{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4RPNIMYCUTEAQL57TLS6AYGGHW","short_pith_number":"pith:4RPNIMYC","canonical_record":{"source":{"id":"1201.1887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-09T19:54:49Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8cbf0225397fd7fd6c31e02f74fe8266ac971cb33f0a8b0149aebe4e2e0cf8d1","abstract_canon_sha256":"500d05856805c1ac2d29f787f54155bb31eb4fbccd821cad1d2d09d90029d3e3"},"schema_version":"1.0"},"canonical_sha256":"e45ed43302a4c8082fbf9ae5e060c63d8c235757646400521acd07bc85e40af2","source":{"kind":"arxiv","id":"1201.1887","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1887","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1887v2","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1887","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"pith_short_12","alias_value":"4RPNIMYCUTEA","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4RPNIMYCUTEAQL57","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4RPNIMYC","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4RPNIMYCUTEAQL57TLS6AYGGHW","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-09T19:54:49Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8cbf0225397fd7fd6c31e02f74fe8266ac971cb33f0a8b0149aebe4e2e0cf8d1","abstract_canon_sha256":"500d05856805c1ac2d29f787f54155bb31eb4fbccd821cad1d2d09d90029d3e3"},"schema_version":"1.0"},"canonical_sha256":"e45ed43302a4c8082fbf9ae5e060c63d8c235757646400521acd07bc85e40af2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:53.837632Z","signature_b64":"i6IfHQZOE2aBgLxdO25bo5Tgtr0nrqhgSEOxtN1sXqn8vr5GuPxmv6s+rJLN9HBc+OEBQA4CXtM+wX9UhXe4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e45ed43302a4c8082fbf9ae5e060c63d8c235757646400521acd07bc85e40af2","last_reissued_at":"2026-05-18T01:58:53.836859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:53.836859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1887","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":"2026-05-18T01:58:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qierzInZT+QC5ThJLH3Z5Kilc82+tdA8un2FRgWCxXuT/fGGv0MDV7UBq6LsbdbDRoMKsyxggB31BtSBu9vVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:16:22.058237Z"},"content_sha256":"6192f384f58b4419853f1811293cb58fc964ab2009d04805f338d4f50d28d0b8","schema_version":"1.0","event_id":"sha256:6192f384f58b4419853f1811293cb58fc964ab2009d04805f338d4f50d28d0b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4RPNIMYCUTEAQL57TLS6AYGGHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimizers of the Willmore functional with a small area constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jan Metzger, Tobias Lamm","submitted_at":"2012-01-09T19:54:49Z","abstract_excerpt":"We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1887","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":"2026-05-18T01:58:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ubm4/ZCLD79NyRh5dKYbDOTIfQHCUBWsg66iV6g2eUE2qxUL9M+N6jPlxD8/Ur8rz/EZ1r/hTwZDMrUCNxqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:16:22.058933Z"},"content_sha256":"8d742f16d1ca5480b9eddd2c18123f05fa4dd11b6e7080fd8330aa438b62e0d9","schema_version":"1.0","event_id":"sha256:8d742f16d1ca5480b9eddd2c18123f05fa4dd11b6e7080fd8330aa438b62e0d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/bundle.json","state_url":"https://pith.science/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/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":"2026-06-08T21:16:22Z","links":{"resolver":"https://pith.science/pith/4RPNIMYCUTEAQL57TLS6AYGGHW","bundle":"https://pith.science/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/bundle.json","state":"https://pith.science/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4RPNIMYCUTEAQL57TLS6AYGGHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4RPNIMYCUTEAQL57TLS6AYGGHW","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":"500d05856805c1ac2d29f787f54155bb31eb4fbccd821cad1d2d09d90029d3e3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-09T19:54:49Z","title_canon_sha256":"8cbf0225397fd7fd6c31e02f74fe8266ac971cb33f0a8b0149aebe4e2e0cf8d1"},"schema_version":"1.0","source":{"id":"1201.1887","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1887","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1887v2","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1887","created_at":"2026-05-18T01:58:53Z"},{"alias_kind":"pith_short_12","alias_value":"4RPNIMYCUTEA","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4RPNIMYCUTEAQL57","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4RPNIMYC","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:8d742f16d1ca5480b9eddd2c18123f05fa4dd11b6e7080fd8330aa438b62e0d9","target":"graph","created_at":"2026-05-18T01:58:53Z","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 show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.","authors_text":"Jan Metzger, Tobias Lamm","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-09T19:54:49Z","title":"Minimizers of the Willmore functional with a small area constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1887","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":"sha256:6192f384f58b4419853f1811293cb58fc964ab2009d04805f338d4f50d28d0b8","target":"record","created_at":"2026-05-18T01:58:53Z","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":"500d05856805c1ac2d29f787f54155bb31eb4fbccd821cad1d2d09d90029d3e3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-09T19:54:49Z","title_canon_sha256":"8cbf0225397fd7fd6c31e02f74fe8266ac971cb33f0a8b0149aebe4e2e0cf8d1"},"schema_version":"1.0","source":{"id":"1201.1887","kind":"arxiv","version":2}},"canonical_sha256":"e45ed43302a4c8082fbf9ae5e060c63d8c235757646400521acd07bc85e40af2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e45ed43302a4c8082fbf9ae5e060c63d8c235757646400521acd07bc85e40af2","first_computed_at":"2026-05-18T01:58:53.836859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:53.836859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6IfHQZOE2aBgLxdO25bo5Tgtr0nrqhgSEOxtN1sXqn8vr5GuPxmv6s+rJLN9HBc+OEBQA4CXtM+wX9UhXe4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:53.837632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1887","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6192f384f58b4419853f1811293cb58fc964ab2009d04805f338d4f50d28d0b8","sha256:8d742f16d1ca5480b9eddd2c18123f05fa4dd11b6e7080fd8330aa438b62e0d9"],"state_sha256":"9d0fed175f56b977df35b6ce6732938eaf1079c3e89c1280d4161fa849925b6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BzCKPDaEnFOeFrE6IP+chiUgsOm/O+6EuM+DLt0dalC9KGuUhT4ab8AvbZ3uY+Ok/1RFtg0JzJsu0T6s7eiSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:16:22.063797Z","bundle_sha256":"1f51686efd29a15322eb19ee802d599a8dc1d877eec97293d6c7bb958405ecee"}}