{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EKF7NCTCL5N3N2TFT34V3IPWTB","short_pith_number":"pith:EKF7NCTC","schema_version":"1.0","canonical_sha256":"228bf68a625f5bb6ea659ef95da1f6987dbeb66c618ec2a6801e22c20fc3d8e1","source":{"kind":"arxiv","id":"1403.6024","version":2},"attestation_state":"computed","paper":{"title":"Superdiffusion in the periodic Lorentz gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR","nlin.CD"],"primary_cat":"math-ph","authors_text":"Balint Toth, Jens Marklof","submitted_at":"2014-03-24T16:21:58Z","abstract_excerpt":"We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $\\sqrt{t\\log t}$, where $t$ is measured in units of the mean collision time. This result holds in any dimension and for a general class of finite-range scattering potentials. We also establish the corresponding invariance principle, i.e., the weak convergence of the particle dynamics to Brownian motion."},"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":"1403.6024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-24T16:21:58Z","cross_cats_sorted":["math.DS","math.MP","math.PR","nlin.CD"],"title_canon_sha256":"a2138462f464c98f8a9bb260604e294d875cf738b5b9667380730e76b8463bfb","abstract_canon_sha256":"361705113cfa238d87f75562fe71999ef6f088bb79e70f4a2e3068c308cc9d0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:58.468014Z","signature_b64":"/y/YoC/mKwZD4w/wT83aPWWrPuIwm1C7XFM3WFq4M+i5lQRz2jOAy4us55Bjf7p86RA44HoNYaNMhT2s+iJIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"228bf68a625f5bb6ea659ef95da1f6987dbeb66c618ec2a6801e22c20fc3d8e1","last_reissued_at":"2026-05-18T01:26:58.467467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:58.467467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superdiffusion in the periodic Lorentz gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR","nlin.CD"],"primary_cat":"math-ph","authors_text":"Balint Toth, Jens Marklof","submitted_at":"2014-03-24T16:21:58Z","abstract_excerpt":"We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $\\sqrt{t\\log t}$, where $t$ is measured in units of the mean collision time. This result holds in any dimension and for a general class of finite-range scattering potentials. We also establish the corresponding invariance principle, i.e., the weak convergence of the particle dynamics to Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6024","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":"1403.6024","created_at":"2026-05-18T01:26:58.467548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.6024v2","created_at":"2026-05-18T01:26:58.467548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6024","created_at":"2026-05-18T01:26:58.467548+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKF7NCTCL5N3","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKF7NCTCL5N3N2TF","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKF7NCTC","created_at":"2026-05-18T12:28:28.263976+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/EKF7NCTCL5N3N2TFT34V3IPWTB","json":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB.json","graph_json":"https://pith.science/api/pith-number/EKF7NCTCL5N3N2TFT34V3IPWTB/graph.json","events_json":"https://pith.science/api/pith-number/EKF7NCTCL5N3N2TFT34V3IPWTB/events.json","paper":"https://pith.science/paper/EKF7NCTC"},"agent_actions":{"view_html":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB","download_json":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB.json","view_paper":"https://pith.science/paper/EKF7NCTC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.6024&json=true","fetch_graph":"https://pith.science/api/pith-number/EKF7NCTCL5N3N2TFT34V3IPWTB/graph.json","fetch_events":"https://pith.science/api/pith-number/EKF7NCTCL5N3N2TFT34V3IPWTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB/action/storage_attestation","attest_author":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB/action/author_attestation","sign_citation":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB/action/citation_signature","submit_replication":"https://pith.science/pith/EKF7NCTCL5N3N2TFT34V3IPWTB/action/replication_record"}},"created_at":"2026-05-18T01:26:58.467548+00:00","updated_at":"2026-05-18T01:26:58.467548+00:00"}