6i+387SS6aVcmt4kqfhg3yEpph529yq1eMq6OV1CUA7/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T03:19:17.101693Z","bundle_sha256":"d5c29bfa760deab28d1c3430246b229ce154fd7cf5e31309d571ed0f52ad6862"}}