{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P6AAZVHR3P4AX3Z7NJHFROYVOA","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":"5f054dcfc035fb32e3dc44566b349ce8dc408b88d27f988fef221b5bf6eda73d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-21T10:02:23Z","title_canon_sha256":"f77307c9c34eae9593fb814cff2252fb00ba923b082963cdeefa3c2a94cf86d0"},"schema_version":"1.0","source":{"id":"1611.06704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06704","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06704v1","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06704","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"P6AAZVHR3P4A","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P6AAZVHR3P4AX3Z7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P6AAZVHR","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:b834a31b5c2b77f66235436101a8756bc72e273bf9c4c54fb01f3a2bca701e35","target":"graph","created_at":"2026-05-18T00:57:33Z","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 a quantitative Faber-Krahn inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions. The asymmetry term involves the square power of the Fraenkel asymmetry, multiplied by a constant depending on the Robin parameter, the dimension of the space and the measure of the set.","authors_text":"C. Nitsch, C. Trombetti, D. Bucur, V. Ferone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-21T10:02:23Z","title":"The quantitative Faber-Krahn inequality for the Robin Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06704","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":"sha256:41ad56dad8496655f3ae542e8096d0d3ea1f3e055bf808db866ef0c3b1fd7a3d","target":"record","created_at":"2026-05-18T00:57:33Z","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":"5f054dcfc035fb32e3dc44566b349ce8dc408b88d27f988fef221b5bf6eda73d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-21T10:02:23Z","title_canon_sha256":"f77307c9c34eae9593fb814cff2252fb00ba923b082963cdeefa3c2a94cf86d0"},"schema_version":"1.0","source":{"id":"1611.06704","kind":"arxiv","version":1}},"canonical_sha256":"7f800cd4f1dbf80bef3f6a4e58bb15700d70fe6eb15b91cb4ff527fb6a4da8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f800cd4f1dbf80bef3f6a4e58bb15700d70fe6eb15b91cb4ff527fb6a4da8df","first_computed_at":"2026-05-18T00:57:33.125766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:33.125766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hqx6czUeodXtGlvkEH0suUCts7+1At+fz3qxMyqDfGfWcVG6artAnYbM5ty+IuyFTQJVbs5PuRyviZnxYFL2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:33.126447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ad56dad8496655f3ae542e8096d0d3ea1f3e055bf808db866ef0c3b1fd7a3d","sha256:b834a31b5c2b77f66235436101a8756bc72e273bf9c4c54fb01f3a2bca701e35"],"state_sha256":"009c07d2ce839eaf4fc1dfddde76723b4e6f3184987214d47ee0d198740d5b61"}