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This implies that the functional dimension of every such architecture is exactly the number of parameters minus the number of hidden neurons.","weakest_assumption":"The assumption that the architecture has input and hidden layer widths at least two; the result is stated only for open sets of parameters and does not claim identifiability for every parameter vector."}},"verdict_id":"b8222945-9e03-48bf-a14c-ee97883a465a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:01be2a18a1de66f1395b8d6f5c9dff6bc12cbcb07003d864d8caabf83b1ea930","target":"record","created_at":"2026-05-21T01:04:26Z","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":"e1b1a8bd998b8122674b64d1b2627b4781114aa017e7d3ea2b12b63cc0042308","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-05T10:25:28Z","title_canon_sha256":"8d8de95237a580c8e2cc2a2929b8bfbaf69d3c1624b9d6c310908c60cdca5d60"},"schema_version":"1.0","source":{"id":"2605.03601","kind":"arxiv","version":2}},"canonical_sha256":"f5933bb4f40a52e53dbde879a30d1017c7edc2e69231f152d426bace7d206a21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5933bb4f40a52e53dbde879a30d1017c7edc2e69231f152d426bace7d206a21","first_computed_at":"2026-05-21T01:04:26.728429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:26.728429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZSHZwDaQs3n4D6sRIx408vs547YkY38Tas7Fs9+ibXugt1bnVEzaiUt93f9p/snV6D2H1euzLsC2xul73G+DQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:26.728920Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.03601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d5c466b22fdec32efadccf2150c8ee33a478f2592e779060064a52d7caceb7f","sha256:01be2a18a1de66f1395b8d6f5c9dff6bc12cbcb07003d864d8caabf83b1ea930","sha256:40300ddc9e03a8fa2eb3af0ca59dc9166ee85a2d70447437515698141083191a"],"state_sha256":"f0066de20094ae31aeb5cf07519cb906adc868a84592e151888d5622fd389790"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erANRZo6rtKS1w4VJWTPgaYLGuTfVLRgBxtyEo78+E9ysFJOl4iRzDkx/eumrNdlJ1bMDSPMwaBuFC/t8MBdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:08:38.432575Z","bundle_sha256":"f7aabf73efb9df8b11d1d63e0cb8834368a1988daee5dd93b1853c64a983e56a"}}