{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GFF6DOKVJNWYCNL6SML7XSJVC3","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":"82e8f32a052aa1afe601ae997351a92dbd9822b646a1c7ff84eabf1deb94d89c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-28T15:24:02Z","title_canon_sha256":"a64c2e8d8e48f95744ca9c429d87b5699f32508b582aae2f0c4e4216e97e385b"},"schema_version":"1.0","source":{"id":"1404.7019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7019","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7019v1","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7019","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"GFF6DOKVJNWY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFF6DOKVJNWYCNL6","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFF6DOKV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:517fd680c9ed5bf8ef650628922a49ee12c0c5b7480ab2e5242c797cb09729d4","target":"graph","created_at":"2026-05-18T02:53:05Z","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":"It is known that an $n$-dimensional convex body which is typical in the sense of Baire category, shows a simple, but highly non-intuitive curvature behaviour: at almost all of its boundary points, in the sense of measure, all curvatures are zero, but there is also a dense and uncountable set of boundary points at which all curvatures are infinite. The purpose of this paper is to find a counterpart to this phenomenon for typical convex bodies of given constant width. Such bodies cannot have zero curvatures. A main result says that for a typical $n$-dimensional convex body of constant width $1$ ","authors_text":"Imre Barany, Rolf Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-28T15:24:02Z","title":"Typical curvature behaviour of bodies of constant width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7019","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:cfbbbc27ca1e0a7e22007fb28c2c1ceac9ec20c439a5cbd56d1b0377f8d5dc03","target":"record","created_at":"2026-05-18T02:53:05Z","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":"82e8f32a052aa1afe601ae997351a92dbd9822b646a1c7ff84eabf1deb94d89c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-28T15:24:02Z","title_canon_sha256":"a64c2e8d8e48f95744ca9c429d87b5699f32508b582aae2f0c4e4216e97e385b"},"schema_version":"1.0","source":{"id":"1404.7019","kind":"arxiv","version":1}},"canonical_sha256":"314be1b9554b6d81357e9317fbc93516c312f0228b8c7f49ede06108210a560f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"314be1b9554b6d81357e9317fbc93516c312f0228b8c7f49ede06108210a560f","first_computed_at":"2026-05-18T02:53:05.323289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:05.323289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJaVYCW2JKgXRquCm0Gcpbm4YYtFCdqR87pnMzyuikcCW++JjFfOA4fCKNBPG0bFOQDqBk898xpABt4kNDLSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:05.323990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfbbbc27ca1e0a7e22007fb28c2c1ceac9ec20c439a5cbd56d1b0377f8d5dc03","sha256:517fd680c9ed5bf8ef650628922a49ee12c0c5b7480ab2e5242c797cb09729d4"],"state_sha256":"796220c031d034a97f01774cf3c5e0be17f4db158ec502e1d71241456323f960"}