{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5ZYZ5ROOM2D46HPJFDAPCXCPW7","short_pith_number":"pith:5ZYZ5ROO","schema_version":"1.0","canonical_sha256":"ee719ec5ce6687cf1de928c0f15c4fb7c5b147469332ebc990533fe28fd06046","source":{"kind":"arxiv","id":"2506.03632","version":2},"attestation_state":"computed","paper":{"title":"Existence and stability of non-equilibrium steady states of a weakly non-linear kinetic Fokker-Planck equation in a domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J Evans (WMI), R Medina (CEREMADE)","submitted_at":"2025-06-04T07:22:11Z","abstract_excerpt":"We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-dependent accommodation coefficient and a space-dependent temperature on the spatial boundary. The model is based from a problem introduced in [E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra, and C. Mouhot. Approach to the steady state in kinetic models with thermal reservoirs at different temperatures. J. Stat. Phys., 172(2):522--543, 2018] where the authors studied the properties of the non-equilibrium steady states"},"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":"2506.03632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-04T07:22:11Z","cross_cats_sorted":[],"title_canon_sha256":"8cd97ff79bc87b9f205370431476b2c2ac64ab36be25bcd42b26a2ae8af73325","abstract_canon_sha256":"ac806d7c3a100901ae38109af796603ca662f8ce4ab6929f7739ae3d31a2a17e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:07.808203Z","signature_b64":"XczsbqoAYzpe1u6WrsizvGr7NehaVteWcQK6VTuIRB2DIQYmgHBE55KlQP+KmoaxqkEiepf4BPTq/8X9quyzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee719ec5ce6687cf1de928c0f15c4fb7c5b147469332ebc990533fe28fd06046","last_reissued_at":"2026-07-05T11:19:07.807700Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:07.807700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and stability of non-equilibrium steady states of a weakly non-linear kinetic Fokker-Planck equation in a domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J Evans (WMI), R Medina (CEREMADE)","submitted_at":"2025-06-04T07:22:11Z","abstract_excerpt":"We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-dependent accommodation coefficient and a space-dependent temperature on the spatial boundary. The model is based from a problem introduced in [E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra, and C. Mouhot. Approach to the steady state in kinetic models with thermal reservoirs at different temperatures. J. Stat. Phys., 172(2):522--543, 2018] where the authors studied the properties of the non-equilibrium steady states"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03632","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03632/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":"2506.03632","created_at":"2026-07-05T11:19:07.807759+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.03632v2","created_at":"2026-07-05T11:19:07.807759+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03632","created_at":"2026-07-05T11:19:07.807759+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZYZ5ROOM2D4","created_at":"2026-07-05T11:19:07.807759+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZYZ5ROOM2D46HPJ","created_at":"2026-07-05T11:19:07.807759+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZYZ5ROO","created_at":"2026-07-05T11:19:07.807759+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/5ZYZ5ROOM2D46HPJFDAPCXCPW7","json":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7.json","graph_json":"https://pith.science/api/pith-number/5ZYZ5ROOM2D46HPJFDAPCXCPW7/graph.json","events_json":"https://pith.science/api/pith-number/5ZYZ5ROOM2D46HPJFDAPCXCPW7/events.json","paper":"https://pith.science/paper/5ZYZ5ROO"},"agent_actions":{"view_html":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7","download_json":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7.json","view_paper":"https://pith.science/paper/5ZYZ5ROO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.03632&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZYZ5ROOM2D46HPJFDAPCXCPW7/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZYZ5ROOM2D46HPJFDAPCXCPW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7/action/storage_attestation","attest_author":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7/action/author_attestation","sign_citation":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7/action/citation_signature","submit_replication":"https://pith.science/pith/5ZYZ5ROOM2D46HPJFDAPCXCPW7/action/replication_record"}},"created_at":"2026-07-05T11:19:07.807759+00:00","updated_at":"2026-07-05T11:19:07.807759+00:00"}