{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GZV54VDMDLR63CEJZ7HJMVBVCU","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":"26b55ae905d39bbf4a2b5d0044ec6ce43c5cf30df85780cc4fba9664f088fb5e","cross_cats_sorted":["math-ph","math.CA","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-07-25T18:59:04Z","title_canon_sha256":"c5bde1fd5601555ccbc2cd8b37baf380743873bb963144659293cae6160c58e6"},"schema_version":"1.0","source":{"id":"2307.13769","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.13769","created_at":"2026-07-05T07:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"2307.13769v3","created_at":"2026-07-05T07:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.13769","created_at":"2026-07-05T07:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"GZV54VDMDLR6","created_at":"2026-07-05T07:15:57Z"},{"alias_kind":"pith_short_16","alias_value":"GZV54VDMDLR63CEJ","created_at":"2026-07-05T07:15:57Z"},{"alias_kind":"pith_short_8","alias_value":"GZV54VDM","created_at":"2026-07-05T07:15:57Z"}],"graph_snapshots":[{"event_id":"sha256:4e7e51bdcae9b3dde402e08745d2db08fb3aef491aad87da68b41c6931c8e575","target":"graph","created_at":"2026-07-05T07:15:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.13769/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.","authors_text":"Rupert L. Frank, Ryan W. Matzke","cross_cats":["math-ph","math.CA","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-07-25T18:59:04Z","title":"Minimizers for an aggregation model with attractive-repulsive interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.13769","kind":"arxiv","version":3},"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":"sha256:28e6ffa1d7360235fb0e4f8a97122714b28d1a0bfff9e1ca4cf317d828e00fb0","target":"record","created_at":"2026-07-05T07:15:57Z","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":"26b55ae905d39bbf4a2b5d0044ec6ce43c5cf30df85780cc4fba9664f088fb5e","cross_cats_sorted":["math-ph","math.CA","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-07-25T18:59:04Z","title_canon_sha256":"c5bde1fd5601555ccbc2cd8b37baf380743873bb963144659293cae6160c58e6"},"schema_version":"1.0","source":{"id":"2307.13769","kind":"arxiv","version":3}},"canonical_sha256":"366bde546c1ae3ed8889cfce9654351520c7fa0f0f8153cfe479871603be94df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"366bde546c1ae3ed8889cfce9654351520c7fa0f0f8153cfe479871603be94df","first_computed_at":"2026-07-05T07:15:57.911089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:15:57.911089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nk39lT3RFmxtfWNGUy4mQfFbqcY/h74DUARvlcbQ1Ms1YughhCJGU0+n0z10Md84zktLrGRPOnawzwhquh3GAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:15:57.911692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.13769","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e6ffa1d7360235fb0e4f8a97122714b28d1a0bfff9e1ca4cf317d828e00fb0","sha256:4e7e51bdcae9b3dde402e08745d2db08fb3aef491aad87da68b41c6931c8e575"],"state_sha256":"f21d088a96167106b75c18d54e26d5a5023e1b433d762ae095b4542fdefb940e"}