{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KF54GHMRBTPQXPBZSLAAFH2QSW","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":"028178e9be6aeda7db7d17ab19314c76bf034b671cd7d0123f99ecbb8262972d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-29T09:13:47Z","title_canon_sha256":"65bfbf78583ed5d187c879f3861658a45dc02e61627390ae4a39a4a4bcad28ba"},"schema_version":"1.0","source":{"id":"1101.5685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5685","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5685v1","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5685","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"KF54GHMRBTPQ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KF54GHMRBTPQXPBZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KF54GHMR","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:c484f3239488c91e074118600599810d869d66f5a7df6f1d9f6796ba6d3d3e5b","target":"graph","created_at":"2026-05-18T04:30:25Z","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 in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.","authors_text":"Du\\v{s}an Repov\\v{s}, Maxim V. Balashov","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-29T09:13:47Z","title":"Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5685","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":"sha256:2198e6f9883903b51da84af7ae7f8def8e8a9859f612a4f77bd93576ad20f51d","target":"record","created_at":"2026-05-18T04:30:25Z","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":"028178e9be6aeda7db7d17ab19314c76bf034b671cd7d0123f99ecbb8262972d","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-29T09:13:47Z","title_canon_sha256":"65bfbf78583ed5d187c879f3861658a45dc02e61627390ae4a39a4a4bcad28ba"},"schema_version":"1.0","source":{"id":"1101.5685","kind":"arxiv","version":1}},"canonical_sha256":"517bc31d910cdf0bbc3992c0029f5095a1b095db42276c1829d01dcf4a8baefb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517bc31d910cdf0bbc3992c0029f5095a1b095db42276c1829d01dcf4a8baefb","first_computed_at":"2026-05-18T04:30:25.056132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:25.056132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"84wKBXmEe5l22QOOjhGqpN8gbgi4x5wgVBvNZv8vEmyx0NxZTSIH8FgesyTTLq5fWOWfuYfQiDcPn0gLvjkQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:25.056816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2198e6f9883903b51da84af7ae7f8def8e8a9859f612a4f77bd93576ad20f51d","sha256:c484f3239488c91e074118600599810d869d66f5a7df6f1d9f6796ba6d3d3e5b"],"state_sha256":"987ee39dabc95af265985960fbe40883b05069e68e323f51421640e62a3ec398"}