{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:RUY4VBRUUF6MAHMPUYQ2YPIGPE","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":"b5527dc9d2172b8d1f3b60a7a19118e9d853e1138447ea130a1fe5d24de4eecd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-09-11T14:58:55Z","title_canon_sha256":"233d8116bd899fa574032e3243db8cf4ef00713d8e7f6f0f1004efd2c23e210a"},"schema_version":"1.0","source":{"id":"0709.1644","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1644","created_at":"2026-07-04T15:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1644v3","created_at":"2026-07-04T15:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1644","created_at":"2026-07-04T15:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"RUY4VBRUUF6M","created_at":"2026-07-04T15:50:10Z"},{"alias_kind":"pith_short_16","alias_value":"RUY4VBRUUF6MAHMP","created_at":"2026-07-04T15:50:10Z"},{"alias_kind":"pith_short_8","alias_value":"RUY4VBRU","created_at":"2026-07-04T15:50:10Z"}],"graph_snapshots":[{"event_id":"sha256:f5d84a37b9ce264cff1f24a174781026011317f36c86278b208e37ed93cf8f21","target":"graph","created_at":"2026-07-04T15:50:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0709.1644/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The expression for the variation of the area functional of the second fundamental form of a hypersurface in a Euclidean space involves the so-called \"mean curvature of the second fundamental form\". Several new characteristic properties of (hyper)spheres, in which the mean curvature of the second fundamental form occurs, are given. In particular, it is shown that the spheres are the only ovaloids which are a critical point of the area functional of the second fundamental form under various constraints.","authors_text":"Steven Verpoort","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-09-11T14:58:55Z","title":"On the Area Functional of the Second Fundamental Form of Ovaloids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1644","kind":"arxiv","version":3},"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":"sha256:0c364725bc71ef32466c6d8e5ff7d37e4064dc15df3aff2fd8a52c66636fb7c0","target":"record","created_at":"2026-07-04T15:50:10Z","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":"b5527dc9d2172b8d1f3b60a7a19118e9d853e1138447ea130a1fe5d24de4eecd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-09-11T14:58:55Z","title_canon_sha256":"233d8116bd899fa574032e3243db8cf4ef00713d8e7f6f0f1004efd2c23e210a"},"schema_version":"1.0","source":{"id":"0709.1644","kind":"arxiv","version":3}},"canonical_sha256":"8d31ca8634a17cc01d8fa621ac3d06792599eb5f3f55f1d97135911221c1b7a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d31ca8634a17cc01d8fa621ac3d06792599eb5f3f55f1d97135911221c1b7a5","first_computed_at":"2026-07-04T15:50:10.898729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:50:10.898729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e7YF/4n6MSL2QsC9MzuksvqqjxhQb/C43efE+yLr1brq7948Dwq7AURIiY1vAscfS0cSZDq4a8nTTVAy7QQXDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:50:10.899075Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.1644","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c364725bc71ef32466c6d8e5ff7d37e4064dc15df3aff2fd8a52c66636fb7c0","sha256:f5d84a37b9ce264cff1f24a174781026011317f36c86278b208e37ed93cf8f21"],"state_sha256":"14347cd9b03414ce504f8445df07cc1cedcd522a5d62c2dadc8163152008b3a2"}