{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EQR5WPEE2NXEKMA5FY4THFOW5K","short_pith_number":"pith:EQR5WPEE","schema_version":"1.0","canonical_sha256":"2423db3c84d36e45301d2e393395d6eaa8abd35091ec95d09bb7db687e5fa4d6","source":{"kind":"arxiv","id":"1010.5590","version":1},"attestation_state":"computed","paper":{"title":"Bounded Solutions of the Boltzmann Equation in the Whole Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao-Jiang Xu (LMRS), Radjesvarane Alexandre (IRENAV), Seiji Ukai (Mr.), Tong Yang, Yoshinori Morimoto","submitted_at":"2010-10-27T07:37:34Z","abstract_excerpt":"We construct bounded classical solutions of the Boltzmann equation in the whole space without specifying any limit behaviors at the spatial infinity and without assuming the smallness condition on initial data. More precisely, we show that if the initial data is non-negative and belongs to a uniformly local Sobolev space in the space variable with Maxwellian type decay property in the velocity variable, then the Cauchy problem of the Boltzmann equation possesses a unique non-negative local solution in the same function space, both for the cutoff and non-cutoff collision cross section with mild"},"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":"1010.5590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-27T07:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"e3fb10a3b47787dc6fc8da3cf646914a8ae68798fc02c172b7708a3f469535fa","abstract_canon_sha256":"6dc835f796fc2cb78084d0dd5b8aa4a9e0c89b57644f0fd55e93a0977ddbd1f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:16.325605Z","signature_b64":"pzeBUFaPLxB2j/C5/kXj1Y3djyK+FsWmTEIU9ecEbwL4Vt4xT6gcRXycyHz09vRm4wHpO/0TEoRZe+UO9SleCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2423db3c84d36e45301d2e393395d6eaa8abd35091ec95d09bb7db687e5fa4d6","last_reissued_at":"2026-05-18T04:38:16.324957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:16.324957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded Solutions of the Boltzmann Equation in the Whole Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao-Jiang Xu (LMRS), Radjesvarane Alexandre (IRENAV), Seiji Ukai (Mr.), Tong Yang, Yoshinori Morimoto","submitted_at":"2010-10-27T07:37:34Z","abstract_excerpt":"We construct bounded classical solutions of the Boltzmann equation in the whole space without specifying any limit behaviors at the spatial infinity and without assuming the smallness condition on initial data. More precisely, we show that if the initial data is non-negative and belongs to a uniformly local Sobolev space in the space variable with Maxwellian type decay property in the velocity variable, then the Cauchy problem of the Boltzmann equation possesses a unique non-negative local solution in the same function space, both for the cutoff and non-cutoff collision cross section with mild"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5590","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":"1010.5590","created_at":"2026-05-18T04:38:16.325057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5590v1","created_at":"2026-05-18T04:38:16.325057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5590","created_at":"2026-05-18T04:38:16.325057+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQR5WPEE2NXE","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQR5WPEE2NXEKMA5","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQR5WPEE","created_at":"2026-05-18T12:26:06.534383+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/EQR5WPEE2NXEKMA5FY4THFOW5K","json":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K.json","graph_json":"https://pith.science/api/pith-number/EQR5WPEE2NXEKMA5FY4THFOW5K/graph.json","events_json":"https://pith.science/api/pith-number/EQR5WPEE2NXEKMA5FY4THFOW5K/events.json","paper":"https://pith.science/paper/EQR5WPEE"},"agent_actions":{"view_html":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K","download_json":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K.json","view_paper":"https://pith.science/paper/EQR5WPEE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5590&json=true","fetch_graph":"https://pith.science/api/pith-number/EQR5WPEE2NXEKMA5FY4THFOW5K/graph.json","fetch_events":"https://pith.science/api/pith-number/EQR5WPEE2NXEKMA5FY4THFOW5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K/action/storage_attestation","attest_author":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K/action/author_attestation","sign_citation":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K/action/citation_signature","submit_replication":"https://pith.science/pith/EQR5WPEE2NXEKMA5FY4THFOW5K/action/replication_record"}},"created_at":"2026-05-18T04:38:16.325057+00:00","updated_at":"2026-05-18T04:38:16.325057+00:00"}