{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ECXUGH4YQ4FA4ZT7FAE72PZAVK","short_pith_number":"pith:ECXUGH4Y","canonical_record":{"source":{"id":"1503.05910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T19:47:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"777bd2631495b7321d7eaa882bf33e64efae68ab9ad08cca5b5b6f236dc6ce6e","abstract_canon_sha256":"f59062d941c1ce48ae39ebc9876fcc10dcea7dab7a63918e74e0afe37642feeb"},"schema_version":"1.0"},"canonical_sha256":"20af431f98870a0e667f2809fd3f20aa90c95359f4da0f7c37dca5b11bf9ad5e","source":{"kind":"arxiv","id":"1503.05910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05910","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05910v2","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05910","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"ECXUGH4YQ4FA","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ECXUGH4YQ4FA4ZT7","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ECXUGH4Y","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ECXUGH4YQ4FA4ZT7FAE72PZAVK","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T19:47:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"777bd2631495b7321d7eaa882bf33e64efae68ab9ad08cca5b5b6f236dc6ce6e","abstract_canon_sha256":"f59062d941c1ce48ae39ebc9876fcc10dcea7dab7a63918e74e0afe37642feeb"},"schema_version":"1.0"},"canonical_sha256":"20af431f98870a0e667f2809fd3f20aa90c95359f4da0f7c37dca5b11bf9ad5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:41.702762Z","signature_b64":"705EHdOBcZxA+qUuYsr7Nj+ORqJDFvYdtfWV56NhRy525ClCsOD3+AkzWPwoZSVN8JQUoh7Jvjfzi33QUg0EBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20af431f98870a0e667f2809fd3f20aa90c95359f4da0f7c37dca5b11bf9ad5e","last_reissued_at":"2026-05-18T00:54:41.702261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:41.702261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05910","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":"2026-05-18T00:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/A7vNIgOLsogKSSSgQT6riF0mjHH2q9KSLYJbsdPfFKMcW06kjURVwyrD+mgBIAzuzfM+xdDX3ZuJawBvBCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:06:46.144667Z"},"content_sha256":"65f24c55b760368f8f3b1fdc18707923793159ae6f8099f990c8fc521f7ded9d","schema_version":"1.0","event_id":"sha256:65f24c55b760368f8f3b1fdc18707923793159ae6f8099f990c8fc521f7ded9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ECXUGH4YQ4FA4ZT7FAE72PZAVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective versions of the positive mass theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Alessandro Carlotto, Michael Eichmair, Otis Chodosh","submitted_at":"2015-03-19T19:47:20Z","abstract_excerpt":"The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem in terms of isoperimetric or, more generally, closed volume-preserving stable CMC surfaces that is appealing from both a physical and a purely geometric point of view. We also include a proof of the following conjecture of R. Schoen: An asymptotically flat Riemannian $3$-manifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05910","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":"2026-05-18T00:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7IFR7dII7A2aqGKywzkTkpXlnvQIAKIkTHrWPhdltA//K1UKz00qSBUvIvMYKiH2oci8OzZlp7HxrwXAGX3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:06:46.145352Z"},"content_sha256":"23395a5f4b06392477a311485273c03be71812447acf548424c0f8f3b984a15d","schema_version":"1.0","event_id":"sha256:23395a5f4b06392477a311485273c03be71812447acf548424c0f8f3b984a15d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/bundle.json","state_url":"https://pith.science/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/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":"2026-06-05T06:06:46Z","links":{"resolver":"https://pith.science/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK","bundle":"https://pith.science/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/bundle.json","state":"https://pith.science/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECXUGH4YQ4FA4ZT7FAE72PZAVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ECXUGH4YQ4FA4ZT7FAE72PZAVK","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":"f59062d941c1ce48ae39ebc9876fcc10dcea7dab7a63918e74e0afe37642feeb","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T19:47:20Z","title_canon_sha256":"777bd2631495b7321d7eaa882bf33e64efae68ab9ad08cca5b5b6f236dc6ce6e"},"schema_version":"1.0","source":{"id":"1503.05910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05910","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05910v2","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05910","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"ECXUGH4YQ4FA","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ECXUGH4YQ4FA4ZT7","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ECXUGH4Y","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:23395a5f4b06392477a311485273c03be71812447acf548424c0f8f3b984a15d","target":"graph","created_at":"2026-05-18T00:54:41Z","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":"The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem in terms of isoperimetric or, more generally, closed volume-preserving stable CMC surfaces that is appealing from both a physical and a purely geometric point of view. We also include a proof of the following conjecture of R. Schoen: An asymptotically flat Riemannian $3$-manifold","authors_text":"Alessandro Carlotto, Michael Eichmair, Otis Chodosh","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T19:47:20Z","title":"Effective versions of the positive mass theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05910","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":"sha256:65f24c55b760368f8f3b1fdc18707923793159ae6f8099f990c8fc521f7ded9d","target":"record","created_at":"2026-05-18T00:54:41Z","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":"f59062d941c1ce48ae39ebc9876fcc10dcea7dab7a63918e74e0afe37642feeb","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T19:47:20Z","title_canon_sha256":"777bd2631495b7321d7eaa882bf33e64efae68ab9ad08cca5b5b6f236dc6ce6e"},"schema_version":"1.0","source":{"id":"1503.05910","kind":"arxiv","version":2}},"canonical_sha256":"20af431f98870a0e667f2809fd3f20aa90c95359f4da0f7c37dca5b11bf9ad5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20af431f98870a0e667f2809fd3f20aa90c95359f4da0f7c37dca5b11bf9ad5e","first_computed_at":"2026-05-18T00:54:41.702261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:41.702261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"705EHdOBcZxA+qUuYsr7Nj+ORqJDFvYdtfWV56NhRy525ClCsOD3+AkzWPwoZSVN8JQUoh7Jvjfzi33QUg0EBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:41.702762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65f24c55b760368f8f3b1fdc18707923793159ae6f8099f990c8fc521f7ded9d","sha256:23395a5f4b06392477a311485273c03be71812447acf548424c0f8f3b984a15d"],"state_sha256":"dc78ce3a6715e0135e39d0c5e5f8a187f7c39cf2dbc87e2f0942642dcf0914f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NASES8tXlBp33C+mwjTtkjBa8+tHoD5y0uLZq9l+simrVMOzT6DkXtWc+JSvkXzZLMNAW5TjONECH2ePHOaeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:06:46.149187Z","bundle_sha256":"4a6ea79a255dd511ee1a86c2c56ff177db3346b17b8f9b1566a6ec28b600635b"}}