{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FZDXANJWDDTUZLD4K4NCWET633","short_pith_number":"pith:FZDXANJW","schema_version":"1.0","canonical_sha256":"2e4770353618e74cac7c571a2b127edefd0bd8741f6dc5e0af9afb30c61b3faa","source":{"kind":"arxiv","id":"1510.08611","version":1},"attestation_state":"computed","paper":{"title":"On the Boltzmann equation with the symmetric stable Levy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong-Kum Cho","submitted_at":"2015-10-29T09:23:55Z","abstract_excerpt":"As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the stochastic time-evolution of characteristic functions associated with the symmetric stable Levy process and the Maxwellian collision dynamics. Under a non-cutoff assumption on the kernel, we establish a global existence theorem with maximum growth estimate, uniqueness and stability of solutions."},"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":"1510.08611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-29T09:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"222210ae555e6afe4174221a54f15982ca727a5ae472dc67938f7208b990806f","abstract_canon_sha256":"f4b20ababf847b871739e6f40c561c13134519014385fa11be6a9225870e6d88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:28.295469Z","signature_b64":"ORkPBYujr8musgw99l60eKcyE5OLbAqKDnNNymznZykwc8n6PPq/bqVFbq3liO1DqvYnffxZd2aSDxCxo2y0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e4770353618e74cac7c571a2b127edefd0bd8741f6dc5e0af9afb30c61b3faa","last_reissued_at":"2026-05-18T01:28:28.294798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:28.294798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Boltzmann equation with the symmetric stable Levy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong-Kum Cho","submitted_at":"2015-10-29T09:23:55Z","abstract_excerpt":"As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the stochastic time-evolution of characteristic functions associated with the symmetric stable Levy process and the Maxwellian collision dynamics. Under a non-cutoff assumption on the kernel, we establish a global existence theorem with maximum growth estimate, uniqueness and stability of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08611","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":"1510.08611","created_at":"2026-05-18T01:28:28.294905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08611v1","created_at":"2026-05-18T01:28:28.294905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08611","created_at":"2026-05-18T01:28:28.294905+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZDXANJWDDTU","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZDXANJWDDTUZLD4","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZDXANJW","created_at":"2026-05-18T12:29:22.688609+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/FZDXANJWDDTUZLD4K4NCWET633","json":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633.json","graph_json":"https://pith.science/api/pith-number/FZDXANJWDDTUZLD4K4NCWET633/graph.json","events_json":"https://pith.science/api/pith-number/FZDXANJWDDTUZLD4K4NCWET633/events.json","paper":"https://pith.science/paper/FZDXANJW"},"agent_actions":{"view_html":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633","download_json":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633.json","view_paper":"https://pith.science/paper/FZDXANJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08611&json=true","fetch_graph":"https://pith.science/api/pith-number/FZDXANJWDDTUZLD4K4NCWET633/graph.json","fetch_events":"https://pith.science/api/pith-number/FZDXANJWDDTUZLD4K4NCWET633/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633/action/storage_attestation","attest_author":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633/action/author_attestation","sign_citation":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633/action/citation_signature","submit_replication":"https://pith.science/pith/FZDXANJWDDTUZLD4K4NCWET633/action/replication_record"}},"created_at":"2026-05-18T01:28:28.294905+00:00","updated_at":"2026-05-18T01:28:28.294905+00:00"}