{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5U7CNZ5DXSWPQJEENJQROOLKFT","short_pith_number":"pith:5U7CNZ5D","schema_version":"1.0","canonical_sha256":"ed3e26e7a3bcacf824846a6117396a2ce2ad3d8c98a637d49f48364a3dce27a8","source":{"kind":"arxiv","id":"2411.12140","version":1},"attestation_state":"computed","paper":{"title":"Local well-posedness for the periodic Boltzmann equation with constant collision kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Chenmin Sun, Engin Ba\\c{s}ako\\u{g}lu, Nikolay Tzvetkov, Yuzhao Wang","submitted_at":"2024-11-19T00:39:27Z","abstract_excerpt":"We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain $\\mathbb{T}^d$, $d\\geq 2$. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in $L^{2,r}_vH^s_x$ for $s>\\frac{d}{2}-\\frac{1}{4}$ and $r>\\frac{d}{2}$. To reach the result, the main tool we establish is the $L^4$ Strichartz estimate for solutions to the corresponding linear equation."},"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":"2411.12140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-19T00:39:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7a19f0ed2a66e3a5e73eca4a37151b846896cee6a12ec4d0cae468c094a1bf31","abstract_canon_sha256":"484ac197176396cbfb0cf0b212b5fef6d8fe4df5be61a25694e5b3798a77a5ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:16.586038Z","signature_b64":"/I7TId6f+0N3hif00gLpHQFt67K7M6h9f7OAxyVOEq25PCI9F9Gl7Pvp2IGx68YkJGFE1a+LIV+rNDBojmV4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed3e26e7a3bcacf824846a6117396a2ce2ad3d8c98a637d49f48364a3dce27a8","last_reissued_at":"2026-07-05T09:37:16.585571Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:16.585571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local well-posedness for the periodic Boltzmann equation with constant collision kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Chenmin Sun, Engin Ba\\c{s}ako\\u{g}lu, Nikolay Tzvetkov, Yuzhao Wang","submitted_at":"2024-11-19T00:39:27Z","abstract_excerpt":"We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain $\\mathbb{T}^d$, $d\\geq 2$. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in $L^{2,r}_vH^s_x$ for $s>\\frac{d}{2}-\\frac{1}{4}$ and $r>\\frac{d}{2}$. To reach the result, the main tool we establish is the $L^4$ Strichartz estimate for solutions to the corresponding linear equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12140","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12140/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.12140","created_at":"2026-07-05T09:37:16.585632+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12140v1","created_at":"2026-07-05T09:37:16.585632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12140","created_at":"2026-07-05T09:37:16.585632+00:00"},{"alias_kind":"pith_short_12","alias_value":"5U7CNZ5DXSWP","created_at":"2026-07-05T09:37:16.585632+00:00"},{"alias_kind":"pith_short_16","alias_value":"5U7CNZ5DXSWPQJEE","created_at":"2026-07-05T09:37:16.585632+00:00"},{"alias_kind":"pith_short_8","alias_value":"5U7CNZ5D","created_at":"2026-07-05T09:37:16.585632+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2501.14697","citing_title":"$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT","json":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT.json","graph_json":"https://pith.science/api/pith-number/5U7CNZ5DXSWPQJEENJQROOLKFT/graph.json","events_json":"https://pith.science/api/pith-number/5U7CNZ5DXSWPQJEENJQROOLKFT/events.json","paper":"https://pith.science/paper/5U7CNZ5D"},"agent_actions":{"view_html":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT","download_json":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT.json","view_paper":"https://pith.science/paper/5U7CNZ5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12140&json=true","fetch_graph":"https://pith.science/api/pith-number/5U7CNZ5DXSWPQJEENJQROOLKFT/graph.json","fetch_events":"https://pith.science/api/pith-number/5U7CNZ5DXSWPQJEENJQROOLKFT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT/action/storage_attestation","attest_author":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT/action/author_attestation","sign_citation":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT/action/citation_signature","submit_replication":"https://pith.science/pith/5U7CNZ5DXSWPQJEENJQROOLKFT/action/replication_record"}},"created_at":"2026-07-05T09:37:16.585632+00:00","updated_at":"2026-07-05T09:37:16.585632+00:00"}