{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VPSB3OECAC755TY3O4CLBLNJIZ","short_pith_number":"pith:VPSB3OEC","canonical_record":{"source":{"id":"1006.5683","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-06-29T17:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"ab9fa522947754339a0efc2e8ac506916bc0d06079815e05039c51cd5c53e84b","abstract_canon_sha256":"6592333e83c5daa0ea201fa0d3350007b9a4f0a9b700091058e39782787fac76"},"schema_version":"1.0"},"canonical_sha256":"abe41db88200bfdecf1b7704b0ada94646dbe6fe2597c4393c10aea7f1e82f7f","source":{"kind":"arxiv","id":"1006.5683","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5683","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5683v2","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5683","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"VPSB3OECAC75","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VPSB3OECAC755TY3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VPSB3OEC","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VPSB3OECAC755TY3O4CLBLNJIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5683","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-06-29T17:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"ab9fa522947754339a0efc2e8ac506916bc0d06079815e05039c51cd5c53e84b","abstract_canon_sha256":"6592333e83c5daa0ea201fa0d3350007b9a4f0a9b700091058e39782787fac76"},"schema_version":"1.0"},"canonical_sha256":"abe41db88200bfdecf1b7704b0ada94646dbe6fe2597c4393c10aea7f1e82f7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:01.684893Z","signature_b64":"0TRyBdl5W/EeGomNbqvsbVhHKUMgrmo9a+THo4QPT+K+450FBJQQLZYyL86HcOUd5G83gaGwYj3tY1m+3MzrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe41db88200bfdecf1b7704b0ada94646dbe6fe2597c4393c10aea7f1e82f7f","last_reissued_at":"2026-05-18T02:33:01.684533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:01.684533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5683","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:33:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I0ABBVgH5veWsY//+zQCM+eqQoUhBl53RVxV99hFme0fNijKr2ngTjnZdix1yZdCkVD0OIzuFjADGhaKwhQ8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:32:28.364376Z"},"content_sha256":"3d5093bbafe7dbd451eb97c47eac92431d65c5f3f3d6cbe205d23afa3400f89b","schema_version":"1.0","event_id":"sha256:3d5093bbafe7dbd451eb97c47eac92431d65c5f3f3d6cbe205d23afa3400f89b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VPSB3OECAC755TY3O4CLBLNJIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for constant mean curvature graphs in MxR","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jos\\'e M. Manzano","submitted_at":"2010-06-29T17:20:52Z","abstract_excerpt":"We will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reaches in MxR. We will also give a lower bound for the distance from an interior point to the boundary in terms of the height at that point, and characterize when these bounds are attained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5683","kind":"arxiv","version":2},"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":"2026-05-18T02:33:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/m5tAHnB2BUeajysfOPTB2S3SUGLMezCsiuLYptOa/qnfT51q5bhlp4hf3umD+pji6FxNm/puuquUeEeDxpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:32:28.364722Z"},"content_sha256":"98b5571e8bd8b9feafcb46887199fce3b787c892604b364be1f6062b928899b9","schema_version":"1.0","event_id":"sha256:98b5571e8bd8b9feafcb46887199fce3b787c892604b364be1f6062b928899b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPSB3OECAC755TY3O4CLBLNJIZ/bundle.json","state_url":"https://pith.science/pith/VPSB3OECAC755TY3O4CLBLNJIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPSB3OECAC755TY3O4CLBLNJIZ/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":"2026-06-24T03:32:28Z","links":{"resolver":"https://pith.science/pith/VPSB3OECAC755TY3O4CLBLNJIZ","bundle":"https://pith.science/pith/VPSB3OECAC755TY3O4CLBLNJIZ/bundle.json","state":"https://pith.science/pith/VPSB3OECAC755TY3O4CLBLNJIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPSB3OECAC755TY3O4CLBLNJIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VPSB3OECAC755TY3O4CLBLNJIZ","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":"6592333e83c5daa0ea201fa0d3350007b9a4f0a9b700091058e39782787fac76","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-06-29T17:20:52Z","title_canon_sha256":"ab9fa522947754339a0efc2e8ac506916bc0d06079815e05039c51cd5c53e84b"},"schema_version":"1.0","source":{"id":"1006.5683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5683","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5683v2","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5683","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"VPSB3OECAC75","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VPSB3OECAC755TY3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VPSB3OEC","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:98b5571e8bd8b9feafcb46887199fce3b787c892604b364be1f6062b928899b9","target":"graph","created_at":"2026-05-18T02:33:01Z","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 will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reaches in MxR. We will also give a lower bound for the distance from an interior point to the boundary in terms of the height at that point, and characterize when these bounds are attained.","authors_text":"Jos\\'e M. Manzano","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-06-29T17:20:52Z","title":"Estimates for constant mean curvature graphs in MxR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5683","kind":"arxiv","version":2},"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":"sha256:3d5093bbafe7dbd451eb97c47eac92431d65c5f3f3d6cbe205d23afa3400f89b","target":"record","created_at":"2026-05-18T02:33:01Z","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":"6592333e83c5daa0ea201fa0d3350007b9a4f0a9b700091058e39782787fac76","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2010-06-29T17:20:52Z","title_canon_sha256":"ab9fa522947754339a0efc2e8ac506916bc0d06079815e05039c51cd5c53e84b"},"schema_version":"1.0","source":{"id":"1006.5683","kind":"arxiv","version":2}},"canonical_sha256":"abe41db88200bfdecf1b7704b0ada94646dbe6fe2597c4393c10aea7f1e82f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe41db88200bfdecf1b7704b0ada94646dbe6fe2597c4393c10aea7f1e82f7f","first_computed_at":"2026-05-18T02:33:01.684533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:01.684533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0TRyBdl5W/EeGomNbqvsbVhHKUMgrmo9a+THo4QPT+K+450FBJQQLZYyL86HcOUd5G83gaGwYj3tY1m+3MzrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:01.684893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d5093bbafe7dbd451eb97c47eac92431d65c5f3f3d6cbe205d23afa3400f89b","sha256:98b5571e8bd8b9feafcb46887199fce3b787c892604b364be1f6062b928899b9"],"state_sha256":"23e54f1e0daa1da72cefc02bc14ad292d2f2a36a421a8057c15bb5734ac9f34b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvpjNSHv/MA9H+DiUUm50RmvzHLN/RK+FeivxhMQFD2vxvxJXx2y7c/g8vKozvwNmO+ZRMUBwRiQL+DYrMVgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:32:28.366689Z","bundle_sha256":"5f0efdbdb28bbb163a0357f75adaef1ee93366111d1ea8108a79c7eb448de358"}}