{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:I25XI6JH3KRMJMOT76XMXUHCSK","short_pith_number":"pith:I25XI6JH","canonical_record":{"source":{"id":"2102.02631","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-04T14:30:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"e8ce0a99e856cecacd2fec082a06fb3feff8339beed00293fe07be395ab7cf3e","abstract_canon_sha256":"64236772433a87fefc214a4c91006596f5f3bf82fbf92a94f40d9c3ac4e1492d"},"schema_version":"1.0"},"canonical_sha256":"46bb747927daa2c4b1d3ffaecbd0e292b73ed3cb2dfdbb7653227a9de4c6a0bc","source":{"kind":"arxiv","id":"2102.02631","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.02631","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"arxiv_version","alias_value":"2102.02631v1","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.02631","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_12","alias_value":"I25XI6JH3KRM","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_16","alias_value":"I25XI6JH3KRMJMOT","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_8","alias_value":"I25XI6JH","created_at":"2026-07-05T02:12:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:I25XI6JH3KRMJMOT76XMXUHCSK","target":"record","payload":{"canonical_record":{"source":{"id":"2102.02631","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-04T14:30:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"e8ce0a99e856cecacd2fec082a06fb3feff8339beed00293fe07be395ab7cf3e","abstract_canon_sha256":"64236772433a87fefc214a4c91006596f5f3bf82fbf92a94f40d9c3ac4e1492d"},"schema_version":"1.0"},"canonical_sha256":"46bb747927daa2c4b1d3ffaecbd0e292b73ed3cb2dfdbb7653227a9de4c6a0bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:12:50.133031Z","signature_b64":"0acAmSlY5RDuYFHCHE1k4xxigW45x+qIBwCV9zlKMqw+yk1tCtm8NYjn46inwc/POZ+3Z/B7RWcrZboA10Y4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46bb747927daa2c4b1d3ffaecbd0e292b73ed3cb2dfdbb7653227a9de4c6a0bc","last_reissued_at":"2026-07-05T02:12:50.132532Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:12:50.132532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.02631","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":"2026-07-05T02:12:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCyGTXJ6+EbWtjsz19pDpIgEdsoy9J3252NkbVIr6b53C3ox38j7YipUMO5d7hg3w1+pxax9987ZvisExNBkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:13:57.740078Z"},"content_sha256":"e81001d86537c720d60b31e5071570f3aa9923066227b2edf2c8ce97f5884d73","schema_version":"1.0","event_id":"sha256:e81001d86537c720d60b31e5071570f3aa9923066227b2edf2c8ce97f5884d73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:I25XI6JH3KRMJMOT76XMXUHCSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Approximation Theorems of Fully Connected Binarized Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Burim Ramosaj, Jian-Jia Chen, Mario G\\\"unzel, Mikail Yayla","submitted_at":"2021-02-04T14:30:24Z","abstract_excerpt":"Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized Neural Networks (BNNs) significantly reduce time and memory demands by restricting the weight and activation domains to two values. Despite the practical advantages, theoretical guarantees based on UA theorems of BNNs are rather sparse in the literature. We close this gap by providing UA theorems for fully connected BNNs under the following scenarios: (1) for bin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.02631","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.02631/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":"2026-07-05T02:12:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rNqPoJtVF3TNT8U3cXHCtgmDv51qEqEP39t7sFbjgPn3SBN7ZWayZO9RFTS8Ba6cDjNXwHhul9VGZl+hgbXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:13:57.740589Z"},"content_sha256":"c865d46a2de1c78b1e4dbd01d3f85b9e2e8ebbfd4e819bcc77b95a8715013260","schema_version":"1.0","event_id":"sha256:c865d46a2de1c78b1e4dbd01d3f85b9e2e8ebbfd4e819bcc77b95a8715013260"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I25XI6JH3KRMJMOT76XMXUHCSK/bundle.json","state