{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DKB3VJUNNIJQIAYVWCWVUJLITD","short_pith_number":"pith:DKB3VJUN","canonical_record":{"source":{"id":"1607.00038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-30T20:47:18Z","cross_cats_sorted":[],"title_canon_sha256":"87ef45740752b510b0220c6bf129a3bc964c4e26bceaf3de4fa92cfb0d229f6d","abstract_canon_sha256":"8e94c555d1c39c711b492b13eb08925d079fd320c86c96ac86816297ef43e2e4"},"schema_version":"1.0"},"canonical_sha256":"1a83baa68d6a13040315b0ad5a256898f6ca02689bb6943e78a5631df72ee36d","source":{"kind":"arxiv","id":"1607.00038","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DKB3VJUNNIJQIAYVWCWVUJLITD","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-30T20:47:18Z","cross_cats_sorted":[],"title_canon_sha256":"87ef45740752b510b0220c6bf129a3bc964c4e26bceaf3de4fa92cfb0d229f6d","abstract_canon_sha256":"8e94c555d1c39c711b492b13eb08925d079fd320c86c96ac86816297ef43e2e4"},"schema_version":"1.0"},"canonical_sha256":"1a83baa68d6a13040315b0ad5a256898f6ca02689bb6943e78a5631df72ee36d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:38.149057Z","signature_b64":"3TZwoN4qMBsD9xw0GG0/Rs/nT9zKW5KUJhpj3Ziy9kp8yDf69WupKcVBCUSfr2TXBD5HWtiAZVD+GzcEG9MfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a83baa68d6a13040315b0ad5a256898f6ca02689bb6943e78a5631df72ee36d","last_reissued_at":"2026-05-18T01:11:38.148693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:38.148693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00038","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/DpRm+O6Klhz+uyLUAiAxznMOQ7jkHTb8mNAbwKE22f5ZqI3HNF475n91La8ZvIkMUeb3flfnQPwx5j6Mr/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:40:49.713481Z"},"content_sha256":"f72b8f89ec3d40abcf0394ab1e4ff6cd8f906bbc751023ddcfca7e6060e48b5e","schema_version":"1.0","event_id":"sha256:f72b8f89ec3d40abcf0394ab1e4ff6cd8f906bbc751023ddcfca7e6060e48b5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DKB3VJUNNIJQIAYVWCWVUJLITD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On stable CMC hypersurfaces with free-boundary in a Euclidean Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ezequiel Barbosa","submitted_at":"2016-06-30T20:47:18Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00038","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2fK0Fh1/2a93kos8UVsRwyNJhf4UPU8HeZcHS3uTjdB2h9EFSh/j8z+72hQmTfqkukEx2w3ljzst7gfKdq7MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:40:49.713829Z"},"content_sha256":"bb3c37f82aaad6cd2836c3ed63d8b48f9ebb3ed891553518cfe1f4b81168133d","schema_version":"1.0","event_id":"sha256:bb3c37f82aaad6cd2836c3ed63d8b48f9ebb3ed891553518cfe1f4b81168133d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/bundle.json","state_url":"https://pith.science/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-19T23:40:49Z","links":{"resolver":"https://pith.science/pith/DKB3VJUNNIJQIAYVWCWVUJLITD","bundle":"https://pith.science/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/bundle.json","state":"https://pith.science/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKB3VJUNNIJQIAYVWCWVUJLITD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYnaYE6ra+VE41zIn7Dxn43GttMmLjkRp1Yutof6gOX5212+8IegB8CzSuI55I4GKDvG+NF1l/axVfTySW5PBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:40:49.715844Z","bundle_sha256":"9d1b0516142741e0feb77c7597ce6cdc0abda426a6eea72deaf5b3732af57c8a"}}