{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:D2ZMRA6R5OBKL5TLNV4KFRXD2K","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":"21d501435dd9c9120c698f371d52e71e6a72eb09eca38e8f85b7d5cef5911dc5","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-17T13:21:53Z","title_canon_sha256":"e084363496860cfd501ba33fffb3dd16d653b15582e86fa8d687105860480e23"},"schema_version":"1.0","source":{"id":"2407.12895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.12895","created_at":"2026-07-05T08:45:13Z"},{"alias_kind":"arxiv_version","alias_value":"2407.12895v1","created_at":"2026-07-05T08:45:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12895","created_at":"2026-07-05T08:45:13Z"},{"alias_kind":"pith_short_12","alias_value":"D2ZMRA6R5OBK","created_at":"2026-07-05T08:45:13Z"},{"alias_kind":"pith_short_16","alias_value":"D2ZMRA6R5OBKL5TL","created_at":"2026-07-05T08:45:13Z"},{"alias_kind":"pith_short_8","alias_value":"D2ZMRA6R","created_at":"2026-07-05T08:45:13Z"}],"graph_snapshots":[{"event_id":"sha256:9332a55ed071bcf5449b367708dd568a6883386f153532df69793a9906a0d6f7","target":"graph","created_at":"2026-07-05T08:45:13Z","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/2407.12895/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper discusses various theorems on the approximation capabilities of neural networks (NNs), which are known as universal approximation theorems (UATs). The paper gives a systematic overview of UATs starting from the preliminary results on function approximation, such as Taylor's theorem, Fourier's theorem, Weierstrass approximation theorem, Kolmogorov - Arnold representation theorem, etc. Theoretical and numerical aspects of UATs are covered from both arbitrary width and depth.","authors_text":"Midhun T Augustine","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-17T13:21:53Z","title":"A Survey on Universal Approximation Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12895","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":"sha256:6858964bdfc81b691fb39ee0b3c7abd53d9d1f2b219e57266a727753a55cae4b","target":"record","created_at":"2026-07-05T08:45:13Z","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":"21d501435dd9c9120c698f371d52e71e6a72eb09eca38e8f85b7d5cef5911dc5","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-17T13:21:53Z","title_canon_sha256":"e084363496860cfd501ba33fffb3dd16d653b15582e86fa8d687105860480e23"},"schema_version":"1.0","source":{"id":"2407.12895","kind":"arxiv","version":1}},"canonical_sha256":"1eb2c883d1eb82a5f66b6d78a2c6e3d2bf1cd80efa27a7240c4de7d87b8eaee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eb2c883d1eb82a5f66b6d78a2c6e3d2bf1cd80efa27a7240c4de7d87b8eaee4","first_computed_at":"2026-07-05T08:45:13.295592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:45:13.295592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SilwHvS8V7SeCpkVKYr0D1Y4APNz21rKN5UHguNrtpLITlGLBiNRaxNonmDBPq38yBTsLDK7Q22ftG6bZRz7DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:45:13.296055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.12895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6858964bdfc81b691fb39ee0b3c7abd53d9d1f2b219e57266a727753a55cae4b","sha256:9332a55ed071bcf5449b367708dd568a6883386f153532df69793a9906a0d6f7"],"state_sha256":"9fbb728529d30d86c2fd16e7cd2b6649cc2460d84c117f7e982db0c25c849c51"}