{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IQKGOKLYEEYYR3GY73YIT6RFIB","short_pith_number":"pith:IQKGOKLY","canonical_record":{"source":{"id":"1808.04341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-13T17:31:36Z","cross_cats_sorted":[],"title_canon_sha256":"54b01474a0651595e30a5178722a926f0c2b82cac8cb908c87d66a889b0b72b7","abstract_canon_sha256":"57183083cf4d548389d139651400142698d544135029bbde38ac6a6a96cc5a0a"},"schema_version":"1.0"},"canonical_sha256":"4414672978213188ecd8fef089fa25405e6b5e858b7704a0b84b4cd20793b95a","source":{"kind":"arxiv","id":"1808.04341","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04341","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04341v1","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04341","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"IQKGOKLYEEYY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IQKGOKLYEEYYR3GY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IQKGOKLY","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IQKGOKLYEEYYR3GY73YIT6RFIB","target":"record","payload":{"canonical_record":{"source":{"id":"1808.04341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-13T17:31:36Z","cross_cats_sorted":[],"title_canon_sha256":"54b01474a0651595e30a5178722a926f0c2b82cac8cb908c87d66a889b0b72b7","abstract_canon_sha256":"57183083cf4d548389d139651400142698d544135029bbde38ac6a6a96cc5a0a"},"schema_version":"1.0"},"canonical_sha256":"4414672978213188ecd8fef089fa25405e6b5e858b7704a0b84b4cd20793b95a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:16.627164Z","signature_b64":"O4x/TfTvaGpEyYhd9QBTBEkp5k7n7tvw6rEJkSZ5TOyOKgJpujINxe5s3/dzvKxki0FEbVTfm2nmFgZGRNWSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4414672978213188ecd8fef089fa25405e6b5e858b7704a0b84b4cd20793b95a","last_reissued_at":"2026-05-18T00:08:16.626619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:16.626619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.04341","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":"2026-05-18T00:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMRNNSdIchIqdm0MV9mohz6Vr87Ze0biAdyUznbahEHegvEw8QSQ9+tdcSa7GqmX8gz1qNLIMt541IvNsoreAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:16:15.358153Z"},"content_sha256":"6eb5216aee04be6335865bdab5d3ec869f99ee649dec9881ad13444dd97b1047","schema_version":"1.0","event_id":"sha256:6eb5216aee04be6335865bdab5d3ec869f99ee649dec9881ad13444dd97b1047"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IQKGOKLYEEYYR3GY73YIT6RFIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on a curvature gap for minimal surfaces in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Celso Viana, Ezequiel Barbosa","submitted_at":"2018-08-13T17:31:36Z","abstract_excerpt":"We extend to higher codimension earlier characterization of the equatorial disk and the critical catenoid by a pinching condition on the length of their second fundamental form among free boundary minimal surfaces in the three dimensional Euclidean ball due to L. Ambrozio and I. Nunes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04341","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":"2026-05-18T00:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMaQLvMEfnl/wEdgE8K2hj5T6xaK31Z1VvN0ksPWc4WfFuYJRaq5ujT0NpxHNXcIya6Nn0JOdnNgh/yfEBm+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:16:15.358511Z"},"content_sha256":"1edcbf105bfc256ef79dad2eddf4226187fdd5d383e65cbc7ebbf8dcdc7f71cf","schema_version":"1.0","event_id":"sha256:1edcbf105bfc256ef79dad2eddf4226187fdd5d383e65cbc7ebbf8dcdc7f71cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/bundle.json","state_url":"https://pith.science/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/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":"2026-06-20T05:16:15Z","links":{"resolver":"https://pith.science/pith/IQKGOKLYEEYYR3GY73YIT6RFIB","bundle":"https://pith.science/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/bundle.json","state":"https://pith.science/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQKGOKLYEEYYR3GY73YIT6RFIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IQKGOKLYEEYYR3GY73YIT6RFIB","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":"57183083cf4d548389d139651400142698d544135029bbde38ac6a6a96cc5a0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-13T17:31:36Z","title_canon_sha256":"54b01474a0651595e30a5178722a926f0c2b82cac8cb908c87d66a889b0b72b7"},"schema_version":"1.0","source":{"id":"1808.04341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04341","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04341v1","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04341","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"IQKGOKLYEEYY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IQKGOKLYEEYYR3GY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IQKGOKLY","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:1edcbf105bfc256ef79dad2eddf4226187fdd5d383e65cbc7ebbf8dcdc7f71cf","target":"graph","created_at":"2026-05-18T00:08:16Z","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 extend to higher codimension earlier characterization of the equatorial disk and the critical catenoid by a pinching condition on the length of their second fundamental form among free boundary minimal surfaces in the three dimensional Euclidean ball due to L. Ambrozio and I. Nunes.","authors_text":"Celso Viana, Ezequiel Barbosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-13T17:31:36Z","title":"A remark on a curvature gap for minimal surfaces in the ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04341","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":"sha256:6eb5216aee04be6335865bdab5d3ec869f99ee649dec9881ad13444dd97b1047","target":"record","created_at":"2026-05-18T00:08:16Z","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":"57183083cf4d548389d139651400142698d544135029bbde38ac6a6a96cc5a0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-13T17:31:36Z","title_canon_sha256":"54b01474a0651595e30a5178722a926f0c2b82cac8cb908c87d66a889b0b72b7"},"schema_version":"1.0","source":{"id":"1808.04341","kind":"arxiv","version":1}},"canonical_sha256":"4414672978213188ecd8fef089fa25405e6b5e858b7704a0b84b4cd20793b95a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4414672978213188ecd8fef089fa25405e6b5e858b7704a0b84b4cd20793b95a","first_computed_at":"2026-05-18T00:08:16.626619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:16.626619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O4x/TfTvaGpEyYhd9QBTBEkp5k7n7tvw6rEJkSZ5TOyOKgJpujINxe5s3/dzvKxki0FEbVTfm2nmFgZGRNWSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:16.627164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eb5216aee04be6335865bdab5d3ec869f99ee649dec9881ad13444dd97b1047","sha256:1edcbf105bfc256ef79dad2eddf4226187fdd5d383e65cbc7ebbf8dcdc7f71cf"],"state_sha256":"a9c9cd0683fd08646d41769bcc5cf88088c6245dff4413228f25fa8ad7f58e7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lx4xj9ZEBQRwnA4XuYejt9cQXMYNjDnHN/xv9jFWqLjdAReUdv/azu6Dypz1ROEUjv0JWm+t+Ac9ytWdd3oTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:16:15.360485Z","bundle_sha256":"15e4eda04a95ba1a70c80c197a43a51e8a47ec8de8b4a76c0ef16a68937f950e"}}