{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:T4RKOZWHQ6IUP4LVEW2TDDWMF2","short_pith_number":"pith:T4RKOZWH","schema_version":"1.0","canonical_sha256":"9f22a766c7879147f17525b5318ecc2e84ae9b88413e4c5edc0a172d653df6d1","source":{"kind":"arxiv","id":"1903.02693","version":4},"attestation_state":"computed","paper":{"title":"Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","nlin.CD"],"primary_cat":"math.AP","authors_text":"Gui-Qiang G. Chen, Peter H.C. Pang","submitted_at":"2019-03-07T02:17:02Z","abstract_excerpt":"We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A unified framework is established for the continuous dependence estimates, fractional BV regularity estimates, and well-posedness for stochastic entropy solutions of the nonlinear stochastic degenerate parabolic-hyperbolic equation. In particular, we establish the well-posedness of the nonlinear stochastic equation in $L^p \\cap N^{\\kappa,1}$ for $p\\in (1,\\infty)$ and the $\\kappa$--Nikolskii space $N^{\\kappa,1}$ with $"},"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":"1903.02693","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-07T02:17:02Z","cross_cats_sorted":["math.FA","math.PR","nlin.CD"],"title_canon_sha256":"2663f8dc81c7b78f390e214ee17a89c8c42dd68438c43bdb466057eca8220752","abstract_canon_sha256":"31dfc3cce5745ad182ab05b3677ad3d3dd68bfa7b35d7138247e75e29f159c04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:48.446037Z","signature_b64":"GZPMYlrAF5+IIzRz8pRDTTLaXKxRvrAeKgBCwe49lmIZHysHKq44wulJtf3WGL0KvTqD/gglsxlxVGP0tVOVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f22a766c7879147f17525b5318ecc2e84ae9b88413e4c5edc0a172d653df6d1","last_reissued_at":"2026-07-05T03:16:48.445674Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:48.445674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","nlin.CD"],"primary_cat":"math.AP","authors_text":"Gui-Qiang G. Chen, Peter H.C. Pang","submitted_at":"2019-03-07T02:17:02Z","abstract_excerpt":"We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A unified framework is established for the continuous dependence estimates, fractional BV regularity estimates, and well-posedness for stochastic entropy solutions of the nonlinear stochastic degenerate parabolic-hyperbolic equation. In particular, we establish the well-posedness of the nonlinear stochastic equation in $L^p \\cap N^{\\kappa,1}$ for $p\\in (1,\\infty)$ and the $\\kappa$--Nikolskii space $N^{\\kappa,1}$ with $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02693","kind":"arxiv","version":4},"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/1903.02693/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":"1903.02693","created_at":"2026-07-05T03:16:48.445728+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.02693v4","created_at":"2026-07-05T03:16:48.445728+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02693","created_at":"2026-07-05T03:16:48.445728+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4RKOZWHQ6IU","created_at":"2026-07-05T03:16:48.445728+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4RKOZWHQ6IUP4LV","created_at":"2026-07-05T03:16:48.445728+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4RKOZWH","created_at":"2026-07-05T03:16:48.445728+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.04879","citing_title":"Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2","json":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2.json","graph_json":"https://pith.science/api/pith-number/T4RKOZWHQ6IUP4LVEW2TDDWMF2/graph.json","events_json":"https://pith.science/api/pith-number/T4RKOZWHQ6IUP4LVEW2TDDWMF2/events.json","paper":"https://pith.science/paper/T4RKOZWH"},"agent_actions":{"view_html":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2","download_json":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2.json","view_paper":"https://pith.science/paper/T4RKOZWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.02693&json=true","fetch_graph":"https://pith.science/api/pith-number/T4RKOZWHQ6IUP4LVEW2TDDWMF2/graph.json","fetch_events":"https://pith.science/api/pith-number/T4RKOZWHQ6IUP4LVEW2TDDWMF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2/action/storage_attestation","attest_author":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2/action/author_attestation","sign_citation":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2/action/citation_signature","submit_replication":"https://pith.science/pith/T4RKOZWHQ6IUP4LVEW2TDDWMF2/action/replication_record"}},"created_at":"2026-07-05T03:16:48.445728+00:00","updated_at":"2026-07-05T03:16:48.445728+00:00"}