{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7L6MP7OOH26ESGJPYUQ2DT35K2","short_pith_number":"pith:7L6MP7OO","schema_version":"1.0","canonical_sha256":"fafcc7fdce3ebc49192fc521a1cf7d56ac494dc0aabe44bdf229ba3f9efeb1ce","source":{"kind":"arxiv","id":"1907.01942","version":1},"attestation_state":"computed","paper":{"title":"Mean Dimension of Ridge Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.CO"],"primary_cat":"math.NA","authors_text":"Art B. Owen, Christopher R. Hoyt","submitted_at":"2019-07-01T19:01:56Z","abstract_excerpt":"We consider the mean dimension of some ridge functions of spherical Gaussian random vectors of dimension $d$. If the ridge function is Lipschitz continuous, then the mean dimension remains bounded as $d\\to\\infty$. If instead, the ridge function is discontinuous, then the mean dimension depends on a measure of the ridge function's sparsity, and absent sparsity the mean dimension can grow proportionally to $\\sqrt{d}$. Preintegrating a ridge function yields a new, potentially much smoother ridge function. We include an example where, if one of the ridge coefficients is bounded away from zero as $"},"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":"1907.01942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-01T19:01:56Z","cross_cats_sorted":["cs.NA","stat.CO"],"title_canon_sha256":"b49ad58fe68052ef0ec09e2fc00383d73bad7ea3867e71404de34197fd01cc3a","abstract_canon_sha256":"8b9801a21c0efec7f99d1b61fd4f347aff5c73b2210f23f661f3d8e6c092dd03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.442414Z","signature_b64":"W67lA53FgDVcrXIOvLkuRYdiQQApyuyWlUef4KCW1Rtq4SeCBE9zvn4cyAfJXOfPvCsc09Cu7+LeGpK967eCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fafcc7fdce3ebc49192fc521a1cf7d56ac494dc0aabe44bdf229ba3f9efeb1ce","last_reissued_at":"2026-05-17T23:41:34.441860Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.441860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean Dimension of Ridge Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.CO"],"primary_cat":"math.NA","authors_text":"Art B. Owen, Christopher R. Hoyt","submitted_at":"2019-07-01T19:01:56Z","abstract_excerpt":"We consider the mean dimension of some ridge functions of spherical Gaussian random vectors of dimension $d$. If the ridge function is Lipschitz continuous, then the mean dimension remains bounded as $d\\to\\infty$. If instead, the ridge function is discontinuous, then the mean dimension depends on a measure of the ridge function's sparsity, and absent sparsity the mean dimension can grow proportionally to $\\sqrt{d}$. Preintegrating a ridge function yields a new, potentially much smoother ridge function. We include an example where, if one of the ridge coefficients is bounded away from zero as $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01942","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.01942","created_at":"2026-05-17T23:41:34.441952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01942v1","created_at":"2026-05-17T23:41:34.441952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01942","created_at":"2026-05-17T23:41:34.441952+00:00"},{"alias_kind":"pith_short_12","alias_value":"7L6MP7OOH26E","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7L6MP7OOH26ESGJP","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7L6MP7OO","created_at":"2026-05-18T12:33:12.712433+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/7L6MP7OOH26ESGJPYUQ2DT35K2","json":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2.json","graph_json":"https://pith.science/api/pith-number/7L6MP7OOH26ESGJPYUQ2DT35K2/graph.json","events_json":"https://pith.science/api/pith-number/7L6MP7OOH26ESGJPYUQ2DT35K2/events.json","paper":"https://pith.science/paper/7L6MP7OO"},"agent_actions":{"view_html":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2","download_json":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2.json","view_paper":"https://pith.science/paper/7L6MP7OO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01942&json=true","fetch_graph":"https://pith.science/api/pith-number/7L6MP7OOH26ESGJPYUQ2DT35K2/graph.json","fetch_events":"https://pith.science/api/pith-number/7L6MP7OOH26ESGJPYUQ2DT35K2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2/action/storage_attestation","attest_author":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2/action/author_attestation","sign_citation":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2/action/citation_signature","submit_replication":"https://pith.science/pith/7L6MP7OOH26ESGJPYUQ2DT35K2/action/replication_record"}},"created_at":"2026-05-17T23:41:34.441952+00:00","updated_at":"2026-05-17T23:41:34.441952+00:00"}