{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BL6VVM2GNEIASUC345M63XDLJD","short_pith_number":"pith:BL6VVM2G","schema_version":"1.0","canonical_sha256":"0afd5ab346691009505be759eddc6b48c1a48abc80777e103377a20353d5ab98","source":{"kind":"arxiv","id":"1503.04826","version":2},"attestation_state":"computed","paper":{"title":"Convergence of regularized nonlocal interaction energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ihsan Topaloglu, Katy Craig","submitted_at":"2015-03-16T20:04:45Z","abstract_excerpt":"Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energies defined via a repulsive-attractive interaction kernel, regularized by convolution with a mollifier. We prove that, with respect to the 2-Wasserstein metric, the regularized energies $\\Gamma$-converge to the unregularized energy and minimizers converge to minimizers. We then apply our results to prove $\\Gamma$-convergence of the gradient flows, when restricted to the space of measures with bounded density."},"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":"1503.04826","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-16T20:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"11de3209bce5312ae0ed36d8d21a21fc5613e86c028894ea4062078d862a0aa6","abstract_canon_sha256":"ed559c1b062f302dadbfaf3abb611e339e7f79b839be89aa847f793bf7e0789e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:43.020292Z","signature_b64":"6b4qyNYglwza0pmdz56hDR7TKXDY5BYRCWkFPUfCEdI3WvQhXIe/EEI7SD2Ct6ZMa02H/7UqqokCYh98tXlvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0afd5ab346691009505be759eddc6b48c1a48abc80777e103377a20353d5ab98","last_reissued_at":"2026-05-18T01:30:43.019721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:43.019721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of regularized nonlocal interaction energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ihsan Topaloglu, Katy Craig","submitted_at":"2015-03-16T20:04:45Z","abstract_excerpt":"Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energies defined via a repulsive-attractive interaction kernel, regularized by convolution with a mollifier. We prove that, with respect to the 2-Wasserstein metric, the regularized energies $\\Gamma$-converge to the unregularized energy and minimizers converge to minimizers. We then apply our results to prove $\\Gamma$-convergence of the gradient flows, when restricted to the space of measures with bounded density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04826","kind":"arxiv","version":2},"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":"1503.04826","created_at":"2026-05-18T01:30:43.019804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.04826v2","created_at":"2026-05-18T01:30:43.019804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04826","created_at":"2026-05-18T01:30:43.019804+00:00"},{"alias_kind":"pith_short_12","alias_value":"BL6VVM2GNEIA","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BL6VVM2GNEIASUC3","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BL6VVM2G","created_at":"2026-05-18T12:29:14.074870+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/BL6VVM2GNEIASUC345M63XDLJD","json":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD.json","graph_json":"https://pith.science/api/pith-number/BL6VVM2GNEIASUC345M63XDLJD/graph.json","events_json":"https://pith.science/api/pith-number/BL6VVM2GNEIASUC345M63XDLJD/events.json","paper":"https://pith.science/paper/BL6VVM2G"},"agent_actions":{"view_html":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD","download_json":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD.json","view_paper":"https://pith.science/paper/BL6VVM2G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.04826&json=true","fetch_graph":"https://pith.science/api/pith-number/BL6VVM2GNEIASUC345M63XDLJD/graph.json","fetch_events":"https://pith.science/api/pith-number/BL6VVM2GNEIASUC345M63XDLJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD/action/storage_attestation","attest_author":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD/action/author_attestation","sign_citation":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD/action/citation_signature","submit_replication":"https://pith.science/pith/BL6VVM2GNEIASUC345M63XDLJD/action/replication_record"}},"created_at":"2026-05-18T01:30:43.019804+00:00","updated_at":"2026-05-18T01:30:43.019804+00:00"}