{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SJMWVRAGY2IW3E73GPER22DVAA","short_pith_number":"pith:SJMWVRAG","schema_version":"1.0","canonical_sha256":"92596ac406c6916d93fb33c91d6875001e3e09471ff3e533c921d38c5e768a05","source":{"kind":"arxiv","id":"1805.01766","version":1},"attestation_state":"computed","paper":{"title":"Vanishing Viscosity Solutions for Conservation Laws with Regulated Flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Bressan, Graziano Guerra, Wen Shen","submitted_at":"2018-05-04T13:33:49Z","abstract_excerpt":"In this paper we introduce a concept of \"regulated function\" $v(t,x)$ of two variables, which reduces to the classical definition when $v$ is independent of $t$. We then consider a scalar conservation law of the form $u_t+F(v(t,x),u)_x=0$, where $F$ is smooth and $v$ is a regulated function, possibly discontinuous w.r.t.both $t$ and $x$. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved, relying on comparison estimates for solutions to the corresponding Hamilton--Jacobi equation."},"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":"1805.01766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-04T13:33:49Z","cross_cats_sorted":[],"title_canon_sha256":"69c0d8be60eeb5f6cc067c4826c3ec89e5ae2894be4d8fbafce4f0006ee979d0","abstract_canon_sha256":"464669fdc8cfb5c798928b6617c9a76a32a8adc83572a059554c92a6c07723a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:46.758767Z","signature_b64":"XlMVacsh0IVynFBiI1JIe/V5cRATnwycVN+JyHunTw3ElKoehnnJLRcefpDBeaYVEs0RQIQCL9rwDwr6QIU6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92596ac406c6916d93fb33c91d6875001e3e09471ff3e533c921d38c5e768a05","last_reissued_at":"2026-05-18T00:16:46.758212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:46.758212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing Viscosity Solutions for Conservation Laws with Regulated Flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Bressan, Graziano Guerra, Wen Shen","submitted_at":"2018-05-04T13:33:49Z","abstract_excerpt":"In this paper we introduce a concept of \"regulated function\" $v(t,x)$ of two variables, which reduces to the classical definition when $v$ is independent of $t$. We then consider a scalar conservation law of the form $u_t+F(v(t,x),u)_x=0$, where $F$ is smooth and $v$ is a regulated function, possibly discontinuous w.r.t.both $t$ and $x$. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved, relying on comparison estimates for solutions to the corresponding Hamilton--Jacobi equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01766","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":"1805.01766","created_at":"2026-05-18T00:16:46.758290+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01766v1","created_at":"2026-05-18T00:16:46.758290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01766","created_at":"2026-05-18T00:16:46.758290+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJMWVRAGY2IW","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJMWVRAGY2IW3E73","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJMWVRAG","created_at":"2026-05-18T12:32:53.628368+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/SJMWVRAGY2IW3E73GPER22DVAA","json":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA.json","graph_json":"https://pith.science/api/pith-number/SJMWVRAGY2IW3E73GPER22DVAA/graph.json","events_json":"https://pith.science/api/pith-number/SJMWVRAGY2IW3E73GPER22DVAA/events.json","paper":"https://pith.science/paper/SJMWVRAG"},"agent_actions":{"view_html":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA","download_json":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA.json","view_paper":"https://pith.science/paper/SJMWVRAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01766&json=true","fetch_graph":"https://pith.science/api/pith-number/SJMWVRAGY2IW3E73GPER22DVAA/graph.json","fetch_events":"https://pith.science/api/pith-number/SJMWVRAGY2IW3E73GPER22DVAA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA/action/storage_attestation","attest_author":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA/action/author_attestation","sign_citation":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA/action/citation_signature","submit_replication":"https://pith.science/pith/SJMWVRAGY2IW3E73GPER22DVAA/action/replication_record"}},"created_at":"2026-05-18T00:16:46.758290+00:00","updated_at":"2026-05-18T00:16:46.758290+00:00"}