{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OTIUTTCBQOZ3CZNAE4MZWLLWVS","short_pith_number":"pith:OTIUTTCB","schema_version":"1.0","canonical_sha256":"74d149cc4183b3b165a027199b2d76aca4b85edd157025da2378d7a5370dded2","source":{"kind":"arxiv","id":"1905.09245","version":1},"attestation_state":"computed","paper":{"title":"On the Restricted Isometry Property of Centered Self Khatri-Rao Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Fengler, Peter Jung","submitted_at":"2019-05-22T17:09:30Z","abstract_excerpt":"In this work we establish the Restricted Isometry Property (RIP) of the centered column-wise self Khatri-Rao (KR) products of $n\\times N$ matrix with iid columns drawn either uniformly from a sphere or with iid sub-Gaussian entries. The self KR product is an $n^2\\times N$-matrix which contains as columns the vectorized (self) outer products of the columns of the original $n\\times N$-matrix. Based on a result of Adamczak et al. we show that such a centered self KR product with independent heavy tailed columns has small RIP constants of order $s$ with probability at least $1-C\\exp(-cn)$ provided"},"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":"1905.09245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-22T17:09:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c6473944131e016e03d922d7b3228616b0a1b1532d9ac4c237188f36da35b7e7","abstract_canon_sha256":"5dfb312295f95da04599ccbe9372d281cb9ea58e8a06ec3ab46972893e3307b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:21.501619Z","signature_b64":"+oL9W4gD0dM1g2rGsdos+4qkXh+73VxaZyBbXMBIFKGd137uwC+IOSBypj/gq8PyVg0N8UXK1FLej/2OEcDcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74d149cc4183b3b165a027199b2d76aca4b85edd157025da2378d7a5370dded2","last_reissued_at":"2026-05-17T23:45:21.500960Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:21.500960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Restricted Isometry Property of Centered Self Khatri-Rao Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Fengler, Peter Jung","submitted_at":"2019-05-22T17:09:30Z","abstract_excerpt":"In this work we establish the Restricted Isometry Property (RIP) of the centered column-wise self Khatri-Rao (KR) products of $n\\times N$ matrix with iid columns drawn either uniformly from a sphere or with iid sub-Gaussian entries. The self KR product is an $n^2\\times N$-matrix which contains as columns the vectorized (self) outer products of the columns of the original $n\\times N$-matrix. Based on a result of Adamczak et al. we show that such a centered self KR product with independent heavy tailed columns has small RIP constants of order $s$ with probability at least $1-C\\exp(-cn)$ provided"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09245","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":"1905.09245","created_at":"2026-05-17T23:45:21.501043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.09245v1","created_at":"2026-05-17T23:45:21.501043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09245","created_at":"2026-05-17T23:45:21.501043+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTIUTTCBQOZ3","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTIUTTCBQOZ3CZNA","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTIUTTCB","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.23556","citing_title":"Is Dimensionality a Barrier for Retrieval Models?","ref_index":88,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS","json":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS.json","graph_json":"https://pith.science/api/pith-number/OTIUTTCBQOZ3CZNAE4MZWLLWVS/graph.json","events_json":"https://pith.science/api/pith-number/OTIUTTCBQOZ3CZNAE4MZWLLWVS/events.json","paper":"https://pith.science/paper/OTIUTTCB"},"agent_actions":{"view_html":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS","download_json":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS.json","view_paper":"https://pith.science/paper/OTIUTTCB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.09245&json=true","fetch_graph":"https://pith.science/api/pith-number/OTIUTTCBQOZ3CZNAE4MZWLLWVS/graph.json","fetch_events":"https://pith.science/api/pith-number/OTIUTTCBQOZ3CZNAE4MZWLLWVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS/action/storage_attestation","attest_author":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS/action/author_attestation","sign_citation":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS/action/citation_signature","submit_replication":"https://pith.science/pith/OTIUTTCBQOZ3CZNAE4MZWLLWVS/action/replication_record"}},"created_at":"2026-05-17T23:45:21.501043+00:00","updated_at":"2026-05-17T23:45:21.501043+00:00"}