{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O5GWOG6Z77J3A7QRNFM5VY6YAM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3c233ce03564eca0863fcbc66d71f77806e5e3cc37dc8293f4fef5acf0d5db84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-04T14:53:32Z","title_canon_sha256":"6e15acaadedc9b5fdb5012fd181660c8ecd8281da639b1d5c8531d973717dd78"},"schema_version":"1.0","source":{"id":"1705.01867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01867","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01867v1","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01867","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"O5GWOG6Z77J3","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O5GWOG6Z77J3A7QR","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O5GWOG6Z","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:5bdef1819edd9caa5eaa6e244aabe6603f3bb1fbe552e1baf855ab0f3b98d5d3","target":"graph","created_at":"2026-05-18T00:45:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that for every convex body $K$ with the center of mass at the origin and every $\\varepsilon\\in \\left(0,\\frac{1}{2}\\right)$, there exists a convex polytope $P$ with at most $e^{O(d)}\\varepsilon^{-\\frac{d-1}{2}}$ vertices such that $(1-\\varepsilon)K\\subset P\\subset K$.","authors_text":"Dmitry Ryabogin, Fedor Nazarov, M\\'arton Nasz\\'odi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-04T14:53:32Z","title":"Fine approximation of convex bodies by polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01867","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:903aa826058a6fc376785b47320f3427375c62cdc2a8f1c3959f71e4164e976b","target":"record","created_at":"2026-05-18T00:45:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3c233ce03564eca0863fcbc66d71f77806e5e3cc37dc8293f4fef5acf0d5db84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-04T14:53:32Z","title_canon_sha256":"6e15acaadedc9b5fdb5012fd181660c8ecd8281da639b1d5c8531d973717dd78"},"schema_version":"1.0","source":{"id":"1705.01867","kind":"arxiv","version":1}},"canonical_sha256":"774d671bd9ffd3b07e116959dae3d8033aaa420b4b84cfea44e7cbf64af44f2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774d671bd9ffd3b07e116959dae3d8033aaa420b4b84cfea44e7cbf64af44f2a","first_computed_at":"2026-05-18T00:45:02.152834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:02.152834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H2I0SVqZj4jJ+qymG5Ty+OR1gAiKsuSH0kiWhfbHVcIj8yF3/NlollG6Z8A4ojWZUvscZia9PesYgDRCVGM6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:02.153302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:903aa826058a6fc376785b47320f3427375c62cdc2a8f1c3959f71e4164e976b","sha256:5bdef1819edd9caa5eaa6e244aabe6603f3bb1fbe552e1baf855ab0f3b98d5d3"],"state_sha256":"dccf648194b3a3393da0a55db8b556e6cd6b1f980f3d9844b62732283f678a65"}