{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WH3WAABOV7EMTD3TSSZB6YDUFP","short_pith_number":"pith:WH3WAABO","schema_version":"1.0","canonical_sha256":"b1f760002eafc8c98f7394b21f60742be1e43fd34d9c86b812d592facd0e0a11","source":{"kind":"arxiv","id":"1803.00379","version":1},"attestation_state":"computed","paper":{"title":"Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcel Braukhoff","submitted_at":"2018-03-01T14:35:43Z","abstract_excerpt":"The global existence of a solution of the semiconductor Boltzmann-Dirac-Benney equation \\[ \\partial_t f + \\nabla\\epsilon(p)\\cdot\\nabla_x f - \\nabla \\rho_f(x,t)\\cdot\\nabla_p f = \\frac{\\mathcal F_\\lambda(p)-f}\\tau, \\quad x\\in\\mathbb{R}^d,\\ p\\in B, \\ t>0 \\] is shown for small $\\tau>0$ assuming that the initial data are analytic and sufficiently close to $\\mathcal F_\\lambda$. This system contains an interaction potential $\\rho_f(x,t):=\\int_{B}f(x,p,t)dp$ being significantly more singular than the Coulomb potential, which causes major structural difficulties in the analysis. The semiconductor Boltz"},"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":"1803.00379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:35:43Z","cross_cats_sorted":[],"title_canon_sha256":"b1c7c9c7f53bcd959518e0f05d1dbfd5cb54ddba8db6eec7e012c876339608cb","abstract_canon_sha256":"562a186e0b087776af1381b6d48e9bd2e7bf8a46e5c6ade97cfbd3b4fb821887"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:12.447680Z","signature_b64":"vN1THlgMJpcEf1xTQiM2GDD/2FJi5cBwEctN+MDQK8KMzMi+VcbCeYzeJiKeXMms6R7NXXfmsabB5O1Z5ww8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1f760002eafc8c98f7394b21f60742be1e43fd34d9c86b812d592facd0e0a11","last_reissued_at":"2026-05-18T00:22:12.447099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:12.447099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcel Braukhoff","submitted_at":"2018-03-01T14:35:43Z","abstract_excerpt":"The global existence of a solution of the semiconductor Boltzmann-Dirac-Benney equation \\[ \\partial_t f + \\nabla\\epsilon(p)\\cdot\\nabla_x f - \\nabla \\rho_f(x,t)\\cdot\\nabla_p f = \\frac{\\mathcal F_\\lambda(p)-f}\\tau, \\quad x\\in\\mathbb{R}^d,\\ p\\in B, \\ t>0 \\] is shown for small $\\tau>0$ assuming that the initial data are analytic and sufficiently close to $\\mathcal F_\\lambda$. This system contains an interaction potential $\\rho_f(x,t):=\\int_{B}f(x,p,t)dp$ being significantly more singular than the Coulomb potential, which causes major structural difficulties in the analysis. The semiconductor Boltz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00379","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":""},"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":"1803.00379","created_at":"2026-05-18T00:22:12.447170+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.00379v1","created_at":"2026-05-18T00:22:12.447170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00379","created_at":"2026-05-18T00:22:12.447170+00:00"},{"alias_kind":"pith_short_12","alias_value":"WH3WAABOV7EM","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WH3WAABOV7EMTD3T","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WH3WAABO","created_at":"2026-05-18T12:32:59.047623+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/WH3WAABOV7EMTD3TSSZB6YDUFP","json":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP.json","graph_json":"https://pith.science/api/pith-number/WH3WAABOV7EMTD3TSSZB6YDUFP/graph.json","events_json":"https://pith.science/api/pith-number/WH3WAABOV7EMTD3TSSZB6YDUFP/events.json","paper":"https://pith.science/paper/WH3WAABO"},"agent_actions":{"view_html":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP","download_json":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP.json","view_paper":"https://pith.science/paper/WH3WAABO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.00379&json=true","fetch_graph":"https://pith.science/api/pith-number/WH3WAABOV7EMTD3TSSZB6YDUFP/graph.json","fetch_events":"https://pith.science/api/pith-number/WH3WAABOV7EMTD3TSSZB6YDUFP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP/action/storage_attestation","attest_author":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP/action/author_attestation","sign_citation":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP/action/citation_signature","submit_replication":"https://pith.science/pith/WH3WAABOV7EMTD3TSSZB6YDUFP/action/replication_record"}},"created_at":"2026-05-18T00:22:12.447170+00:00","updated_at":"2026-05-18T00:22:12.447170+00:00"}