{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IZPLSPSUQLX2WDI2KNEJFJZQBG","short_pith_number":"pith:IZPLSPSU","canonical_record":{"source":{"id":"1904.04861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-09T18:39:43Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f136cc1f1549ec053abe252b472c2fbb2e15c6774e828db6b432e2db41846ab2","abstract_canon_sha256":"902c12ac857af0458cfc49d79da48212b5d19278bbe2c0b19e0e00e24e91a971"},"schema_version":"1.0"},"canonical_sha256":"465eb93e5482efab0d1a534892a730098307181e4148080e784d53b8adf70d52","source":{"kind":"arxiv","id":"1904.04861","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04861","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04861v1","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04861","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"IZPLSPSUQLX2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IZPLSPSUQLX2WDI2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IZPLSPSU","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IZPLSPSUQLX2WDI2KNEJFJZQBG","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-09T18:39:43Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f136cc1f1549ec053abe252b472c2fbb2e15c6774e828db6b432e2db41846ab2","abstract_canon_sha256":"902c12ac857af0458cfc49d79da48212b5d19278bbe2c0b19e0e00e24e91a971"},"schema_version":"1.0"},"canonical_sha256":"465eb93e5482efab0d1a534892a730098307181e4148080e784d53b8adf70d52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:57.804010Z","signature_b64":"j8c+e1IDaGdO+j3DasUneI7377IFX5BrUjTgaotSsxGsrqLXzg7/pCpR4qr+9I8CTK16XaKj46HacwzDkl0wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"465eb93e5482efab0d1a534892a730098307181e4148080e784d53b8adf70d52","last_reissued_at":"2026-05-17T23:48:57.803550Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:57.803550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04861","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":"2026-05-17T23:48:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEKuYB1vO9q3om+tWhonLmcPIi2Rt0DOo1ZuCwO8JLYD/B9dUqiydv83AFvT3ZDmo8nzz53dKN+07o8XqxJTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:22:18.049632Z"},"content_sha256":"871ba65f9d9a7f49efe6b2ab159670a22c16bacbcc0fc9f196a93bb50d754db5","schema_version":"1.0","event_id":"sha256:871ba65f9d9a7f49efe6b2ab159670a22c16bacbcc0fc9f196a93bb50d754db5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IZPLSPSUQLX2WDI2KNEJFJZQBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Lipschitz Approximation in Bounded Depth Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Jeremy E.J. Cohen, Ra Cohen, Todd Huster","submitted_at":"2019-04-09T18:39:43Z","abstract_excerpt":"Adversarial attacks against machine learning models are a rather hefty obstacle to our increasing reliance on these models. Due to this, provably robust (certified) machine learning models are a major topic of interest. Lipschitz continuous models present a promising approach to solving this problem. By leveraging the expressive power of a variant of neural networks which maintain low Lipschitz constants, we prove that three layer neural networks using the FullSort activation function are Universal Lipschitz function Approximators (ULAs). This both explains experimental results and paves the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04861","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":"2026-05-17T23:48:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lcyu/bM1MxGJYqnIH1UZPJL2viJNVwWzBUERdkc75ijg+1u8tQWxEF+K48qAtjp8oBtiT2rd7YjukQlsNVaQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:22:18.050177Z"},"content_sha256":"d14ad820e7cd6cce9292d5812b33f7cdee6309384ff066e649333989d05c08a4","schema_version":"1.0","event_id":"sha256:d14ad820e7cd6cce9292d5812b33f7cdee6309384ff066e649333989d05c08a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/bundle.json","state_url":"https://pith.science/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/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":"2026-06-28T20:22:18Z","links":{"resolver":"https://pith.science/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG","bundle":"https://pith.science/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/bundle.json","state":"https://pith.science/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZPLSPSUQLX2WDI2KNEJFJZQBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IZPLSPSUQLX2WDI2KNEJFJZQBG","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":"902c12ac857af0458cfc49d79da48212b5d19278bbe2c0b19e0e00e24e91a971","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-09T18:39:43Z","title_canon_sha256":"f136cc1f1549ec053abe252b472c2fbb2e15c6774e828db6b432e2db41846ab2"},"schema_version":"1.0","source":{"id":"1904.04861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04861","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04861v1","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04861","created_at":"2026-05-17T23:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"IZPLSPSUQLX2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IZPLSPSUQLX2WDI2","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IZPLSPSU","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:d14ad820e7cd6cce9292d5812b33f7cdee6309384ff066e649333989d05c08a4","target":"graph","created_at":"2026-05-17T23:48:57Z","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":"Adversarial attacks against machine learning models are a rather hefty obstacle to our increasing reliance on these models. Due to this, provably robust (certified) machine learning models are a major topic of interest. Lipschitz continuous models present a promising approach to solving this problem. By leveraging the expressive power of a variant of neural networks which maintain low Lipschitz constants, we prove that three layer neural networks using the FullSort activation function are Universal Lipschitz function Approximators (ULAs). This both explains experimental results and paves the w","authors_text":"Jeremy E.J. Cohen, Ra Cohen, Todd Huster","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-09T18:39:43Z","title":"Universal Lipschitz Approximation in Bounded Depth Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04861","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":"sha256:871ba65f9d9a7f49efe6b2ab159670a22c16bacbcc0fc9f196a93bb50d754db5","target":"record","created_at":"2026-05-17T23:48:57Z","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":"902c12ac857af0458cfc49d79da48212b5d19278bbe2c0b19e0e00e24e91a971","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-04-09T18:39:43Z","title_canon_sha256":"f136cc1f1549ec053abe252b472c2fbb2e15c6774e828db6b432e2db41846ab2"},"schema_version":"1.0","source":{"id":"1904.04861","kind":"arxiv","version":1}},"canonical_sha256":"465eb93e5482efab0d1a534892a730098307181e4148080e784d53b8adf70d52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"465eb93e5482efab0d1a534892a730098307181e4148080e784d53b8adf70d52","first_computed_at":"2026-05-17T23:48:57.803550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:57.803550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j8c+e1IDaGdO+j3DasUneI7377IFX5BrUjTgaotSsxGsrqLXzg7/pCpR4qr+9I8CTK16XaKj46HacwzDkl0wBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:57.804010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871ba65f9d9a7f49efe6b2ab159670a22c16bacbcc0fc9f196a93bb50d754db5","sha256:d14ad820e7cd6cce9292d5812b33f7cdee6309384ff066e649333989d05c08a4"],"state_sha256":"a4b58f45f46d34263b554034d8cb9f7c4189c9412961544133c9ffee4dd74e05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTqN2ZtSweqyJG4uey25Q242KRzgdPYiTpVyAhR+mEUFLVbSebdhIbpTALBLs9RKjwD3ehT6o27zOpwgs5+MBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T20:22:18.052770Z","bundle_sha256":"306f2bb8a7000762e10d398b185f139d052f81b641b96490c1b952bf9edd15e6"}}