{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:M7IW5JTKVWOYORGPUTFKRYZ5SB","short_pith_number":"pith:M7IW5JTK","schema_version":"1.0","canonical_sha256":"67d16ea66aad9d8744cfa4caa8e33d9045e2c9b6626ab723373a3d0c9fbcf4f6","source":{"kind":"arxiv","id":"1112.5649","version":2},"attestation_state":"computed","paper":{"title":"Riemann solver for a kinematic wave traffic model with discontinuous flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Jeffrey K. Wiens, JF Williams, John M. Stockie","submitted_at":"2011-12-23T20:08:28Z","abstract_excerpt":"We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the flux function over a small distance epsilon << 1 and then the analytical solution to the corresponding Riemann problem is derived in the limit as epsilon goes to 0. For certain initial data, the Riemann problem can give rise to zero waves that propagate with infinite speed but have zero strength. We propose a Godunov-type numerical scheme that avoids the otherw"},"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":"1112.5649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T20:08:28Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"02825dbb0832000584b7bcfd56d784f7d5a83574a6577ba8ba6b4cec68b91a42","abstract_canon_sha256":"da3cb2caba5d498d7fbc5f8ccfa15509bffdd847fb7605e6236c368fd48881d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:35.265191Z","signature_b64":"zgAzvlwUNbbcGrehqpxZgZ80TYLV3YvTVV3qkHtu8WRsQeI2LD3/dBL2W4mlYYXOEtSjv/Vo79skoPZRewIeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67d16ea66aad9d8744cfa4caa8e33d9045e2c9b6626ab723373a3d0c9fbcf4f6","last_reissued_at":"2026-05-18T03:25:35.264424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:35.264424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riemann solver for a kinematic wave traffic model with discontinuous flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Jeffrey K. Wiens, JF Williams, John M. Stockie","submitted_at":"2011-12-23T20:08:28Z","abstract_excerpt":"We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the flux function over a small distance epsilon << 1 and then the analytical solution to the corresponding Riemann problem is derived in the limit as epsilon goes to 0. For certain initial data, the Riemann problem can give rise to zero waves that propagate with infinite speed but have zero strength. We propose a Godunov-type numerical scheme that avoids the otherw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5649","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":"1112.5649","created_at":"2026-05-18T03:25:35.264568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5649v2","created_at":"2026-05-18T03:25:35.264568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5649","created_at":"2026-05-18T03:25:35.264568+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7IW5JTKVWOY","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7IW5JTKVWOYORGP","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7IW5JTK","created_at":"2026-05-18T12:26:34.985390+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/M7IW5JTKVWOYORGPUTFKRYZ5SB","json":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB.json","graph_json":"https://pith.science/api/pith-number/M7IW5JTKVWOYORGPUTFKRYZ5SB/graph.json","events_json":"https://pith.science/api/pith-number/M7IW5JTKVWOYORGPUTFKRYZ5SB/events.json","paper":"https://pith.science/paper/M7IW5JTK"},"agent_actions":{"view_html":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB","download_json":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB.json","view_paper":"https://pith.science/paper/M7IW5JTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5649&json=true","fetch_graph":"https://pith.science/api/pith-number/M7IW5JTKVWOYORGPUTFKRYZ5SB/graph.json","fetch_events":"https://pith.science/api/pith-number/M7IW5JTKVWOYORGPUTFKRYZ5SB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB/action/storage_attestation","attest_author":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB/action/author_attestation","sign_citation":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB/action/citation_signature","submit_replication":"https://pith.science/pith/M7IW5JTKVWOYORGPUTFKRYZ5SB/action/replication_record"}},"created_at":"2026-05-18T03:25:35.264568+00:00","updated_at":"2026-05-18T03:25:35.264568+00:00"}