{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AHCMS2ZHXM5PTPRGT4Y5LAGPQF","short_pith_number":"pith:AHCMS2ZH","schema_version":"1.0","canonical_sha256":"01c4c96b27bb3af9be269f31d580cf8174e33e3e0f79a2ee896da560e2570ada","source":{"kind":"arxiv","id":"2605.15629","version":1},"attestation_state":"computed","paper":{"title":"Rigorous Construction of Stop-and-Go Waves in the Optimal Velocity Model via a Difference-Differential Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The optimal velocity model admits rigorous heteroclinic traveling waves and large-period periodic stop-and-go solutions for sufficiently steep velocity functions.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kota Ikeda, Tomoyuki Miyaji","submitted_at":"2026-05-15T05:28:42Z","abstract_excerpt":"Nonlinear wave phenomena such as stop-and-go traffic patterns are widely observed in vehicular flow but remain challenging to describe within a rigorous mathematical framework. Motivated by this, we investigate nonlinear wave structures in the optimal velocity (OV) model, which is a fundamental microscopic traffic flow model describing the car-following dynamics on a circuit. Using a traveling-wave formulation for vehicle headways, we reduce the original ordinary differential system to a difference-differential equation. We focus on steep OV functions approaching a step function, which generat"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.15629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-15T05:28:42Z","cross_cats_sorted":[],"title_canon_sha256":"2c4cfafee2b1958a242c201fef110aae9b0961713bee7daf69faa02142098549","abstract_canon_sha256":"ab35f05acf1ff09dd465a381bdf77b3999a732a59dca37b7d0453a730a342706"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:08.971060Z","signature_b64":"GsqwZw4DElEdkX/FLwmHQ6ALHd6NEW/yVLz3uPt//Wuyvpp+7pRsPXCLZfolC3OO+C6x/Hzomau1o21EIoGVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01c4c96b27bb3af9be269f31d580cf8174e33e3e0f79a2ee896da560e2570ada","last_reissued_at":"2026-05-20T00:01:08.970360Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:08.970360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous Construction of Stop-and-Go Waves in the Optimal Velocity Model via a Difference-Differential Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The optimal velocity model admits rigorous heteroclinic traveling waves and large-period periodic stop-and-go solutions for sufficiently steep velocity functions.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kota Ikeda, Tomoyuki Miyaji","submitted_at":"2026-05-15T05:28:42Z","abstract_excerpt":"Nonlinear wave phenomena such as stop-and-go traffic patterns are widely observed in vehicular flow but remain challenging to describe within a rigorous mathematical framework. Motivated by this, we investigate nonlinear wave structures in the optimal velocity (OV) model, which is a fundamental microscopic traffic flow model describing the car-following dynamics on a circuit. Using a traveling-wave formulation for vehicle headways, we reduce the original ordinary differential system to a difference-differential equation. We focus on steep OV functions approaching a step function, which generat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We rigorously prove the existence of heteroclinic traveling waves for sufficiently steep OV functions, the existence of homoclinic solutions with a necessary condition on the amplitude parameter, and the existence of large-period periodic solutions comprising alternating transition layers and quasi-uniform states under the global road-length constraint.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The optimal velocity function must be sufficiently steep and approach a step function so that the singular-limit analysis produces sharp, explicitly constructible transition layers; this premise is invoked in the traveling-wave formulation and the singular-limit construction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Rigorous existence proofs for heteroclinic, homoclinic, and periodic traveling waves in the optimal velocity model via singular-limit analysis of a difference-differential equation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The optimal velocity model admits rigorous heteroclinic traveling waves and large-period periodic stop-and-go solutions for sufficiently steep velocity functions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9c0c866f7ce2c33f835082bd2d48a216d252d0336cb600d4606bd7f348d63745"},"source":{"id":"2605.15629","kind":"arxiv","version":1},"verdict":{"id":"074e94f5-5cf1-4886-aebe-9e81865301a1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:50:22.961739Z","strongest_claim":"We rigorously prove the existence of heteroclinic traveling waves for sufficiently steep OV functions, the existence of homoclinic solutions with