{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DJSI7T5M7M7ZT5WZL5MWJCWBV3","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":"ccbefe8e9116c437b664c2972e98c85ab00c82fe1feb93aa78688f26f4a4314b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-15T10:46:05Z","title_canon_sha256":"23617ebbbcf596c3a3bb6e8a08e8ec233d1dfd67103302ebd70024b0aaa08897"},"schema_version":"1.0","source":{"id":"1602.04618","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04618","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04618v5","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04618","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"DJSI7T5M7M7Z","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DJSI7T5M7M7ZT5WZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DJSI7T5M","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:4415636f7f8007713ccabf6255f3e2aeb1dd0257b8b73a33e8078a6c133c5979","target":"graph","created_at":"2026-05-18T00:47:38Z","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 $\\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\\Omega|$. We obtain some properties of the set function $F:\\Omega\\mapsto \\R^+$ defined by $$ F(\\Omega)=\\frac{T(\\Omega)\\lambda_1(\\Omega)}{|\\Omega|} ,$$ where $T(\\Omega)$ and $\\lambda_1(\\Omega)$ are the torsional rigidity and the first eigenvalue of the Dirichlet Laplacian respectively. We improve the classical P\\'olya bound $F(\\Omega)\\le 1,$ and show that $$F(\\Omega)\\le 1- \\nu_m T(\\Omega)|\\Omega|^{-1-\\frac2m},$$ where $\\nu_m$ depends only on $m$. For any $m=2,3,\\dots$ and $\\epsilon\\in (0,1)$ we construct an open set $","authors_text":"C. Nitsch, C. Trombetti, M. van den Berg, V. Ferone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-15T10:46:05Z","title":"On Polya's inequality for torsional rigidity and first Dirichlet eigenvalue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04618","kind":"arxiv","version":5},"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":"sha256:932fd05fb03c700323dc9828e9e7e46600b0210930a0e7369db0c6150b055901","target":"record","created_at":"2026-05-18T00:47:38Z","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":"ccbefe8e9116c437b664c2972e98c85ab00c82fe1feb93aa78688f26f4a4314b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-15T10:46:05Z","title_canon_sha256":"23617ebbbcf596c3a3bb6e8a08e8ec233d1dfd67103302ebd70024b0aaa08897"},"schema_version":"1.0","source":{"id":"1602.04618","kind":"arxiv","version":5}},"canonical_sha256":"1a648fcfacfb3f99f6d95f59648ac1aef739a92c7aa4870205d5902a821b428a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a648fcfacfb3f99f6d95f59648ac1aef739a92c7aa4870205d5902a821b428a","first_computed_at":"2026-05-18T00:47:38.292944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:38.292944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iV1janzkoUh5/Tc+lQCnGqRUkShjtVTdLK9usQnKIUQhv2YyF5nZ7Crm6lepN2hAXCdVhc6TR03rFX8gc01iCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:38.293531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04618","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932fd05fb03c700323dc9828e9e7e46600b0210930a0e7369db0c6150b055901","sha256:4415636f7f8007713ccabf6255f3e2aeb1dd0257b8b73a33e8078a6c133c5979"],"state_sha256":"25774703273eb474f5420b980396f375aa92aa50644693b176d49c16ec90101b"}