_url":"https://pith.science/pith/I25XI6JH3KRMJMOT76XMXUHCSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I25XI6JH3KRMJMOT76XMXUHCSK/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":"2026-08-05T09:13:57Z","links":{"resolver":"https://pith.science/pith/I25XI6JH3KRMJMOT76XMXUHCSK","bundle":"https://pith.science/pith/I25XI6JH3KRMJMOT76XMXUHCSK/bundle.json","state":"https://pith.science/pith/I25XI6JH3KRMJMOT76XMXUHCSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I25XI6JH3KRMJMOT76XMXUHCSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:I25XI6JH3KRMJMOT76XMXUHCSK","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":"64236772433a87fefc214a4c91006596f5f3bf82fbf92a94f40d9c3ac4e1492d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-04T14:30:24Z","title_canon_sha256":"e8ce0a99e856cecacd2fec082a06fb3feff8339beed00293fe07be395ab7cf3e"},"schema_version":"1.0","source":{"id":"2102.02631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.02631","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"arxiv_version","alias_value":"2102.02631v1","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.02631","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_12","alias_value":"I25XI6JH3KRM","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_16","alias_value":"I25XI6JH3KRMJMOT","created_at":"2026-07-05T02:12:50Z"},{"alias_kind":"pith_short_8","alias_value":"I25XI6JH","created_at":"2026-07-05T02:12:50Z"}],"graph_snapshots":[{"event_id":"sha256:c865d46a2de1c78b1e4dbd01d3f85b9e2e8ebbfd4e819bcc77b95a8715013260","target":"graph","created_at":"2026-07-05T02:12:50Z","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/2102.02631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized Neural Networks (BNNs) significantly reduce time and memory demands by restricting the weight and activation domains to two values. Despite the practical advantages, theoretical guarantees based on UA theorems of BNNs are rather sparse in the literature. We close this gap by providing UA theorems for fully connected BNNs under the following scenarios: (1) for bin","authors_text":"Burim Ramosaj, Jian-Jia Chen, Mario G\\\"unzel, Mikail Yayla","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-04T14:30:24Z","title":"Universal Approximation Theorems of Fully Connected Binarized Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.02631","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:e81001d86537c720d60b31e5071570f3aa9923066227b2edf2c8ce97f5884d73","target":"record","created_at":"2026-07-05T02:12:50Z","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":"64236772433a87fefc214a4c91006596f5f3bf82fbf92a94f40d9c3ac4e1492d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-04T14:30:24Z","title_canon_sha256":"e8ce0a99e856cecacd2fec082a06fb3feff8339beed00293fe07be395ab7cf3e"},"schema_version":"1.0","source":{"id":"2102.02631","kind":"arxiv","version":1}},"canonical_sha256":"46bb747927daa2c4b1d3ffaecbd0e292b73ed3cb2dfdbb7653227a9de4c6a0bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46bb747927daa2c4b1d3ffaecbd0e292b73ed3cb2dfdbb7653227a9de4c6a0bc","first_computed_at":"2026-07-05T02:12:50.132532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:12:50.132532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0acAmSlY5RDuYFHCHE1k4xxigW45x+qIBwCV9zlKMqw+yk1tCtm8NYjn46inwc/POZ+3Z/B7RWcrZboA10Y4AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:12:50.133031Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.02631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e81001d86537c720d60b31e5071570f3aa9923066227b2edf2c8ce97f5884d73","sha256:c865d46a2de1c78b1e4dbd01d3f85b9e2e8ebbfd4e819bcc77b95a8715013260"],"state_sha256":"ae0068b4485d1d2b02fa14b67d25c5bf49be04843c797d3df60f0214a3e66442"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNbEvtDmsZmDmnJno3qp5bMPc7HQthw8EI4n7wDtKV3kTMp7SKkaJ0e7aVQShnn48gnVSOoA83yOEYuAbQI6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T09:13:57.745825Z","bundle_sha256":"9a5da55bfc2837d89fc9e64e81d4c5212ea9c2dafc6c9f863afc29eea4cbb712"}}