{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:J7ZLWM2M5KWOMUWE3TLNOVZU72","short_pith_number":"pith:J7ZLWM2M","schema_version":"1.0","canonical_sha256":"4ff2bb334ceaace652c4dcd6d75734fe95cc93cd5aec597e2666d16b4c87846f","source":{"kind":"arxiv","id":"2606.11159","version":1},"attestation_state":"computed","paper":{"title":"Unidirectional Entropic Solutions of the Pressureless Euler Alignment System","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joshua O. Adeleke, Trevor M. Leslie","submitted_at":"2026-06-09T17:41:34Z","abstract_excerpt":"We study the pressureless Euler Alignment system with unidirectional velocity (u,0,...,0). By re-casting the system as a family of coupled scalar balance laws, one for each horizontal slice of R^d, we are able to prove existence, uniqueness, and stability within the class of unidirectional solutions, under the assumption of a bounded Lipschitz communication protocol. The nonlocal coupling between horizontal slices provides the system with a rich structure that is absent from the 1D setting and also constitutes the main technical difficulty of the present work. We construct our solutions as lim"},"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":"2606.11159","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T17:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"ee4a7243c8ad95282ed819a6a3859ccb0ab0d3af8ddbc3570e62f27c311bfa36","abstract_canon_sha256":"a1ee786403f1413f7f2614f4a38ce07685dc7529403ec53f9cd9f996c524b8b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:11:14.522304Z","signature_b64":"jVoeeEvVO7kHh7ABa4J2vL6JYkyDTcrNHSCAYQUgqXoHxAw/AXenpaUI2suqg+IChbZu1BD2EuoylZJexcZuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff2bb334ceaace652c4dcd6d75734fe95cc93cd5aec597e2666d16b4c87846f","last_reissued_at":"2026-06-10T01:11:14.521442Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:11:14.521442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unidirectional Entropic Solutions of the Pressureless Euler Alignment System","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joshua O. Adeleke, Trevor M. Leslie","submitted_at":"2026-06-09T17:41:34Z","abstract_excerpt":"We study the pressureless Euler Alignment system with unidirectional velocity (u,0,...,0). By re-casting the system as a family of coupled scalar balance laws, one for each horizontal slice of R^d, we are able to prove existence, uniqueness, and stability within the class of unidirectional solutions, under the assumption of a bounded Lipschitz communication protocol. The nonlocal coupling between horizontal slices provides the system with a rich structure that is absent from the 1D setting and also constitutes the main technical difficulty of the present work. We construct our solutions as lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11159","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.11159","created_at":"2026-06-10T01:11:14.521578+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.11159v1","created_at":"2026-06-10T01:11:14.521578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11159","created_at":"2026-06-10T01:11:14.521578+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7ZLWM2M5KWO","created_at":"2026-06-10T01:11:14.521578+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7ZLWM2M5KWOMUWE","created_at":"2026-06-10T01:11:14.521578+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7ZLWM2M","created_at":"2026-06-10T01:11:14.521578+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/J7ZLWM2M5KWOMUWE3TLNOVZU72","json":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72.json","graph_json":"https://pith.science/api/pith-number/J7ZLWM2M5KWOMUWE3TLNOVZU72/graph.json","events_json":"https://pith.science/api/pith-number/J7ZLWM2M5KWOMUWE3TLNOVZU72/events.json","paper":"https://pith.science/paper/J7ZLWM2M"},"agent_actions":{"view_html":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72","download_json":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72.json","view_paper":"https://pith.science/paper/J7ZLWM2M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.11159&json=true","fetch_graph":"https://pith.science/api/pith-number/J7ZLWM2M5KWOMUWE3TLNOVZU72/graph.json","fetch_events":"https://pith.science/api/pith-number/J7ZLWM2M5KWOMUWE3TLNOVZU72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72/action/storage_attestation","attest_author":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72/action/author_attestation","sign_citation":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72/action/citation_signature","submit_replication":"https://pith.science/pith/J7ZLWM2M5KWOMUWE3TLNOVZU72/action/replication_record"}},"created_at":"2026-06-10T01:11:14.521578+00:00","updated_at":"2026-06-10T01:11:14.521578+00:00"}