{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:TD3T7BL4IBG6QMNCTKFWARCPGN","short_pith_number":"pith:TD3T7BL4","schema_version":"1.0","canonical_sha256":"98f73f857c404de831a29a8b60444f334aa0021de8e4160dbecf8f890a2d11c8","source":{"kind":"arxiv","id":"0906.0191","version":2},"attestation_state":"computed","paper":{"title":"Recent Results on the Periodic Lorentz Gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fran\\c{c}ois Golse","submitted_at":"2009-06-01T00:02:32Z","abstract_excerpt":"The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some appropriate scaling assumption -- known as the Boltzmann-Grad scaling by analogy with the kinetic theory of rarefied gases -- this system can be described in some limit by a linear Boltzmann equation, assuming that the configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185 (1969), 308]). The case of a periodic configuration of obstacles "},"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":"0906.0191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-06-01T00:02:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c5415a462f4104230ddd85f273165b06a817216769d055542aaea1cc059a740f","abstract_canon_sha256":"a704e325081ced2ae5f172a2a8766d75e470f130c8dc7aafe00032212345495d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.154527Z","signature_b64":"g+JQC4o3nCMz+eYGXij9PpoDDtFryPF6mMDtXS8elzPTdtkACbBEXI137lDeFKtlS49+G3fTJRFDn+e6RVMCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98f73f857c404de831a29a8b60444f334aa0021de8e4160dbecf8f890a2d11c8","last_reissued_at":"2026-05-18T01:11:52.154187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.154187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recent Results on the Periodic Lorentz Gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fran\\c{c}ois Golse","submitted_at":"2009-06-01T00:02:32Z","abstract_excerpt":"The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some appropriate scaling assumption -- known as the Boltzmann-Grad scaling by analogy with the kinetic theory of rarefied gases -- this system can be described in some limit by a linear Boltzmann equation, assuming that the configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185 (1969), 308]). The case of a periodic configuration of obstacles "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0191","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":""},"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":"0906.0191","created_at":"2026-05-18T01:11:52.154240+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.0191v2","created_at":"2026-05-18T01:11:52.154240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0191","created_at":"2026-05-18T01:11:52.154240+00:00"},{"alias_kind":"pith_short_12","alias_value":"TD3T7BL4IBG6","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"TD3T7BL4IBG6QMNC","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"TD3T7BL4","created_at":"2026-05-18T12:26:01.383474+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/TD3T7BL4IBG6QMNCTKFWARCPGN","json":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN.json","graph_json":"https://pith.science/api/pith-number/TD3T7BL4IBG6QMNCTKFWARCPGN/graph.json","events_json":"https://pith.science/api/pith-number/TD3T7BL4IBG6QMNCTKFWARCPGN/events.json","paper":"https://pith.science/paper/TD3T7BL4"},"agent_actions":{"view_html":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN","download_json":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN.json","view_paper":"https://pith.science/paper/TD3T7BL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.0191&json=true","fetch_graph":"https://pith.science/api/pith-number/TD3T7BL4IBG6QMNCTKFWARCPGN/graph.json","fetch_events":"https://pith.science/api/pith-number/TD3T7BL4IBG6QMNCTKFWARCPGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN/action/storage_attestation","attest_author":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN/action/author_attestation","sign_citation":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN/action/citation_signature","submit_replication":"https://pith.science/pith/TD3T7BL4IBG6QMNCTKFWARCPGN/action/replication_record"}},"created_at":"2026-05-18T01:11:52.154240+00:00","updated_at":"2026-05-18T01:11:52.154240+00:00"}