{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5MOOSZNUP7N7YBE6QUIE4GC3H3","short_pith_number":"pith:5MOOSZNU","schema_version":"1.0","canonical_sha256":"eb1ce965b47fdbfc049e85104e185b3ef1773c1581d987333594eb26b29706ae","source":{"kind":"arxiv","id":"1703.00859","version":3},"attestation_state":"computed","paper":{"title":"On the minimum trace norm of (0,1)-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Natalia Agudelo, Vladimir Nikiforov","submitted_at":"2017-03-02T17:21:56Z","abstract_excerpt":"The trace norm of a matrix is the sum of its singular values. This paper presents results on the minimum trace norm $\\psi_{n}\\left( m\\right) $ of $\\left( 0,1\\right) $-matrices of size $n\\times n$ with exactly $m$ ones. It is shown that:\n  (1) if $n\\geq2$ and $n<m\\leq2n,$ then $\\psi_{n}\\left( m\\right) \\leq \\sqrt{m+\\sqrt{2\\left( m-1\\right) }}$ , with equality if and only if $m$ is a prime;\n  (2) if $n\\geq4$ and $2n<m\\leq3n,$ then $\\psi_{n}\\left( m\\right) \\leq \\sqrt{m+2\\sqrt{2\\left\\lfloor m/3\\right\\rfloor }}$ , with equality if and only if $m$ is a prime or a double of a prime;\n  (3) if $3n<m\\leq"},"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":"1703.00859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-02T17:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"cca7327904d91eddca3aa2525c0ea36316465228cbb65ffd4ab23e7c46fb9032","abstract_canon_sha256":"21bd01f8c794490ec9c8da5f3a1dadc19a185826ca33decb4204e5eff14f8fdf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:25.744558Z","signature_b64":"ZNSANLNiG6P1GIRMGsPgR9o/wVuQX5ZWxwm0wX+t6BCtY4fgT1hRa/WcQOdExid5vuZHSTonjF/ac+ld3GRIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb1ce965b47fdbfc049e85104e185b3ef1773c1581d987333594eb26b29706ae","last_reissued_at":"2026-05-18T00:48:25.743991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:25.743991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the minimum trace norm of (0,1)-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Natalia Agudelo, Vladimir Nikiforov","submitted_at":"2017-03-02T17:21:56Z","abstract_excerpt":"The trace norm of a matrix is the sum of its singular values. This paper presents results on the minimum trace norm $\\psi_{n}\\left( m\\right) $ of $\\left( 0,1\\right) $-matrices of size $n\\times n$ with exactly $m$ ones. It is shown that:\n  (1) if $n\\geq2$ and $n<m\\leq2n,$ then $\\psi_{n}\\left( m\\right) \\leq \\sqrt{m+\\sqrt{2\\left( m-1\\right) }}$ , with equality if and only if $m$ is a prime;\n  (2) if $n\\geq4$ and $2n<m\\leq3n,$ then $\\psi_{n}\\left( m\\right) \\leq \\sqrt{m+2\\sqrt{2\\left\\lfloor m/3\\right\\rfloor }}$ , with equality if and only if $m$ is a prime or a double of a prime;\n  (3) if $3n<m\\leq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00859","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":"1703.00859","created_at":"2026-05-18T00:48:25.744088+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.00859v3","created_at":"2026-05-18T00:48:25.744088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00859","created_at":"2026-05-18T00:48:25.744088+00:00"},{"alias_kind":"pith_short_12","alias_value":"5MOOSZNUP7N7","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5MOOSZNUP7N7YBE6","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5MOOSZNU","created_at":"2026-05-18T12:31:00.734936+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/5MOOSZNUP7N7YBE6QUIE4GC3H3","json":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3.json","graph_json":"https://pith.science/api/pith-number/5MOOSZNUP7N7YBE6QUIE4GC3H3/graph.json","events_json":"https://pith.science/api/pith-number/5MOOSZNUP7N7YBE6QUIE4GC3H3/events.json","paper":"https://pith.science/paper/5MOOSZNU"},"agent_actions":{"view_html":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3","download_json":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3.json","view_paper":"https://pith.science/paper/5MOOSZNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.00859&json=true","fetch_graph":"https://pith.science/api/pith-number/5MOOSZNUP7N7YBE6QUIE4GC3H3/graph.json","fetch_events":"https://pith.science/api/pith-number/5MOOSZNUP7N7YBE6QUIE4GC3H3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3/action/storage_attestation","attest_author":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3/action/author_attestation","sign_citation":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3/action/citation_signature","submit_replication":"https://pith.science/pith/5MOOSZNUP7N7YBE6QUIE4GC3H3/action/replication_record"}},"created_at":"2026-05-18T00:48:25.744088+00:00","updated_at":"2026-05-18T00:48:25.744088+00:00"}