{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Y3SZ2LZE36ZREOVUYGAF767T3X","short_pith_number":"pith:Y3SZ2LZE","canonical_record":{"source":{"id":"1102.2999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-15T08:51:46Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"34bd04e0485f971fd19434ae15310cd117977c87f8686a6d470efbc08e55ff35","abstract_canon_sha256":"ed486e657ace70bb74eb88aa6fac295103580d1c1fdf5250d876644b8c684b92"},"schema_version":"1.0"},"canonical_sha256":"c6e59d2f24dfb3123ab4c1805ffbf3ddc7372c7c67150aabf3828732ed9485f6","source":{"kind":"arxiv","id":"1102.2999","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2999","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2999v2","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2999","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"Y3SZ2LZE36ZR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y3SZ2LZE36ZREOVU","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y3SZ2LZE","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Y3SZ2LZE36ZREOVUYGAF767T3X","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-15T08:51:46Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"34bd04e0485f971fd19434ae15310cd117977c87f8686a6d470efbc08e55ff35","abstract_canon_sha256":"ed486e657ace70bb74eb88aa6fac295103580d1c1fdf5250d876644b8c684b92"},"schema_version":"1.0"},"canonical_sha256":"c6e59d2f24dfb3123ab4c1805ffbf3ddc7372c7c67150aabf3828732ed9485f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:02.386120Z","signature_b64":"lSDfR4AfxkQfzLtE9P68HkdjLkHnPkcqjEpK0cfmCOy9KZciTJuVImrvXmrXTQc88lOy2uWn/PC/8RuAcveyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e59d2f24dfb3123ab4c1805ffbf3ddc7372c7c67150aabf3828732ed9485f6","last_reissued_at":"2026-05-18T03:35:02.385403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:02.385403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2999","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":"2026-05-18T03:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SzFzJHLenJs0JreBPv54EHaiVJCnb9vCQaBIvNFfE5x5kHTXArk4AJDtjcap9krLLqnxmOtuEjkrK9/tzDPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:12:43.983144Z"},"content_sha256":"15eb1debe00523378a1bca53e15768a435b9bb14819feb3e91f5c5cec42a91c8","schema_version":"1.0","event_id":"sha256:15eb1debe00523378a1bca53e15768a435b9bb14819feb3e91f5c5cec42a91c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Y3SZ2LZE36ZREOVUYGAF767T3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large isoperimetric surfaces in initial data sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Jan Metzger, Michael Eichmair","submitted_at":"2011-02-15T08:51:46Z","abstract_excerpt":"We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all sufficiently large volumes, and that they are close to centered coordinate spheres. This implies that the volume-preserving stable constant mean curvature spheres constructed by G. Huisken and S.-T. Yau as well as R. Ye as perturbations of large centered coordinate spheres minimize ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2999","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":"2026-05-18T03:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzqNz1EAouQIc0Jc63cfo55j7vBVb7DbWEAQFvC+GXO+K8ZTXBVhgwEW+RvsRWgeLGUm04NXFtR/93tGjngTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:12:43.983534Z"},"content_sha256":"dafa5faf799a36c39987fb2d6f328152dbe1c559529fe3339eaedfd43d92e04f","schema_version":"1.0","event_id":"sha256:dafa5faf799a36c39987fb2d6f328152dbe1c559529fe3339eaedfd43d92e04f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/bundle.json","state_url":"https://pith.science/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/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":"2026-06-08T19:12:43Z","links":{"resolver":"https://pith.science/pith/Y3SZ2LZE36ZREOVUYGAF767T3X","bundle":"https://pith.science/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/bundle.json","state":"https://pith.science/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3SZ2LZE36ZREOVUYGAF767T3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y3SZ2LZE36ZREOVUYGAF767T3X","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":"ed486e657ace70bb74eb88aa6fac295103580d1c1fdf5250d876644b8c684b92","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-15T08:51:46Z","title_canon_sha256":"34bd04e0485f971fd19434ae15310cd117977c87f8686a6d470efbc08e55ff35"},"schema_version":"1.0","source":{"id":"1102.2999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2999","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2999v2","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2999","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"Y3SZ2LZE36ZR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y3SZ2LZE36ZREOVU","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y3SZ2LZE","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:dafa5faf799a36c39987fb2d6f328152dbe1c559529fe3339eaedfd43d92e04f","target":"graph","created_at":"2026-05-18T03:35:02Z","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 study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all sufficiently large volumes, and that they are close to centered coordinate spheres. This implies that the volume-preserving stable constant mean curvature spheres constructed by G. Huisken and S.-T. Yau as well as R. Ye as perturbations of large centered coordinate spheres minimize ar","authors_text":"Jan Metzger, Michael Eichmair","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-15T08:51:46Z","title":"Large isoperimetric surfaces in initial data sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2999","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":"sha256:15eb1debe00523378a1bca53e15768a435b9bb14819feb3e91f5c5cec42a91c8","target":"record","created_at":"2026-05-18T03:35:02Z","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":"ed486e657ace70bb74eb88aa6fac295103580d1c1fdf5250d876644b8c684b92","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-15T08:51:46Z","title_canon_sha256":"34bd04e0485f971fd19434ae15310cd117977c87f8686a6d470efbc08e55ff35"},"schema_version":"1.0","source":{"id":"1102.2999","kind":"arxiv","version":2}},"canonical_sha256":"c6e59d2f24dfb3123ab4c1805ffbf3ddc7372c7c67150aabf3828732ed9485f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e59d2f24dfb3123ab4c1805ffbf3ddc7372c7c67150aabf3828732ed9485f6","first_computed_at":"2026-05-18T03:35:02.385403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:02.385403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lSDfR4AfxkQfzLtE9P68HkdjLkHnPkcqjEpK0cfmCOy9KZciTJuVImrvXmrXTQc88lOy2uWn/PC/8RuAcveyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:02.386120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15eb1debe00523378a1bca53e15768a435b9bb14819feb3e91f5c5cec42a91c8","sha256:dafa5faf799a36c39987fb2d6f328152dbe1c559529fe3339eaedfd43d92e04f"],"state_sha256":"0edb0fac5f623e54f198856aa8c50545079d3fd2d9225861841a2b868b9c2089"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ys+r+3y/2jn97zW6smYZ9fuaCw6RA+coNarsulJnDtN+virx5yijEuYF5H6PauDgUJCuDVgzRC+jX2KJf3qkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:12:43.986867Z","bundle_sha256":"dcd975b7eca9bb07d82b049afef2979c6c1dcf9258d72c4803496eb5e1eaa159"}}