{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LLLODYG633HK6YZWFKXQCMNTIQ","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":"ff73e1082b8c1e00db7da3140c7ff7cccb3cdf4ee98cb74fb80d96ba4c1e3682","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T22:49:23Z","title_canon_sha256":"1c8b027bfee3c43fad136ea3a9870fd74e38ab9112b86fefdac265eddf30c169"},"schema_version":"1.0","source":{"id":"1301.5032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5032","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5032v2","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5032","created_at":"2026-05-18T03:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"LLLODYG633HK","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LLLODYG633HK6YZW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LLLODYG6","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:87820bbcd96fa7650e8a17a68a5a06c6c0dc3a8521f40fdab856a6b0c3b32243","target":"graph","created_at":"2026-05-18T03:25:46Z","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":"There is a family of potentials that minimize the lowest eigenvalue of a Schr\\\"odinger eigenvalue under the constraint of a given L^p norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We also prove a stability estimate for H\\\"older's inequality, which we believe to be new.","authors_text":"Elliott H. Lieb, Eric A. Carlen, Rupert L. Frank","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T22:49:23Z","title":"Stability estimates for the lowest eigenvalue of a Schr\\\"odinger operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5032","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":"sha256:25a087839514fa2d04644d8d2bffb8bfd1481182d57bdd59930fd70c4312d36a","target":"record","created_at":"2026-05-18T03:25:46Z","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":"ff73e1082b8c1e00db7da3140c7ff7cccb3cdf4ee98cb74fb80d96ba4c1e3682","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T22:49:23Z","title_canon_sha256":"1c8b027bfee3c43fad136ea3a9870fd74e38ab9112b86fefdac265eddf30c169"},"schema_version":"1.0","source":{"id":"1301.5032","kind":"arxiv","version":2}},"canonical_sha256":"5ad6e1e0dedeceaf63362aaf0131b34414db85a8269b3501fad3fb6454c27585","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ad6e1e0dedeceaf63362aaf0131b34414db85a8269b3501fad3fb6454c27585","first_computed_at":"2026-05-18T03:25:46.125594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:46.125594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xd/kbgekScX8bq5rnQsJ4DJP8NiELVLwFfM3a9Th7Ae2lubwBwkjGzk6FGL1/ej9DfO2vfnXYzWfczxn/qR2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:46.126422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a087839514fa2d04644d8d2bffb8bfd1481182d57bdd59930fd70c4312d36a","sha256:87820bbcd96fa7650e8a17a68a5a06c6c0dc3a8521f40fdab856a6b0c3b32243"],"state_sha256":"09ea9d1b95505fca971f80d050d0457a8c3bf8c2ab464619e6ca93f9b94919ee"}