{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MWCLTYYWPZJ2WJBCRBLU52QY5T","short_pith_number":"pith:MWCLTYYW","schema_version":"1.0","canonical_sha256":"6584b9e3167e53ab242288574eea18ecc4b4897221707c708ebe5ed924264bdc","source":{"kind":"arxiv","id":"1404.7062","version":2},"attestation_state":"computed","paper":{"title":"Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marco Di Francesco, Massimiliano D. Rosini","submitted_at":"2014-04-28T17:16:53Z","abstract_excerpt":"We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $L^1_{loc}$) to the unique Kruzkov entropy solution of t"},"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":"1404.7062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-28T17:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"6da0cb57ed62159bb3e4b5eb4f74f7be987eff46d287ab2fbd400a529989c92b","abstract_canon_sha256":"510d2a65f5569b05e8cebab541276104317eeb0b2377b789f294943416cc066a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:22.549347Z","signature_b64":"hMAyjVQagFFxjX8c9W8KZoDYk2hqjfwR01zVyzQcFX9KM+52iRs+77wPYR5V56bVC2vD/xSfzTNkLu1jWtMBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6584b9e3167e53ab242288574eea18ecc4b4897221707c708ebe5ed924264bdc","last_reissued_at":"2026-05-18T01:43:22.548628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:22.548628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marco Di Francesco, Massimiliano D. Rosini","submitted_at":"2014-04-28T17:16:53Z","abstract_excerpt":"We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $L^1_{loc}$) to the unique Kruzkov entropy solution of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7062","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":"1404.7062","created_at":"2026-05-18T01:43:22.548740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.7062v2","created_at":"2026-05-18T01:43:22.548740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7062","created_at":"2026-05-18T01:43:22.548740+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWCLTYYWPZJ2","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWCLTYYWPZJ2WJBC","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWCLTYYW","created_at":"2026-05-18T12:28:38.356838+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/MWCLTYYWPZJ2WJBCRBLU52QY5T","json":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T.json","graph_json":"https://pith.science/api/pith-number/MWCLTYYWPZJ2WJBCRBLU52QY5T/graph.json","events_json":"https://pith.science/api/pith-number/MWCLTYYWPZJ2WJBCRBLU52QY5T/events.json","paper":"https://pith.science/paper/MWCLTYYW"},"agent_actions":{"view_html":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T","download_json":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T.json","view_paper":"https://pith.science/paper/MWCLTYYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.7062&json=true","fetch_graph":"https://pith.science/api/pith-number/MWCLTYYWPZJ2WJBCRBLU52QY5T/graph.json","fetch_events":"https://pith.science/api/pith-number/MWCLTYYWPZJ2WJBCRBLU52QY5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T/action/storage_attestation","attest_author":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T/action/author_attestation","sign_citation":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T/action/citation_signature","submit_replication":"https://pith.science/pith/MWCLTYYWPZJ2WJBCRBLU52QY5T/action/replication_record"}},"created_at":"2026-05-18T01:43:22.548740+00:00","updated_at":"2026-05-18T01:43:22.548740+00:00"}