{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PEOPSQ43A4XKNYMTD4IQIH3BOX","short_pith_number":"pith:PEOPSQ43","schema_version":"1.0","canonical_sha256":"791cf9439b072ea6e1931f11041f6175ed366ddec166b691f1b1afc8698b06d0","source":{"kind":"arxiv","id":"1410.0780","version":3},"attestation_state":"computed","paper":{"title":"Small ball estimates for quasi-norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ohad Giladi, Olivier Gu\\'edon, Omer Friedland","submitted_at":"2014-10-03T08:41:46Z","abstract_excerpt":"This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained by Friedland and Sodin and by Rudelson and Vershynin."},"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":"1410.0780","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-03T08:41:46Z","cross_cats_sorted":[],"title_canon_sha256":"58fd81fca96ea2f6fbb628750187896663d3331f1ee660d6cdf07bb59f6fad73","abstract_canon_sha256":"83b726c5d5866611cf0c6cdbcefa41b9a7b566337908cad12b8e8e1a2dd55853"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:11.175457Z","signature_b64":"b37g+H/jYF4g+YS2TXXNGd/g2old1iMu1XyrFRAdHsDIRwQTyWkE1uvfgsuxXMzlUFuClFJilCKEWaYtuOp+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"791cf9439b072ea6e1931f11041f6175ed366ddec166b691f1b1afc8698b06d0","last_reissued_at":"2026-05-18T01:36:11.174745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:11.174745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small ball estimates for quasi-norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ohad Giladi, Olivier Gu\\'edon, Omer Friedland","submitted_at":"2014-10-03T08:41:46Z","abstract_excerpt":"This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained by Friedland and Sodin and by Rudelson and Vershynin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0780","kind":"arxiv","version":3},"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":"1410.0780","created_at":"2026-05-18T01:36:11.174855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.0780v3","created_at":"2026-05-18T01:36:11.174855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0780","created_at":"2026-05-18T01:36:11.174855+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEOPSQ43A4XK","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEOPSQ43A4XKNYMT","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEOPSQ43","created_at":"2026-05-18T12:28:43.426989+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/PEOPSQ43A4XKNYMTD4IQIH3BOX","json":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX.json","graph_json":"https://pith.science/api/pith-number/PEOPSQ43A4XKNYMTD4IQIH3BOX/graph.json","events_json":"https://pith.science/api/pith-number/PEOPSQ43A4XKNYMTD4IQIH3BOX/events.json","paper":"https://pith.science/paper/PEOPSQ43"},"agent_actions":{"view_html":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX","download_json":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX.json","view_paper":"https://pith.science/paper/PEOPSQ43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.0780&json=true","fetch_graph":"https://pith.science/api/pith-number/PEOPSQ43A4XKNYMTD4IQIH3BOX/graph.json","fetch_events":"https://pith.science/api/pith-number/PEOPSQ43A4XKNYMTD4IQIH3BOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX/action/storage_attestation","attest_author":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX/action/author_attestation","sign_citation":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX/action/citation_signature","submit_replication":"https://pith.science/pith/PEOPSQ43A4XKNYMTD4IQIH3BOX/action/replication_record"}},"created_at":"2026-05-18T01:36:11.174855+00:00","updated_at":"2026-05-18T01:36:11.174855+00:00"}