{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CKIBDK5FMCUB5HSF62YCEQU252","short_pith_number":"pith:CKIBDK5F","schema_version":"1.0","canonical_sha256":"129011aba560a81e9e45f6b022429aeebb140ed105c61e4718031800a7268a7b","source":{"kind":"arxiv","id":"1610.04449","version":1},"attestation_state":"computed","paper":{"title":"Remark on a nonlocal isoperimetric problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vesa Julin","submitted_at":"2016-10-14T13:21:26Z","abstract_excerpt":"We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta-Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.04449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-14T13:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"afc42e236e0b6ae06a205d30eca2a357c1075152591647e6089479e505bc5aa8","abstract_canon_sha256":"98d7fcd2af23c261358e53ee63be9a1e8de79ece72545af580a7602f678fb0c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:15.162444Z","signature_b64":"FmH2+lyNGAg3x53I0vpwqzNQw8VTUz2/eCLg6ocodcgUBWzjnCs1KXT6VE8H67m88g70i0vfYgLYTDSbuYrRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"129011aba560a81e9e45f6b022429aeebb140ed105c61e4718031800a7268a7b","last_reissued_at":"2026-05-18T01:02:15.161876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:15.161876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remark on a nonlocal isoperimetric problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vesa Julin","submitted_at":"2016-10-14T13:21:26Z","abstract_excerpt":"We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta-Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04449","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.04449","created_at":"2026-05-18T01:02:15.161952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04449v1","created_at":"2026-05-18T01:02:15.161952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04449","created_at":"2026-05-18T01:02:15.161952+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKIBDK5FMCUB","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKIBDK5FMCUB5HSF","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKIBDK5F","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252","json":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252.json","graph_json":"https://pith.science/api/pith-number/CKIBDK5FMCUB5HSF62YCEQU252/graph.json","events_json":"https://pith.science/api/pith-number/CKIBDK5FMCUB5HSF62YCEQU252/events.json","paper":"https://pith.science/paper/CKIBDK5F"},"agent_actions":{"view_html":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252","download_json":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252.json","view_paper":"https://pith.science/paper/CKIBDK5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04449&json=true","fetch_graph":"https://pith.science/api/pith-number/CKIBDK5FMCUB5HSF62YCEQU252/graph.json","fetch_events":"https://pith.science/api/pith-number/CKIBDK5FMCUB5HSF62YCEQU252/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252/action/storage_attestation","attest_author":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252/action/author_attestation","sign_citation":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252/action/citation_signature","submit_replication":"https://pith.science/pith/CKIBDK5FMCUB5HSF62YCEQU252/action/replication_record"}},"created_at":"2026-05-18T01:02:15.161952+00:00","updated_at":"2026-05-18T01:02:15.161952+00:00"}