{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:72WCNMBURLEULLGZEPFDHNJSYM","short_pith_number":"pith:72WCNMBU","canonical_record":{"source":{"id":"2303.03169","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-06T14:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"102ed018d7be61aee80197e97f328c0d232778b1e66441c0fc111ae70f61ed29","abstract_canon_sha256":"bcca42513c229c6bd9ed222982cefdfcd44fe8cd333713fefa33e5f9d279b90e"},"schema_version":"1.0"},"canonical_sha256":"feac26b0348ac945acd923ca33b532c30a495421ea31e5ed4130959a5281c79e","source":{"kind":"arxiv","id":"2303.03169","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.03169","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2303.03169v2","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.03169","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"72WCNMBURLEU","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"72WCNMBURLEULLGZ","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"72WCNMBU","created_at":"2026-07-05T07:05:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:72WCNMBURLEULLGZEPFDHNJSYM","target":"record","payload":{"canonical_record":{"source":{"id":"2303.03169","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-06T14:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"102ed018d7be61aee80197e97f328c0d232778b1e66441c0fc111ae70f61ed29","abstract_canon_sha256":"bcca42513c229c6bd9ed222982cefdfcd44fe8cd333713fefa33e5f9d279b90e"},"schema_version":"1.0"},"canonical_sha256":"feac26b0348ac945acd923ca33b532c30a495421ea31e5ed4130959a5281c79e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:05:41.688632Z","signature_b64":"ZS/sOKIRcm6xV8jvFYW8H0v4OZErv3W/hl4Pju0/8XbCZOFfMffOmhIGHEz2/s9kIuGrmbxwZl5m/jFNBKKRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feac26b0348ac945acd923ca33b532c30a495421ea31e5ed4130959a5281c79e","last_reissued_at":"2026-07-05T07:05:41.688229Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:05:41.688229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.03169","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":"2026-07-05T07:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5uk4vRQNWECrqhzR+Xg2doi7IvDpKpYLChwNMJvdmi2tHuKEY0MlG3JCHs5aMW69x6mbegjauGCqZLZGDc6oDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:39:36.763394Z"},"content_sha256":"e47e72280d69457b72d5e39b9d456723e10add2ce4125cc18a698457d88a9bed","schema_version":"1.0","event_id":"sha256:e47e72280d69457b72d5e39b9d456723e10add2ce4125cc18a698457d88a9bed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:72WCNMBURLEULLGZEPFDHNJSYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Unified Algebraic Perspective on Lipschitz Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aaron Havens, Alexandre Allauzen, Alexandre Araujo, Bin Hu, Blaise Delattre","submitted_at":"2023-03-06T14:31:09Z","abstract_excerpt":"Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising techniques draw inspirations from different backgrounds to design 1-Lipschitz neural networks, just to name a few: convex potential layers derive from the discretization of continuous dynamical systems, Almost-Orthogonal-Layer proposes a tailored method for matrix rescaling. However, it is today important to consider the recent and promising contributions in the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03169","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/2303.03169/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":"2026-07-05T07:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ats0Ey99Egcbtj512AeuOxNPcCsoAno8y3P3Bh29KHCRnVtWkAVnTaU/+NHXrcXq+8eD7kFwXMRIfNRzxtTDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:39:36.763904Z"},"content_sha256":"c71d26d73490b2b72935dbc36438bc1de4ee904bb91e9c5dc492a0cb89fd0478","schema_version":"1.0","event_id":"sha256:c71d26d73490b2b72935dbc36438bc1de4ee904bb91e9c5dc492a0cb89fd0478"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72WCNMBURLEULLGZEPFDHNJSYM/bundle.json","state_url":"https://pith.science/pith/72WCNMBURLEULLGZEPFDHNJSYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72WCNMBURLEULLGZEPFDHNJSYM/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":"2026-08-13T09:39:36Z","links":{"resolver":"https://pith.science/pith/72WCNMBURLEULLGZEPFDHNJSYM","bundle":"https://pith.science/pith/72WCNMBURLEULLGZEPFDHNJSYM/bundle.json","state":"https://pith.science/pith/72WCNMBURLEULLGZEPFDHNJSYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72WCNMBURLEULLGZEPFDHNJSYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:72WCNMBURLEULLGZEPFDHNJSYM","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":"bcca42513c229c6bd9ed222982cefdfcd44fe8cd333713fefa33e5f9d279b90e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-06T14:31:09Z","title_canon_sha256":"102ed018d7be61aee80197e97f328c0d232778b1e66441c0fc111ae70f61ed29"},"schema_version":"1.0","source":{"id":"2303.03169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.03169","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2303.03169v2","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.03169","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"72WCNMBURLEU","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"72WCNMBURLEULLGZ","created_at":"2026-07-05T07:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"72WCNMBU","created_at":"2026-07-05T07:05:41Z"}],"graph_snapshots":[{"event_id":"sha256:c71d26d73490b2b72935dbc36438bc1de4ee904bb91e9c5dc492a0cb89fd0478","target":"graph","created_at":"2026-07-05T07:05:41Z","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/2303.03169/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising techniques draw inspirations from different backgrounds to design 1-Lipschitz neural networks, just to name a few: convex potential layers derive from the discretization of continuous dynamical systems, Almost-Orthogonal-Layer proposes a tailored method for matrix rescaling. However, it is today important to consider the recent and promising contributions in the fi","authors_text":"Aaron Havens, Alexandre Allauzen, Alexandre Araujo, Bin Hu, Blaise Delattre","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-06T14:31:09Z","title":"A Unified Algebraic Perspective on Lipschitz Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03169","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:e47e72280d69457b72d5e39b9d456723e10add2ce4125cc18a698457d88a9bed","target":"record","created_at":"2026-07-05T07:05:41Z","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":"bcca42513c229c6bd9ed222982cefdfcd44fe8cd333713fefa33e5f9d279b90e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-03-06T14:31:09Z","title_canon_sha256":"102ed018d7be61aee80197e97f328c0d232778b1e66441c0fc111ae70f61ed29"},"schema_version":"1.0","source":{"id":"2303.03169","kind":"arxiv","version":2}},"canonical_sha256":"feac26b0348ac945acd923ca33b532c30a495421ea31e5ed4130959a5281c79e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feac26b0348ac945acd923ca33b532c30a495421ea31e5ed4130959a5281c79e","first_computed_at":"2026-07-05T07:05:41.688229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:05:41.688229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZS/sOKIRcm6xV8jvFYW8H0v4OZErv3W/hl4Pju0/8XbCZOFfMffOmhIGHEz2/s9kIuGrmbxwZl5m/jFNBKKRBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:05:41.688632Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.03169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e47e72280d69457b72d5e39b9d456723e10add2ce4125cc18a698457d88a9bed","sha256:c71d26d73490b2b72935dbc36438bc1de4ee904bb91e9c5dc492a0cb89fd0478"],"state_sha256":"0c11e9f055b1867d1120c9ed268381ddb48ce3091f52deaffb80f55b00abea2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fTiKz8/u/Y3VYhtK5ne0rCPxmx/5PACYTxsgxLuwuTcHx3laz24+fBHr7MDlMRmSxb+6fYCxc/EdK77ctr95DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:39:36.767910Z","bundle_sha256":"8411bad2ba7a5969e758c66961df09311ead72d124a4b27ac8c71b0a6c677258"}}