{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5EEA4SOISVHX5IOTW5G5SRYIIC","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":"2aefb2a4b48445c0d1058f04269d884469ae574cba9bc0c23e37362505370a60","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-30T17:05:25Z","title_canon_sha256":"11dacaa969051f270a8020dbc758533786026cd5f7598ef8cc84efbbfd6ef57e"},"schema_version":"1.0","source":{"id":"1501.07845","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07845","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07845v3","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07845","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"5EEA4SOISVHX","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5EEA4SOISVHX5IOT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5EEA4SOI","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:b45b15158328462a85be264b3329be07593e15a4f2f653fc67e1cb1f849a8755","target":"graph","created_at":"2026-05-18T01:23:04Z","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":"We prove the following quantitative version of the celebrated Soap Bubble Theorem of Alexandrov. Let $S$ be a $C^2$ closed embedded hypersurface of $\\mathbb{R}^{n+1}$, $n\\geq1$, and denote by $osc(H)$ the oscillation of its mean curvature. We prove that there exists a positive $\\varepsilon$, depending on $n$ and upper bounds on the area and the $C^2$-regularity of $S$, such that if $osc(H) \\leq \\varepsilon$ then there exist two concentric balls $B_{r_i}$ and $B_{r_e}$ such that $S \\subset \\overline{B}_{r_e} \\setminus B_{r_i}$ and $r_e -r_i \\leq C \\, osc(H)$, with $C$ depending only on $n$ and ","authors_text":"Giulio Ciraolo, Luigi Vezzoni","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-30T17:05:25Z","title":"A sharp quantitative version of Alexandrov's theorem via the method of moving planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07845","kind":"arxiv","version":3},"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:cc55bdac214fbf6a1a6b1a7bf8504330cab9d02e4bb91b89d26ccc583b58f9f8","target":"record","created_at":"2026-05-18T01:23:04Z","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":"2aefb2a4b48445c0d1058f04269d884469ae574cba9bc0c23e37362505370a60","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-30T17:05:25Z","title_canon_sha256":"11dacaa969051f270a8020dbc758533786026cd5f7598ef8cc84efbbfd6ef57e"},"schema_version":"1.0","source":{"id":"1501.07845","kind":"arxiv","version":3}},"canonical_sha256":"e9080e49c8954f7ea1d3b74dd94708408d2bdd67a0fc998bd77cb227bf2ce4d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9080e49c8954f7ea1d3b74dd94708408d2bdd67a0fc998bd77cb227bf2ce4d6","first_computed_at":"2026-05-18T01:23:04.314493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:04.314493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gfKE8nVatEDi23rmFbwmbgGpNCkm69B8H3eLibkDnf6l3EQXYsmGkjenOa6LNa9vTsNzp1Dfs5IdCmrYZjWnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:04.315143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07845","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc55bdac214fbf6a1a6b1a7bf8504330cab9d02e4bb91b89d26ccc583b58f9f8","sha256:b45b15158328462a85be264b3329be07593e15a4f2f653fc67e1cb1f849a8755"],"state_sha256":"a3a90fd825add316792b3a031674faaf9f4ea9bb00bf5423f57d9c8352411d92"}