{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZOMGOEPNVYI7LQC3LXJTCMMDJ4","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":"062b65c16a2db74221783dcacfeba4e98daf134155a1bc7a78a48e73a90672a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-20T21:35:21Z","title_canon_sha256":"83fead9b1022c89e736c116316b66ff617369ef7a45bc767d375beda16bf7e47"},"schema_version":"1.0","source":{"id":"1302.5132","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5132","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5132v6","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5132","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZOMGOEPNVYI7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZOMGOEPNVYI7LQC3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZOMGOEPN","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:7d6bbcdbdf15de8f1a413bbd979ed0fb4a5955acc806c0975501c402243238b6","target":"graph","created_at":"2026-05-18T01:19:18Z","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":"Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in $\\mathbb R^{n\\ge 2}$ as an sharp upper bound of the variational $(1,n)\\ni p$-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \\cite[Problem 59]{Yau} from the surface area to the variational $p$-capacity whose limit as $p\\to 1$ actually induces the surface area.","authors_text":"Jie Xiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-20T21:35:21Z","title":"A Maximum Problem of S.-T. Yau for Variational p-Capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5132","kind":"arxiv","version":6},"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":"sha256:6afe64a2190a1ff54e13b3f949430fcd9a0b97829f77f3798007b2b74c4dd375","target":"record","created_at":"2026-05-18T01:19:18Z","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":"062b65c16a2db74221783dcacfeba4e98daf134155a1bc7a78a48e73a90672a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-20T21:35:21Z","title_canon_sha256":"83fead9b1022c89e736c116316b66ff617369ef7a45bc767d375beda16bf7e47"},"schema_version":"1.0","source":{"id":"1302.5132","kind":"arxiv","version":6}},"canonical_sha256":"cb986711edae11f5c05b5dd33131834f0895a7019f0a947fbe2b969e134bca42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb986711edae11f5c05b5dd33131834f0895a7019f0a947fbe2b969e134bca42","first_computed_at":"2026-05-18T01:19:18.920203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:18.920203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ofkwgjdGS6hIRpgxgl8uU64Z1lSei828KJT1smJ2A+uxK6qH3tfjF5R978r9YPs6GVeHTzi4AsSEVdV4f0xCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:18.920701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5132","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6afe64a2190a1ff54e13b3f949430fcd9a0b97829f77f3798007b2b74c4dd375","sha256:7d6bbcdbdf15de8f1a413bbd979ed0fb4a5955acc806c0975501c402243238b6"],"state_sha256":"4eb9f6375716a67c784174e7a3006413379de3404e1d10ac253fdab0c66a03c4"}