{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FI5A65XOECJUIA34JFIUAH7PZI","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":"73c829ff5bbba449ad75abcd109f45b62b75fd97ebe72d181ffc5ab98b04fa75","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-15T16:04:37Z","title_canon_sha256":"908fe27ba6b70854d249d49674f43527e643591ffca3a06bbe3562073c2317e1"},"schema_version":"1.0","source":{"id":"2607.16329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16329","created_at":"2026-07-21T00:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16329v1","created_at":"2026-07-21T00:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16329","created_at":"2026-07-21T00:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"FI5A65XOECJU","created_at":"2026-07-21T00:20:12Z"},{"alias_kind":"pith_short_16","alias_value":"FI5A65XOECJUIA34","created_at":"2026-07-21T00:20:12Z"},{"alias_kind":"pith_short_8","alias_value":"FI5A65XO","created_at":"2026-07-21T00:20:12Z"}],"graph_snapshots":[{"event_id":"sha256:f0753eb05f9612d7ae15bcf0380bab79fef4b258804b5f0351757ebab4a1ad81","target":"graph","created_at":"2026-07-21T00:20:12Z","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/2607.16329/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations. It plays a pivotal role in deep learning, governing \\textbf{robustness}, \\textbf{generalization} and \\textbf{optimization dynamics}. Despite its importance, research on Lipschitz continuity is scattered across various domains, lacking a unified perspective. This paper addresses this gap by providing a systematic review of Lipschitz continuity in deep learning. We explore its \\textbf{theoretical foundations}, \\textbf{estimation methods}, \\textbf{regularization approache","authors_text":"Colm O'Riordan, James McDermott, R\\'ois\\'in Luo","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-15T16:04:37Z","title":"Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16329","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":"sha256:1ba185c68f487cd63e7ccaef909fe1b4ac22c510c984a919ac363332f4138e51","target":"record","created_at":"2026-07-21T00:20:12Z","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":"73c829ff5bbba449ad75abcd109f45b62b75fd97ebe72d181ffc5ab98b04fa75","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-15T16:04:37Z","title_canon_sha256":"908fe27ba6b70854d249d49674f43527e643591ffca3a06bbe3562073c2317e1"},"schema_version":"1.0","source":{"id":"2607.16329","kind":"arxiv","version":1}},"canonical_sha256":"2a3a0f76ee209344037c4951401fefca2742e5900aba64c722d134cf233073db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a3a0f76ee209344037c4951401fefca2742e5900aba64c722d134cf233073db","first_computed_at":"2026-07-21T00:20:12.697611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:12.697611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BWLzFDMS1zjJfEdlVJu/Y6zQUOC5gFnJ5yYk67U9gin78rMQ8Krrn+IedIa/om2sT5n2rL/9L/VAVE0vmhw8BQ==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:12.698571Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ba185c68f487cd63e7ccaef909fe1b4ac22c510c984a919ac363332f4138e51","sha256:f0753eb05f9612d7ae15bcf0380bab79fef4b258804b5f0351757ebab4a1ad81"],"state_sha256":"7cca74b240e0d615a29746a35a50b34db5e1fb22ad6f7c85f30e35f5e3b5a9b1"}