{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DRNV2ZGRWQNDAUHKEZAS6LGWDS","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":"d00cf34b010b27117763530f222d2f94d0cbd73e6cb63745179b7f6e1b6beaff","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-21T12:07:36Z","title_canon_sha256":"0b87cf9a954f3dc42e0e8c328482c75a6fe89d71fc1921417d29718d7c99e3e5"},"schema_version":"1.0","source":{"id":"1506.06355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06355","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06355v2","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06355","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"DRNV2ZGRWQND","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DRNV2ZGRWQNDAUHK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DRNV2ZGR","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:950dae4c975267b4ee2f71804215190c003a0aba0f87c8528959797f207a4003","target":"graph","created_at":"2026-05-18T01:28:54Z","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":"In this note we prove that the ball is a maximiser of some Schatten $p$-norms of the Riesz potential operators among all domains of a given measure in $\\mathbb R^{d}$. In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one considered by M. Kac in the case of the Laplacian, so we obtain and isoperimetric inequalities for its eigenvalues as well, namely, analogues of Rayleigh-Faber-Krahn and Hong-Krahn-Szeg\\\"o inequalities.","authors_text":"Durvudkhan Suragan, Grigori Rozenblum, Michael Ruzhansky","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-21T12:07:36Z","title":"Isoperimetric inequalities for Schatten norms of Riesz potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06355","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":"sha256:202991929778471d6ff47ecd2f6ca1509ddae73ac1033f15609e29ae29a088b2","target":"record","created_at":"2026-05-18T01:28:54Z","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":"d00cf34b010b27117763530f222d2f94d0cbd73e6cb63745179b7f6e1b6beaff","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-21T12:07:36Z","title_canon_sha256":"0b87cf9a954f3dc42e0e8c328482c75a6fe89d71fc1921417d29718d7c99e3e5"},"schema_version":"1.0","source":{"id":"1506.06355","kind":"arxiv","version":2}},"canonical_sha256":"1c5b5d64d1b41a3050ea26412f2cd61cac84b7cbc8e8af578877cb9b2fef0084","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c5b5d64d1b41a3050ea26412f2cd61cac84b7cbc8e8af578877cb9b2fef0084","first_computed_at":"2026-05-18T01:28:54.758582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:54.758582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Biv9sMu7xzX/Rb1FGQU2W6KxrXgQDO6rIb8ryRFq93NBoOr/TJriiYG1HGUmVOOhb13tztRSUVkLEULbDj4NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:54.759203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202991929778471d6ff47ecd2f6ca1509ddae73ac1033f15609e29ae29a088b2","sha256:950dae4c975267b4ee2f71804215190c003a0aba0f87c8528959797f207a4003"],"state_sha256":"8367cc163b8ee3e7ce8451ee632d3037db9193e4ea2df8b6f53ef7b8bcbacb40"}