{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NSNLEH6T6Y5BK2KVMRX5ONG46N","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":"02b147f6c6449f31f49196db56aa0be14308137ac887bff297a633aeae522ef2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-30T11:08:47Z","title_canon_sha256":"67dea15332cb4ff4e6f24bca1f7a7d62dd660329ce3b66ab2298e00a741cab86"},"schema_version":"1.0","source":{"id":"1309.7796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7796","created_at":"2026-05-18T03:11:48Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7796v1","created_at":"2026-05-18T03:11:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7796","created_at":"2026-05-18T03:11:48Z"},{"alias_kind":"pith_short_12","alias_value":"NSNLEH6T6Y5B","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NSNLEH6T6Y5BK2KV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NSNLEH6T","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:4c4997a7da1ec7b0952c60518c45d320d496ee19cc3e3d3ab9e9b2d47c8289ef","target":"graph","created_at":"2026-05-18T03:11:48Z","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":"Let $\\,(M,g)\\,$ be a $n$-dimensional Riemannian manifold and $\\,\\Omega\\,$ be any compact connected domain in $\\,M$. We study the problem of finding the {\\em maxima} of the functional $\\, {\\mathcal E} (\\Omega)\\,$ (known as {\\em torsional rigidity} associated to $\\Omega$) among all domains of prescribed volume $v$. Our results show that for a given Riemannian manifold which is strictly isoperimetric at one of its points the maximum of such functional is realized by the geodesic ball centered at this point. More generally, we prove estimates for the functional $\\, {\\mathcal E} (\\Omega)\\,$ by comp","authors_text":"Andrea Loi, Lucio Cadeddu, Sylvestre Gallot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-30T11:08:47Z","title":"Maximizing torsional rigidity on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7796","kind":"arxiv","version":1},"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:fed8399b648ded6da66f079dbf348c91298fb932698fcfff633c179fdd81ffc3","target":"record","created_at":"2026-05-18T03:11:48Z","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":"02b147f6c6449f31f49196db56aa0be14308137ac887bff297a633aeae522ef2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-30T11:08:47Z","title_canon_sha256":"67dea15332cb4ff4e6f24bca1f7a7d62dd660329ce3b66ab2298e00a741cab86"},"schema_version":"1.0","source":{"id":"1309.7796","kind":"arxiv","version":1}},"canonical_sha256":"6c9ab21fd3f63a156955646fd734dcf3621e771a1cbf3329a2e2dcdb817dc90c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c9ab21fd3f63a156955646fd734dcf3621e771a1cbf3329a2e2dcdb817dc90c","first_computed_at":"2026-05-18T03:11:48.256276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:48.256276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4UDxGkdnbwxokgUGi2OCzClpP4Wjtfc548lZmxqIiQ1REz+7G3MqL37aKAqa1j8J+VvsBxOYNQNvCETbJC4WBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:48.257128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fed8399b648ded6da66f079dbf348c91298fb932698fcfff633c179fdd81ffc3","sha256:4c4997a7da1ec7b0952c60518c45d320d496ee19cc3e3d3ab9e9b2d47c8289ef"],"state_sha256":"d0cce3348bd230c79f5998e4e150e28d2932f2b9f4bed7b4c0393ec1ee2d14b3"}