{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:53LH2OD2Z7IPRODYHKHALHERJZ","short_pith_number":"pith:53LH2OD2","schema_version":"1.0","canonical_sha256":"eed67d387acfd0f8b8783a8e059c914e63bf84795dc62103a352d911741e2e5d","source":{"kind":"arxiv","id":"1906.03716","version":1},"attestation_state":"computed","paper":{"title":"A note on norms of signed sums of vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Giorgos Chasapis, Nikos Skarmogiannis","submitted_at":"2019-06-09T21:37:21Z","abstract_excerpt":"Our starting point is an improved version of a result of D. Hajela related to a question of Koml\\'{o}s: we show that if $f(n)$ is a function such that $\\lim\\limits_{n\\to\\infty }f(n)=\\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every $n\\geqslant n_0$ and any $S\\subseteq \\{-1,1\\}^n$ with cardinality $|S|\\leqslant 2^{n/f(n)}$ one can find orthonormal vectors $x_1,\\ldots ,x_n\\in {\\mathbb R}^n$ that satisfy $$\\|\\epsilon_1x_1+\\cdots +\\epsilon_nx_n\\|_{\\infty }\\geqslant c\\sqrt{\\log f(n)}$$ for all $(\\epsilon_1,\\ldots ,\\epsilon_n)\\in S$. We obtain analogous results in the case wher"},"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":"1906.03716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-06-09T21:37:21Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"1077b85cf2e571cc62e42341bddc636521322853166197e2d5091b0f8ba9d165","abstract_canon_sha256":"b9342060a80f5835d9cd71aab59e7c652097476f8de4c9e014b1930c1513f1eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:45.210154Z","signature_b64":"itVQ3AjhuXwU4qn27Vu3Jsoj+mn6S7hNga4DnsXsirHBSVRL1tE/GXzQwyXYDp3VX3CJAEz02Mrgs9sO/uRJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed67d387acfd0f8b8783a8e059c914e63bf84795dc62103a352d911741e2e5d","last_reissued_at":"2026-05-17T23:43:45.209539Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:45.209539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on norms of signed sums of vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Giorgos Chasapis, Nikos Skarmogiannis","submitted_at":"2019-06-09T21:37:21Z","abstract_excerpt":"Our starting point is an improved version of a result of D. Hajela related to a question of Koml\\'{o}s: we show that if $f(n)$ is a function such that $\\lim\\limits_{n\\to\\infty }f(n)=\\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every $n\\geqslant n_0$ and any $S\\subseteq \\{-1,1\\}^n$ with cardinality $|S|\\leqslant 2^{n/f(n)}$ one can find orthonormal vectors $x_1,\\ldots ,x_n\\in {\\mathbb R}^n$ that satisfy $$\\|\\epsilon_1x_1+\\cdots +\\epsilon_nx_n\\|_{\\infty }\\geqslant c\\sqrt{\\log f(n)}$$ for all $(\\epsilon_1,\\ldots ,\\epsilon_n)\\in S$. We obtain analogous results in the case wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03716","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":"1906.03716","created_at":"2026-05-17T23:43:45.209642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.03716v1","created_at":"2026-05-17T23:43:45.209642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03716","created_at":"2026-05-17T23:43:45.209642+00:00"},{"alias_kind":"pith_short_12","alias_value":"53LH2OD2Z7IP","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"53LH2OD2Z7IPRODY","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"53LH2OD2","created_at":"2026-05-18T12:33:10.108867+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/53LH2OD2Z7IPRODYHKHALHERJZ","json":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ.json","graph_json":"https://pith.science/api/pith-number/53LH2OD2Z7IPRODYHKHALHERJZ/graph.json","events_json":"https://pith.science/api/pith-number/53LH2OD2Z7IPRODYHKHALHERJZ/events.json","paper":"https://pith.science/paper/53LH2OD2"},"agent_actions":{"view_html":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ","download_json":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ.json","view_paper":"https://pith.science/paper/53LH2OD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.03716&json=true","fetch_graph":"https://pith.science/api/pith-number/53LH2OD2Z7IPRODYHKHALHERJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/53LH2OD2Z7IPRODYHKHALHERJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ/action/storage_attestation","attest_author":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ/action/author_attestation","sign_citation":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ/action/citation_signature","submit_replication":"https://pith.science/pith/53LH2OD2Z7IPRODYHKHALHERJZ/action/replication_record"}},"created_at":"2026-05-17T23:43:45.209642+00:00","updated_at":"2026-05-17T23:43:45.209642+00:00"}