a necessary condition on the amplitude parameter, and the existence of large-period periodic solutions comprising alternating transition layers and quasi-uniform states under the global road-length constraint.","one_line_summary":"Rigorous existence proofs for heteroclinic, homoclinic, and periodic traveling waves in the optimal velocity model via singular-limit analysis of a difference-differential equation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The optimal velocity function must be sufficiently steep and approach a step function so that the singular-limit analysis produces sharp, explicitly constructible transition layers; this premise is invoked in the traveling-wave formulation and the singular-limit construction.","pith_extraction_headline":"The optimal velocity model admits rigorous heteroclinic traveling waves and large-period periodic stop-and-go solutions for sufficiently steep velocity functions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15629/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:01:29.614056Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.274757Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:35.679602Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.028863Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"06afd3299aad20172c740acd5b80c8fef48babaaa0454300755241390bfc86cb"},"references":{"count":42,"sample":[{"doi":"","year":1979,"title":"S. M. Allen and J. W. Cahn. A microscopic theory for antiphase bou ndary motion and its application to antiphase domain coarsening. Acta Metallurgica, 27(6):1085–1095, 1979","work_id":"af934e1c-b06e-4f21-ac12-a578bbc3a738","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, A. Shibata, an d Y. Sugiyama. Phenomenological study of dynamical model of traﬃc ﬂow. Journal de Physique I , 5(11):1389–1399, 1995","work_id":"2af16585-aa62-4957-8b0e-8963be94af3b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama . Structure stability of congestion in traﬃc dynamics. Japan Journal of Industrial and Applied Mathematics , 11:203–223, 1994","work_id":"3f6cc708-8aa7-428d-b458-602b2b59a56f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama . Dynamical model of traﬃc conges- tion and numerical simulation. Physical Review E , 51(2):1035, 1995","work_id":"30954348-da6e-4826-80ca-5e2f1cac888d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"N. Bellomo, M. Delitala, and V. Coscia. On the mathematical theory of vehicular traﬃc ﬂow I: Fluid dynamic and kinetic modelling. Mathematical Models and Methods in Applied Sciences , 12(12):1801– 184","work_id":"4c8ec332-57a1-4a71-8037-84f3b5839085","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":42,"snapshot_sha256":"814e9e4600b0fcb0fa6bdce9afe651e4aed8d2b17d707ff4cbc05a019c105d27","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f5764974511518f981164f501506e94e318cedc853802b9e4d0bbf79d217f2c8"},"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":"2605.15629","created_at":"2026-05-20T00:01:08.970459+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.15629v1","created_at":"2026-05-20T00:01:08.970459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15629","created_at":"2026-05-20T00:01:08.970459+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHCMS2ZHXM5P","created_at":"2026-05-20T00:01:08.970459+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHCMS2ZHXM5PTPRG","created_at":"2026-05-20T00:01:08.970459+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHCMS2ZH","created_at":"2026-05-20T00:01:08.970459+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF","json":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF.json","graph_json":"https://pith.science/api/pith-number/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/graph.json","events_json":"https://pith.science/api/pith-number/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/events.json","paper":"https://pith.science/paper/AHCMS2ZH"},"agent_actions":{"view_html":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF","download_json":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF.json","view_paper":"https://pith.science/paper/AHCMS2ZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.15629&json=true","fetch_graph":"https://pith.science/api/pith-number/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/graph.json","fetch_events":"https://pith.science/api/pith-number/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/action/storage_attestation","attest_author":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/action/author_attestation","sign_citation":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/action/citation_signature","submit_replication":"https://pith.science/pith/AHCMS2ZHXM5PTPRGT4Y5LAGPQF/action/replication_record"}},"created_at":"2026-05-20T00:01:08.970459+00:00","updated_at":"2026-05-20T00:01:08.970459+00:00"}