{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AHQHTYHVHKVXA4ERHBM2WGWFCO","short_pith_number":"pith:AHQHTYHV","canonical_record":{"source":{"id":"1207.3448","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-14T18:44:55Z","cross_cats_sorted":[],"title_canon_sha256":"4d9f173c27ef0e0d9d5095117374fff834154afc9a53cb4d72a0d2158a8ebf35","abstract_canon_sha256":"30354086f383261aa6029cf6c60888e331537c3bdd6881cb432447da73a976a0"},"schema_version":"1.0"},"canonical_sha256":"01e079e0f53aab7070913859ab1ac51386aa7bf848370e249734ca045b3e8621","source":{"kind":"arxiv","id":"1207.3448","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3448","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3448v4","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3448","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"pith_short_12","alias_value":"AHQHTYHVHKVX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHQHTYHVHKVXA4ER","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHQHTYHV","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AHQHTYHVHKVXA4ERHBM2WGWFCO","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3448","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-14T18:44:55Z","cross_cats_sorted":[],"title_canon_sha256":"4d9f173c27ef0e0d9d5095117374fff834154afc9a53cb4d72a0d2158a8ebf35","abstract_canon_sha256":"30354086f383261aa6029cf6c60888e331537c3bdd6881cb432447da73a976a0"},"schema_version":"1.0"},"canonical_sha256":"01e079e0f53aab7070913859ab1ac51386aa7bf848370e249734ca045b3e8621","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:04.785748Z","signature_b64":"/QydJqiLXp6/8teW0ByyOf7ckRpORkteqwASmJMe8e0z9SjyU8GY5coD+WHB97uEUH26R0lZ0mnDInWnkd65Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e079e0f53aab7070913859ab1ac51386aa7bf848370e249734ca045b3e8621","last_reissued_at":"2026-05-18T00:58:04.785300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:04.785300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3448","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YKEM10lHJrSNKYob3e1WxRPfdtB1lH8hCsNd/FNvFGyOa9bqs2+09Dg/swGcqpH+zqDG/A7LP7U5d2F7Gz4lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:49:45.278479Z"},"content_sha256":"583c065767035a9e481a87c3adea81441f9bb22d5461bef93c48b739e7a4ef2e","schema_version":"1.0","event_id":"sha256:583c065767035a9e481a87c3adea81441f9bb22d5461bef93c48b739e7a4ef2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AHQHTYHVHKVXA4ERHBM2WGWFCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controlling Area Blow-up in Minimal or Bounded Mean Curvature Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brian White","submitted_at":"2012-07-14T18:44:55Z","abstract_excerpt":"Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some ways like a minimal variety without boundary: in particular, it satisfies the same maximum and barrier principles that a smooth minimal submanifold satisfies. For suitable open subsets W of N, this allows one to show that if the areas of the M_i are uniformly bounded on compact subsets of W, then the areas are in fact uniformly bounded on all compact subset"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3448","kind":"arxiv","version":4},"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":"2026-05-18T00:58:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5UQzlFaEyGZo1DOLnLcaJ2pmvC6YKWQJ03yJFmJzc9vXbBhh7Zyl/WhlSZ1xIOOTdlR71OhBpc5uLJizmyi+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:49:45.278830Z"},"content_sha256":"c2329bcafc7e47f940143b3a570999e7367729e728ee0111a195ba1f5788b708","schema_version":"1.0","event_id":"sha256:c2329bcafc7e47f940143b3a570999e7367729e728ee0111a195ba1f5788b708"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/bundle.json","state_url":"https://pith.science/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/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":"2026-06-23T02:49:45Z","links":{"resolver":"https://pith.science/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO","bundle":"https://pith.science/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/bundle.json","state":"https://pith.science/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHQHTYHVHKVXA4ERHBM2WGWFCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AHQHTYHVHKVXA4ERHBM2WGWFCO","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":"30354086f383261aa6029cf6c60888e331537c3bdd6881cb432447da73a976a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-14T18:44:55Z","title_canon_sha256":"4d9f173c27ef0e0d9d5095117374fff834154afc9a53cb4d72a0d2158a8ebf35"},"schema_version":"1.0","source":{"id":"1207.3448","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3448","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3448v4","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3448","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"pith_short_12","alias_value":"AHQHTYHVHKVX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHQHTYHVHKVXA4ER","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHQHTYHV","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c2329bcafc7e47f940143b3a570999e7367729e728ee0111a195ba1f5788b708","target":"graph","created_at":"2026-05-18T00:58:04Z","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":"Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some ways like a minimal variety without boundary: in particular, it satisfies the same maximum and barrier principles that a smooth minimal submanifold satisfies. For suitable open subsets W of N, this allows one to show that if the areas of the M_i are uniformly bounded on compact subsets of W, then the areas are in fact uniformly bounded on all compact subset","authors_text":"Brian White","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-14T18:44:55Z","title":"Controlling Area Blow-up in Minimal or Bounded Mean Curvature Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3448","kind":"arxiv","version":4},"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":"sha256:583c065767035a9e481a87c3adea81441f9bb22d5461bef93c48b739e7a4ef2e","target":"record","created_at":"2026-05-18T00:58:04Z","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":"30354086f383261aa6029cf6c60888e331537c3bdd6881cb432447da73a976a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-14T18:44:55Z","title_canon_sha256":"4d9f173c27ef0e0d9d5095117374fff834154afc9a53cb4d72a0d2158a8ebf35"},"schema_version":"1.0","source":{"id":"1207.3448","kind":"arxiv","version":4}},"canonical_sha256":"01e079e0f53aab7070913859ab1ac51386aa7bf848370e249734ca045b3e8621","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e079e0f53aab7070913859ab1ac51386aa7bf848370e249734ca045b3e8621","first_computed_at":"2026-05-18T00:58:04.785300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:04.785300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/QydJqiLXp6/8teW0ByyOf7ckRpORkteqwASmJMe8e0z9SjyU8GY5coD+WHB97uEUH26R0lZ0mnDInWnkd65Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:04.785748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3448","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:583c065767035a9e481a87c3adea81441f9bb22d5461bef93c48b739e7a4ef2e","sha256:c2329bcafc7e47f940143b3a570999e7367729e728ee0111a195ba1f5788b708"],"state_sha256":"bc76029d09668cacc2228fba08ba9e1e42f2618238e17b489a901c02ec291789"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9DYdH8XhRa4PmWxRtTej3uMvoG5nfL3MES9uPkUxKyshE8wX9FfVhNSPrFff5QfCqktEUdHGuT16NUh8dGODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:49:45.280805Z","bundle_sha256":"67bdaca9a55bdda4086e5e83f81b283adb8fd5ccb97f16774702ffa476975e14"}}