{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:35SMIH5WVR3GLVGVAVTOP3PNMM","short_pith_number":"pith:35SMIH5W","schema_version":"1.0","canonical_sha256":"df64c41fb6ac7665d4d50566e7eded6315588e081a1e30aad0de1230b29b1251","source":{"kind":"arxiv","id":"2605.22666","version":1},"attestation_state":"computed","paper":{"title":"Holographic functions and neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"math.CO","authors_text":"Balazs Szegedy","submitted_at":"2026-05-21T16:08:52Z","abstract_excerpt":"A fuzzy Boolean function is a map $f:\\cube^n\\to [0,1]$, where $n\\in\\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered, up to small error and with high probability, from the values of a bounded number of randomly chosen coordinates of $x$. We call this the holographic property. The second is a structural property: $f$ is uniformly close to a bounded-degree polynomial in boundedly many bounded linear coordinate forms. The third is computational: $f$ is uniformly close to the ou"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.22666","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T16:08:52Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"0f552a1c771f36da19a982e2ef980de35cc0eb51974fd8dada05ccbcf2ca436b","abstract_canon_sha256":"7ddf3a87663d617c380777729314ec9f1344c72ef20356dc95c45b619b90fcfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:49.216471Z","signature_b64":"LC/rQOoFrz+mcv3Mq6lncHaBMId2PY9/BK4SkHiVFlvSXNqqIBjAb+s3T9FOJDHmqKCqouPAqHOrh8UWRELIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df64c41fb6ac7665d4d50566e7eded6315588e081a1e30aad0de1230b29b1251","last_reissued_at":"2026-05-22T02:04:49.215376Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:49.215376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holographic functions and neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"math.CO","authors_text":"Balazs Szegedy","submitted_at":"2026-05-21T16:08:52Z","abstract_excerpt":"A fuzzy Boolean function is a map $f:\\cube^n\\to [0,1]$, where $n\\in\\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered, up to small error and with high probability, from the values of a bounded number of randomly chosen coordinates of $x$. We call this the holographic property. The second is a structural property: $f$ is uniformly close to a bounded-degree polynomial in boundedly many bounded linear coordinate forms. The third is computational: $f$ is uniformly close to the ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22666","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/2605.22666/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.22666","created_at":"2026-05-22T02:04:49.215552+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.22666v1","created_at":"2026-05-22T02:04:49.215552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22666","created_at":"2026-05-22T02:04:49.215552+00:00"},{"alias_kind":"pith_short_12","alias_value":"35SMIH5WVR3G","created_at":"2026-05-22T02:04:49.215552+00:00"},{"alias_kind":"pith_short_16","alias_value":"35SMIH5WVR3GLVGV","created_at":"2026-05-22T02:04:49.215552+00:00"},{"alias_kind":"pith_short_8","alias_value":"35SMIH5W","created_at":"2026-05-22T02:04:49.215552+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM","json":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM.json","graph_json":"https://pith.science/api/pith-number/35SMIH5WVR3GLVGVAVTOP3PNMM/graph.json","events_json":"https://pith.science/api/pith-number/35SMIH5WVR3GLVGVAVTOP3PNMM/events.json","paper":"https://pith.science/paper/35SMIH5W"},"agent_actions":{"view_html":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM","download_json":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM.json","view_paper":"https://pith.science/paper/35SMIH5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.22666&json=true","fetch_graph":"https://pith.science/api/pith-number/35SMIH5WVR3GLVGVAVTOP3PNMM/graph.json","fetch_events":"https://pith.science/api/pith-number/35SMIH5WVR3GLVGVAVTOP3PNMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM/action/storage_attestation","attest_author":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM/action/author_attestation","sign_citation":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM/action/citation_signature","submit_replication":"https://pith.science/pith/35SMIH5WVR3GLVGVAVTOP3PNMM/action/replication_record"}},"created_at":"2026-05-22T02:04:49.215552+00:00","updated_at":"2026-05-22T02:04:49.215552+00:00"}