{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L3MHAOWA33WJXQIVCN2Q26PB73","short_pith_number":"pith:L3MHAOWA","canonical_record":{"source":{"id":"1810.00393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-30T14:55:41Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"5132a6d0b913b1d7be0505c25f9963c064ed1479db075369045d42f08ad5d24f","abstract_canon_sha256":"5e161991e583ca97a8da6bca408b5fd374433b454664c8372656d2330937e518"},"schema_version":"1.0"},"canonical_sha256":"5ed8703ac0deec9bc11513750d79e1fee115e675f3d5befbe6ea21a256986522","source":{"kind":"arxiv","id":"1810.00393","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00393","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00393v1","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00393","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"L3MHAOWA33WJ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L3MHAOWA33WJXQIV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L3MHAOWA","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L3MHAOWA33WJXQIVCN2Q26PB73","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-30T14:55:41Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"5132a6d0b913b1d7be0505c25f9963c064ed1479db075369045d42f08ad5d24f","abstract_canon_sha256":"5e161991e583ca97a8da6bca408b5fd374433b454664c8372656d2330937e518"},"schema_version":"1.0"},"canonical_sha256":"5ed8703ac0deec9bc11513750d79e1fee115e675f3d5befbe6ea21a256986522","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:27.995231Z","signature_b64":"PctUy/ShcMb6aqsfYVfzKrcvmPAOO3x484YM8BoOw0ooT+23lVK5GR4vGEmPPUgTBRoM2JGbUWSuU8cxAnKBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ed8703ac0deec9bc11513750d79e1fee115e675f3d5befbe6ea21a256986522","last_reissued_at":"2026-05-18T00:04:27.994773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:27.994773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00393","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":"2026-05-18T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7nOoNLJ5cn76OO0Bbd/nIgn+DCECUyTeoCjv3OTWngYd6or3/nRXUVwfjkdPKIseW95fuKCzJedu6wBJ3FPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:56:19.501263Z"},"content_sha256":"028db6857e1ccec6fccb7d9e834918266aca45bb94bbcaeaf244734812a2d8e7","schema_version":"1.0","event_id":"sha256:028db6857e1ccec6fccb7d9e834918266aca45bb94bbcaeaf244734812a2d8e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L3MHAOWA33WJXQIVCN2Q26PB73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deep, Skinny Neural Networks are not Universal Approximators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Jesse Johnson","submitted_at":"2018-09-30T14:55:41Z","abstract_excerpt":"In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of information theoretic bounds, or by comparing the relative complexity needed to approximate example functions between different architectures. In this paper, we examine the topological constraints that the architecture of a neural network imposes on the level sets of all the functions that it is able to approximate. This approach is novel for both the nature "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00393","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":"2026-05-18T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKThnvo51JnHpQbCllzx3fgmo7Nd20lusgJ9o5iuAYaw6PSdY0uOS6SuzfprzejpNgOExfgRhXypuG9AwPA9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:56:19.501623Z"},"content_sha256":"26de572e9e86160d9325f36d9023c96bcb6e7fbfe9cc26367a37131a52162759","schema_version":"1.0","event_id":"sha256:26de572e9e86160d9325f36d9023c96bcb6e7fbfe9cc26367a37131a52162759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3MHAOWA33WJXQIVCN2Q26PB73/bundle.json","state_url":"https://pith.science/pith/L3MHAOWA33WJXQIVCN2Q26PB73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3MHAOWA33WJXQIVCN2Q26PB73/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":"2026-06-01T06:56:19Z","links":{"resolver":"https://pith.science/pith/L3MHAOWA33WJXQIVCN2Q26PB73","bundle":"https://pith.science/pith/L3MHAOWA33WJXQIVCN2Q26PB73/bundle.json","state":"https://pith.science/pith/L3MHAOWA33WJXQIVCN2Q26PB73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3MHAOWA33WJXQIVCN2Q26PB73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L3MHAOWA33WJXQIVCN2Q26PB73","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":"5e161991e583ca97a8da6bca408b5fd374433b454664c8372656d2330937e518","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-30T14:55:41Z","title_canon_sha256":"5132a6d0b913b1d7be0505c25f9963c064ed1479db075369045d42f08ad5d24f"},"schema_version":"1.0","source":{"id":"1810.00393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00393","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00393v1","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00393","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"L3MHAOWA33WJ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L3MHAOWA33WJXQIV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L3MHAOWA","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:26de572e9e86160d9325f36d9023c96bcb6e7fbfe9cc26367a37131a52162759","target":"graph","created_at":"2026-05-18T00:04:27Z","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":"In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of information theoretic bounds, or by comparing the relative complexity needed to approximate example functions between different architectures. In this paper, we examine the topological constraints that the architecture of a neural network imposes on the level sets of all the functions that it is able to approximate. This approach is novel for both the nature ","authors_text":"Jesse Johnson","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-30T14:55:41Z","title":"Deep, Skinny Neural Networks are not Universal Approximators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00393","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":"sha256:028db6857e1ccec6fccb7d9e834918266aca45bb94bbcaeaf244734812a2d8e7","target":"record","created_at":"2026-05-18T00:04:27Z","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":"5e161991e583ca97a8da6bca408b5fd374433b454664c8372656d2330937e518","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-30T14:55:41Z","title_canon_sha256":"5132a6d0b913b1d7be0505c25f9963c064ed1479db075369045d42f08ad5d24f"},"schema_version":"1.0","source":{"id":"1810.00393","kind":"arxiv","version":1}},"canonical_sha256":"5ed8703ac0deec9bc11513750d79e1fee115e675f3d5befbe6ea21a256986522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed8703ac0deec9bc11513750d79e1fee115e675f3d5befbe6ea21a256986522","first_computed_at":"2026-05-18T00:04:27.994773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:27.994773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PctUy/ShcMb6aqsfYVfzKrcvmPAOO3x484YM8BoOw0ooT+23lVK5GR4vGEmPPUgTBRoM2JGbUWSuU8cxAnKBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:27.995231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:028db6857e1ccec6fccb7d9e834918266aca45bb94bbcaeaf244734812a2d8e7","sha256:26de572e9e86160d9325f36d9023c96bcb6e7fbfe9cc26367a37131a52162759"],"state_sha256":"dc880b3c3f84f41c6c2a27b6916aeb2ba1ea533e538092522ebc7c7864838ba0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i97I0UD00z9M/EPhzuq74C3MUee8HaGshmbJyyKFm7ftSR/mfB9xy7oJO7Cwpig5fDsLVcvq3AsYj1a8p9fWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:56:19.503532Z","bundle_sha256":"91ba9d3ed6a03be44b6643651b066df627fad0d0abae985c61af8c86533bd413"}}