{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DKB3VJUNNIJQIAYVWCWVUJLITD","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":"8e94c555d1c39c711b492b13eb08925d079fd320c86c96ac86816297ef43e2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-30T20:47:18Z","title_canon_sha256":"87ef45740752b510b0220c6bf129a3bc964c4e26bceaf3de4fa92cfb0d229f6d"},"schema_version":"1.0","source":{"id":"1607.00038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00038","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00038v1","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00038","created_at":"2026-05-18T01:11:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKB3VJUNNIJQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DKB3VJUNNIJQIAYV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DKB3VJUN","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:bb3c37f82aaad6cd2836c3ed63d8b48f9ebb3ed891553518cfe1f4b81168133d","target":"graph","created_at":"2026-05-18T01:11:38Z","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":"In this note, we observe that if $B$ is a ball in a Euclidean space with dimension $n$, $n\\geq3$, then a stable CMC hypersurface $\\Sigma$ with free boundary in $B$ satisfies \\[ nA\\leq L\\leq nA\\left( \\frac{1+\\sqrt{1+4(n+1)H^2}}{2} \\right)\\,, \\] where $L$, $A$ and $H$ denote the length of $\\partial \\Sigma$, the area of $\\Sigma$ and the mean curvature of $\\Sigma$, respectively. Consequently, if the boundary $\\partial \\Sigma$ is embedded then $\\Sigma$ must be totally geodesic or starshaped with respect to the center of the ball. This result is an improvement of a theorem proved by A. Ros and E. Ve","authors_text":"Ezequiel Barbosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-30T20:47:18Z","title":"On stable CMC hypersurfaces with free-boundary in a Euclidean Ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00038","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:f72b8f89ec3d40abcf0394ab1e4ff6cd8f906bbc751023ddcfca7e6060e48b5e","target":"record","created_at":"2026-05-18T01:11:38Z","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":"8e94c555d1c39c711b492b13eb08925d079fd320c86c96ac86816297ef43e2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-30T20:47:18Z","title_canon_sha256":"87ef45740752b510b0220c6bf129a3bc964c4e26bceaf3de4fa92cfb0d229f6d"},"schema_version":"1.0","source":{"id":"1607.00038","kind":"arxiv","version":1}},"canonical_sha256":"1a83baa68d6a13040315b0ad5a256898f6ca02689bb6943e78a5631df72ee36d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a83baa68d6a13040315b0ad5a256898f6ca02689bb6943e78a5631df72ee36d","first_computed_at":"2026-05-18T01:11:38.148693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:38.148693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3TZwoN4qMBsD9xw0GG0/Rs/nT9zKW5KUJhpj3Ziy9kp8yDf69WupKcVBCUSfr2TXBD5HWtiAZVD+GzcEG9MfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:38.149057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f72b8f89ec3d40abcf0394ab1e4ff6cd8f906bbc751023ddcfca7e6060e48b5e","sha256:bb3c37f82aaad6cd2836c3ed63d8b48f9ebb3ed891553518cfe1f4b81168133d"],"state_sha256":"1e5730f6b3c0b0380d38f2c1912ef67d6c5bfbe5efd1ca9d0409d7b6e2f3e366"}