{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SAH4QQET4EQT47ZJA2PJ7FMD2F","short_pith_number":"pith:SAH4QQET","schema_version":"1.0","canonical_sha256":"900fc84093e1213e7f29069e9f9583d177664e357db5802609f7ef81a8342fd2","source":{"kind":"arxiv","id":"1310.4110","version":1},"attestation_state":"computed","paper":{"title":"Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni A. Bonaschi, Jos\\'e A. Carrillo, Marco Di Francesco, Mark A. Peletier","submitted_at":"2013-10-15T16:46:03Z","abstract_excerpt":"We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar conservation law on the other. The solution of the former is obtained by spatially differentiating the solution of the latter. The proof uses an intermediate step, namely the $L^2$ gradient flow of the pseudo-inverse distribution function of the gradient flow solution. We use this equivalence to provide a rigorous particle-system approximation to the Wasserstei"},"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":"1310.4110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-15T16:46:03Z","cross_cats_sorted":[],"title_canon_sha256":"6e7f3a81a4ce0cb143822e909535b67f3c149fb69ca5963db0d465320e19b7e0","abstract_canon_sha256":"50c5a11158e130afa6f9039ada42d286b06286c7fcacf921e1dca316b37cf735"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:25.018773Z","signature_b64":"n+qnKX9xgJv6px5NZntK8oIE9Le0C3J6YNFnfGJAz/z5Du18LC9KY6DCafZA0J7KSnYjpfUSNV0UZmhb0oMtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"900fc84093e1213e7f29069e9f9583d177664e357db5802609f7ef81a8342fd2","last_reissued_at":"2026-05-18T03:10:25.018006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:25.018006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni A. Bonaschi, Jos\\'e A. Carrillo, Marco Di Francesco, Mark A. Peletier","submitted_at":"2013-10-15T16:46:03Z","abstract_excerpt":"We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar conservation law on the other. The solution of the former is obtained by spatially differentiating the solution of the latter. The proof uses an intermediate step, namely the $L^2$ gradient flow of the pseudo-inverse distribution function of the gradient flow solution. We use this equivalence to provide a rigorous particle-system approximation to the Wasserstei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4110","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":"1310.4110","created_at":"2026-05-18T03:10:25.018145+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4110v1","created_at":"2026-05-18T03:10:25.018145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4110","created_at":"2026-05-18T03:10:25.018145+00:00"},{"alias_kind":"pith_short_12","alias_value":"SAH4QQET4EQT","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SAH4QQET4EQT47ZJ","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SAH4QQET","created_at":"2026-05-18T12:27:59.945178+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/SAH4QQET4EQT47ZJA2PJ7FMD2F","json":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F.json","graph_json":"https://pith.science/api/pith-number/SAH4QQET4EQT47ZJA2PJ7FMD2F/graph.json","events_json":"https://pith.science/api/pith-number/SAH4QQET4EQT47ZJA2PJ7FMD2F/events.json","paper":"https://pith.science/paper/SAH4QQET"},"agent_actions":{"view_html":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F","download_json":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F.json","view_paper":"https://pith.science/paper/SAH4QQET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4110&json=true","fetch_graph":"https://pith.science/api/pith-number/SAH4QQET4EQT47ZJA2PJ7FMD2F/graph.json","fetch_events":"https://pith.science/api/pith-number/SAH4QQET4EQT47ZJA2PJ7FMD2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F/action/storage_attestation","attest_author":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F/action/author_attestation","sign_citation":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F/action/citation_signature","submit_replication":"https://pith.science/pith/SAH4QQET4EQT47ZJA2PJ7FMD2F/action/replication_record"}},"created_at":"2026-05-18T03:10:25.018145+00:00","updated_at":"2026-05-18T03:10:25.018145+00:00"}