{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YJGX25UKUA3IB7FQX6DXX2YVNT","short_pith_number":"pith:YJGX25UK","schema_version":"1.0","canonical_sha256":"c24d7d768aa03680fcb0bf877beb156cd7cdeb3b7b9a91999fd65aecb992138a","source":{"kind":"arxiv","id":"1803.06847","version":1},"attestation_state":"computed","paper":{"title":"The square negative correlation on l_p^n balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"David Alonso-Guti\\'errez, Julio Bernu\\'es","submitted_at":"2018-03-19T09:45:13Z","abstract_excerpt":"In this paper we prove that for any $p\\in[2,\\infty)$ the $\\ell_p^n$ unit ball, $B_p^n$, satisfies the square negative correlation property with respect to every orthonormal basis, while we show it is not always the case for $1\\le p\\le 2$. In order to do that we regard $B_p^n$ as the orthogonal projection of $B_p^{n+1}$ onto the hyperplane $e_{n+1}^\\perp$. We will also study the orthogonal projection of $B_p^n$ onto the hyperplane orthogonal to the diagonal vector $(1,\\dots,1)$. In this case, the property holds for all $p\\ge 1$ and $n$ large enough."},"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":"1803.06847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-19T09:45:13Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"770f7e1aa396febd050125fbd95b5fb614d59db546ea2ad48ca53236f9d0d03c","abstract_canon_sha256":"f6d30adfea4505b3ac58e5bc4e2bd5910f3397c7dad16d36ef0560e109957637"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:41.182024Z","signature_b64":"jeYr3Sx9dL1rf1Fcf7/J4cXukf7u999Jnf9XkhAXwZew3NkA23bgu0EPqSqGNNzY+t/62g9T2bYnXkzb8T8gCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24d7d768aa03680fcb0bf877beb156cd7cdeb3b7b9a91999fd65aecb992138a","last_reissued_at":"2026-05-18T00:20:41.181326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:41.181326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The square negative correlation on l_p^n balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"David Alonso-Guti\\'errez, Julio Bernu\\'es","submitted_at":"2018-03-19T09:45:13Z","abstract_excerpt":"In this paper we prove that for any $p\\in[2,\\infty)$ the $\\ell_p^n$ unit ball, $B_p^n$, satisfies the square negative correlation property with respect to every orthonormal basis, while we show it is not always the case for $1\\le p\\le 2$. In order to do that we regard $B_p^n$ as the orthogonal projection of $B_p^{n+1}$ onto the hyperplane $e_{n+1}^\\perp$. We will also study the orthogonal projection of $B_p^n$ onto the hyperplane orthogonal to the diagonal vector $(1,\\dots,1)$. In this case, the property holds for all $p\\ge 1$ and $n$ large enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06847","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":"1803.06847","created_at":"2026-05-18T00:20:41.181437+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.06847v1","created_at":"2026-05-18T00:20:41.181437+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06847","created_at":"2026-05-18T00:20:41.181437+00:00"},{"alias_kind":"pith_short_12","alias_value":"YJGX25UKUA3I","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YJGX25UKUA3IB7FQ","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YJGX25UK","created_at":"2026-05-18T12:33:04.347982+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/YJGX25UKUA3IB7FQX6DXX2YVNT","json":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT.json","graph_json":"https://pith.science/api/pith-number/YJGX25UKUA3IB7FQX6DXX2YVNT/graph.json","events_json":"https://pith.science/api/pith-number/YJGX25UKUA3IB7FQX6DXX2YVNT/events.json","paper":"https://pith.science/paper/YJGX25UK"},"agent_actions":{"view_html":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT","download_json":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT.json","view_paper":"https://pith.science/paper/YJGX25UK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.06847&json=true","fetch_graph":"https://pith.science/api/pith-number/YJGX25UKUA3IB7FQX6DXX2YVNT/graph.json","fetch_events":"https://pith.science/api/pith-number/YJGX25UKUA3IB7FQX6DXX2YVNT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT/action/storage_attestation","attest_author":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT/action/author_attestation","sign_citation":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT/action/citation_signature","submit_replication":"https://pith.science/pith/YJGX25UKUA3IB7FQX6DXX2YVNT/action/replication_record"}},"created_at":"2026-05-18T00:20:41.181437+00:00","updated_at":"2026-05-18T00:20:41.181437+00:00"}