{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:664OGVQJZXKQLLFAZJWEMQNXBW","short_pith_number":"pith:664OGVQJ","canonical_record":{"source":{"id":"1910.06956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-15T17:52:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"447918c314960a454875437ce1a807a129209085101e4085b2e2f93983dada66","abstract_canon_sha256":"e9b74c773601851bb9463c003883b935d5180f3f90461c07a2279b22dcd8829d"},"schema_version":"1.0"},"canonical_sha256":"f7b8e35609cdd505aca0ca6c4641b70d9bac56a3f1f4f99cfb28fbe1e129cf0d","source":{"kind":"arxiv","id":"1910.06956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.06956","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"arxiv_version","alias_value":"1910.06956v2","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.06956","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_12","alias_value":"664OGVQJZXKQ","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_16","alias_value":"664OGVQJZXKQLLFA","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_8","alias_value":"664OGVQJ","created_at":"2026-07-05T00:40:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:664OGVQJZXKQLLFAZJWEMQNXBW","target":"record","payload":{"canonical_record":{"source":{"id":"1910.06956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-15T17:52:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"447918c314960a454875437ce1a807a129209085101e4085b2e2f93983dada66","abstract_canon_sha256":"e9b74c773601851bb9463c003883b935d5180f3f90461c07a2279b22dcd8829d"},"schema_version":"1.0"},"canonical_sha256":"f7b8e35609cdd505aca0ca6c4641b70d9bac56a3f1f4f99cfb28fbe1e129cf0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:40:59.514711Z","signature_b64":"VsI2g9NuNeXACQFfx0TFge1Lejyom5HrlxNgnKhd1fLDjybkRJNvbmjMdGtDxJ3AbTFNRgN0/aw0zz+m2fR1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7b8e35609cdd505aca0ca6c4641b70d9bac56a3f1f4f99cfb28fbe1e129cf0d","last_reissued_at":"2026-07-05T00:40:59.514224Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:40:59.514224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.06956","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":"2026-07-05T00:40:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsxyJtnHULgZasGS3+N7kIax9jm1MIlQpxLIJe9DGvGyTns6Dr9fmO6P/vwfghTVuck6y8rpGkmWtwTg29cLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:15:14.762659Z"},"content_sha256":"272dc536b94c376bd1980c4bcef6f0a73d83c91bde9dd2e82b7ad6d97ab0ee49","schema_version":"1.0","event_id":"sha256:272dc536b94c376bd1980c4bcef6f0a73d83c91bde9dd2e82b7ad6d97ab0ee49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:664OGVQJZXKQLLFAZJWEMQNXBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neural tangent kernels, transportation mappings, and universal approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Matus Telgarsky, Ruicheng Xian, Ziwei Ji","submitted_at":"2019-10-15T17:52:49Z","abstract_excerpt":"This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.06956","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/1910.06956/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":"2026-07-05T00:40:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mmzWK305e7E0jlri8UEJ0zztQQwJ7fSlBQ4VTX4mSMG8iVPih4q0JPbDTgZMTcAwJ2R+X9LNhPnFyCu3DBmVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:15:14.763161Z"},"content_sha256":"29f79064ab2a0cbe62a406e9d918ed635a3b2dc094cfcb5b7eddebc4ae6f6b39","schema_version":"1.0","event_id":"sha256:29f79064ab2a0cbe62a406e9d918ed635a3b2dc094cfcb5b7eddebc4ae6f6b39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/664OGVQJZXKQLLFAZJWEMQNXBW/bundle.json","state_url":"https://pith.science/pith/664OGVQJZXKQLLFAZJWEMQNXBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/664OGVQJZXKQLLFAZJWEMQNXBW/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":"2026-08-05T20:15:14Z","links":{"resolver":"https://pith.science/pith/664OGVQJZXKQLLFAZJWEMQNXBW","bundle":"https://pith.science/pith/664OGVQJZXKQLLFAZJWEMQNXBW/bundle.json","state":"https://pith.science/pith/664OGVQJZXKQLLFAZJWEMQNXBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/664OGVQJZXKQLLFAZJWEMQNXBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:664OGVQJZXKQLLFAZJWEMQNXBW","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":"e9b74c773601851bb9463c003883b935d5180f3f90461c07a2279b22dcd8829d","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-15T17:52:49Z","title_canon_sha256":"447918c314960a454875437ce1a807a129209085101e4085b2e2f93983dada66"},"schema_version":"1.0","source":{"id":"1910.06956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.06956","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"arxiv_version","alias_value":"1910.06956v2","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.06956","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_12","alias_value":"664OGVQJZXKQ","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_16","alias_value":"664OGVQJZXKQLLFA","created_at":"2026-07-05T00:40:59Z"},{"alias_kind":"pith_short_8","alias_value":"664OGVQJ","created_at":"2026-07-05T00:40:59Z"}],"graph_snapshots":[{"event_id":"sha256:29f79064ab2a0cbe62a406e9d918ed635a3b2dc094cfcb5b7eddebc4ae6f6b39","target":"graph","created_at":"2026-07-05T00:40:59Z","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/1910.06956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof ","authors_text":"Matus Telgarsky, Ruicheng Xian, Ziwei Ji","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-15T17:52:49Z","title":"Neural tangent kernels, transportation mappings, and universal approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.06956","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":"sha256:272dc536b94c376bd1980c4bcef6f0a73d83c91bde9dd2e82b7ad6d97ab0ee49","target":"record","created_at":"2026-07-05T00:40:59Z","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":"e9b74c773601851bb9463c003883b935d5180f3f90461c07a2279b22dcd8829d","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-15T17:52:49Z","title_canon_sha256":"447918c314960a454875437ce1a807a129209085101e4085b2e2f93983dada66"},"schema_version":"1.0","source":{"id":"1910.06956","kind":"arxiv","version":2}},"canonical_sha256":"f7b8e35609cdd505aca0ca6c4641b70d9bac56a3f1f4f99cfb28fbe1e129cf0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7b8e35609cdd505aca0ca6c4641b70d9bac56a3f1f4f99cfb28fbe1e129cf0d","first_computed_at":"2026-07-05T00:40:59.514224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:40:59.514224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VsI2g9NuNeXACQFfx0TFge1Lejyom5HrlxNgnKhd1fLDjybkRJNvbmjMdGtDxJ3AbTFNRgN0/aw0zz+m2fR1Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:40:59.514711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.06956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:272dc536b94c376bd1980c4bcef6f0a73d83c91bde9dd2e82b7ad6d97ab0ee49","sha256:29f79064ab2a0cbe62a406e9d918ed635a3b2dc094cfcb5b7eddebc4ae6f6b39"],"state_sha256":"c9c32327e08224b065a6e895a262627f73ce4521ab9eb0628e367ce8980237a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHh9uyUD5eSZvl3R3rSwXD1PlheOPWWqx1uKSNhsnwmKjyjEvh4dQe9n3bZ17R05gZ1kuPpzXp8aOQNnnUkoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T20:15:14.768705Z","bundle_sha256":"8ba099c9bbfcd972ea6804f0aff406504a9a7d6fd31d800867c64e438f8f422b"}}