{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GZV54VDMDLR63CEJZ7HJMVBVCU","short_pith_number":"pith:GZV54VDM","canonical_record":{"source":{"id":"2307.13769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-07-25T18:59:04Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.OC"],"title_canon_sha256":"c5bde1fd5601555ccbc2cd8b37baf380743873bb963144659293cae6160c58e6","abstract_canon_sha256":"26b55ae905d39bbf4a2b5d0044ec6ce43c5cf30df85780cc4fba9664f088fb5e"},"schema_version":"1.0"},"canonical_sha256":"366bde546c1ae3ed8889cfce9654351520c7fa0f0f8153cfe479871603be94df","source":{"kind":"arxiv","id":"2307.13769","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GZV54VDMDLR63CEJZ7HJMVBVCU","target":"record","payload":{"canonical_record":{"source":{"id":"2307.13769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-07-25T18:59:04Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.OC"],"title_canon_sha256":"c5bde1fd5601555ccbc2cd8b37baf380743873bb963144659293cae6160c58e6","abstract_canon_sha256":"26b55ae905d39bbf4a2b5d0044ec6ce43c5cf30df85780cc4fba9664f088fb5e"},"schema_version":"1.0"},"canonical_sha256":"366bde546c1ae3ed8889cfce9654351520c7fa0f0f8153cfe479871603be94df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:15:57.911692Z","signature_b64":"Nk39lT3RFmxtfWNGUy4mQfFbqcY/h74DUARvlcbQ1Ms1YughhCJGU0+n0z10Md84zktLrGRPOnawzwhquh3GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"366bde546c1ae3ed8889cfce9654351520c7fa0f0f8153cfe479871603be94df","last_reissued_at":"2026-07-05T07:15:57.911089Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:15:57.911089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.13769","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GN7EJQOxfOGigotupj0HgaZsETKAI9lkLC6Jf8+26KYXK0E566GPvmkSwQrP2MdOP9gOkIZ/hkTBLH2bsF6EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:47:35.386016Z"},"content_sha256":"28e6ffa1d7360235fb0e4f8a97122714b28d1a0bfff9e1ca4cf317d828e00fb0","schema_version":"1.0","event_id":"sha256:28e6ffa1d7360235fb0e4f8a97122714b28d1a0bfff9e1ca4cf317d828e00fb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GZV54VDMDLR63CEJZ7HJMVBVCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimizers for an aggregation model with attractive-repulsive interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.OC"],"primary_cat":"math.AP","authors_text":"Rupert L. Frank, Ryan W. Matzke","submitted_at":"2023-07-25T18:59:04Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.13769","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.13769/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNgkrjAMJe4/4nOBhUrci40/EthSZRdxortNmo6nlW1vwI1d9VThFMfRgNSgCY4imgg0yJymgfyk63KA3VM+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:47:35.386635Z"},"content_sha256":"4e7e51bdcae9b3dde402e08745d2db08fb3aef491aad87da68b41c6931c8e575","schema_version":"1.0","event_id":"sha256:4e7e51bdcae9b3dde402e08745d2db08fb3aef491aad87da68b41c6931c8e575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/bundle.json","state_url":"https://pith.science/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T23:47:35Z","links":{"resolver":"https://pith.science/pith/GZV54VDMDLR63CEJZ7HJMVBVCU","bundle":"https://pith.science/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/bundle.json","state":"https://pith.science/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZV54VDMDLR63CEJZ7HJMVBVCU/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fo7K15iNlL3GBatnEukkO44KEKQbsoBpSy6d39Ijn0jrYIRVdIIj1x89s7CxZFopnflOd3kxxDA1LeZPeowDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T23:47:35.391375Z","bundle_sha256":"0111faf998a9ce3fa8f3949b895b2d6dbe805c4395c95f3a3f0d2d91d977667e"}}