{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QVVWHSNTDQOR5MY2YH7PSPQESM","short_pith_number":"pith:QVVWHSNT","schema_version":"1.0","canonical_sha256":"856b63c9b31c1d1eb31ac1fef93e04932c69ef7783abd2144fb7e41ce2ef2ab2","source":{"kind":"arxiv","id":"1804.08212","version":2},"attestation_state":"computed","paper":{"title":"On the Banach-Mazur distance to cross-polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Konstantin Tikhomirov","submitted_at":"2018-04-23T01:18:39Z","abstract_excerpt":"Let $n\\geq 3$, and let $B_1^n$ be the standard $n$-dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a symmetric convex body $\\mathcal G_m$ in ${\\mathbb R}^n$ such that the Banach--Mazur distance $d(B_1^n,\\mathcal G_m)$ satisfies $d(B_1^n,\\mathcal G_m)\\geq n^{5/9}\\log^{-C}n$, where $C>0$ is a universal constant. The body $\\mathcal G_m$ is obtained as a typical realization of a random polytope in ${\\mathbb R}^n$ with $2m:=2n^C$ vertices (for a large constant $C$). The result improves upon an earlier estimate of S.Szar"},"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":"1804.08212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-23T01:18:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7a333fb5a4003e90293a57f96fbb85ba5a83bdbfbdcaf553c05a4124b6fae90a","abstract_canon_sha256":"29ba050893dbd1885ee682791f42e3f662cd5dd10908ff3f93250b86d3ce1492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:27.710197Z","signature_b64":"iY7q46GVCjhBgjD4wyAIQrZ0Bvsu++jwXY0yVNMw0UKysDOguqhBIKes68/PnkJQLvi4UssBqRajsls8pkPYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"856b63c9b31c1d1eb31ac1fef93e04932c69ef7783abd2144fb7e41ce2ef2ab2","last_reissued_at":"2026-05-18T00:15:27.709533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:27.709533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Banach-Mazur distance to cross-polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Konstantin Tikhomirov","submitted_at":"2018-04-23T01:18:39Z","abstract_excerpt":"Let $n\\geq 3$, and let $B_1^n$ be the standard $n$-dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a symmetric convex body $\\mathcal G_m$ in ${\\mathbb R}^n$ such that the Banach--Mazur distance $d(B_1^n,\\mathcal G_m)$ satisfies $d(B_1^n,\\mathcal G_m)\\geq n^{5/9}\\log^{-C}n$, where $C>0$ is a universal constant. The body $\\mathcal G_m$ is obtained as a typical realization of a random polytope in ${\\mathbb R}^n$ with $2m:=2n^C$ vertices (for a large constant $C$). The result improves upon an earlier estimate of S.Szar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08212","kind":"arxiv","version":2},"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":"1804.08212","created_at":"2026-05-18T00:15:27.709629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.08212v2","created_at":"2026-05-18T00:15:27.709629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08212","created_at":"2026-05-18T00:15:27.709629+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVVWHSNTDQOR","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVVWHSNTDQOR5MY2","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVVWHSNT","created_at":"2026-05-18T12:32:46.962924+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/QVVWHSNTDQOR5MY2YH7PSPQESM","json":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM.json","graph_json":"https://pith.science/api/pith-number/QVVWHSNTDQOR5MY2YH7PSPQESM/graph.json","events_json":"https://pith.science/api/pith-number/QVVWHSNTDQOR5MY2YH7PSPQESM/events.json","paper":"https://pith.science/paper/QVVWHSNT"},"agent_actions":{"view_html":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM","download_json":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM.json","view_paper":"https://pith.science/paper/QVVWHSNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.08212&json=true","fetch_graph":"https://pith.science/api/pith-number/QVVWHSNTDQOR5MY2YH7PSPQESM/graph.json","fetch_events":"https://pith.science/api/pith-number/QVVWHSNTDQOR5MY2YH7PSPQESM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM/action/storage_attestation","attest_author":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM/action/author_attestation","sign_citation":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM/action/citation_signature","submit_replication":"https://pith.science/pith/QVVWHSNTDQOR5MY2YH7PSPQESM/action/replication_record"}},"created_at":"2026-05-18T00:15:27.709629+00:00","updated_at":"2026-05-18T00:15:27.709629+00:00"}