{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PWBEZJP4H6T7VQMHLLEPIVFCXM","short_pith_number":"pith:PWBEZJP4","schema_version":"1.0","canonical_sha256":"7d824ca5fc3fa7fac1875ac8f454a2bb373512839d8e2ea01f7562b62d69fa92","source":{"kind":"arxiv","id":"2605.24685","version":1},"attestation_state":"computed","paper":{"title":"Self-similarity and diffusive limits for linear kinetic equations: a Wild sum approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Jos\\'e A. Ca\\~nizo, Niccol\\`o Tassi, St\\'ephane Mischler","submitted_at":"2026-05-23T17:45:37Z","abstract_excerpt":"We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour.\n  This drastically improves the recently known results (decay estimates) about the solutions in such a context, providing the first result regarding this self-similar behaviour. As a consequence, we also establish a uniform-in-time convergence of the suitably rescaled solutions to their diffusion limit, which is also new.\n  The class of equations considered includes some BGK type equations, some kinetic nonlocal Fokker--Planck-type equations and\n  some"},"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":"2605.24685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-23T17:45:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c0be8c41a35f2271596e1b0ddb19b4c1d56fde3ee1575f8b136390457b8d3580","abstract_canon_sha256":"6500b7263886eae5cd0fe527db7e9428e12615ec7d9b4a686db33826c6bbd625"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:53.203695Z","signature_b64":"gUt6XmNJq1eUCOmTrZJLYjJmgn+zm2YlZE1uXDBTmCn1te9xqXWUsRuvcttPFtvZryYK7oz7UQBnp5b9c/FNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d824ca5fc3fa7fac1875ac8f454a2bb373512839d8e2ea01f7562b62d69fa92","last_reissued_at":"2026-05-26T01:03:53.202883Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:53.202883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-similarity and diffusive limits for linear kinetic equations: a Wild sum approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Jos\\'e A. Ca\\~nizo, Niccol\\`o Tassi, St\\'ephane Mischler","submitted_at":"2026-05-23T17:45:37Z","abstract_excerpt":"We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour.\n  This drastically improves the recently known results (decay estimates) about the solutions in such a context, providing the first result regarding this self-similar behaviour. As a consequence, we also establish a uniform-in-time convergence of the suitably rescaled solutions to their diffusion limit, which is also new.\n  The class of equations considered includes some BGK type equations, some kinetic nonlocal Fokker--Planck-type equations and\n  some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24685","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/2605.24685/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":"2605.24685","created_at":"2026-05-26T01:03:53.203004+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.24685v1","created_at":"2026-05-26T01:03:53.203004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24685","created_at":"2026-05-26T01:03:53.203004+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWBEZJP4H6T7","created_at":"2026-05-26T01:03:53.203004+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWBEZJP4H6T7VQMH","created_at":"2026-05-26T01:03:53.203004+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWBEZJP4","created_at":"2026-05-26T01:03:53.203004+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/PWBEZJP4H6T7VQMHLLEPIVFCXM","json":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM.json","graph_json":"https://pith.science/api/pith-number/PWBEZJP4H6T7VQMHLLEPIVFCXM/graph.json","events_json":"https://pith.science/api/pith-number/PWBEZJP4H6T7VQMHLLEPIVFCXM/events.json","paper":"https://pith.science/paper/PWBEZJP4"},"agent_actions":{"view_html":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM","download_json":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM.json","view_paper":"https://pith.science/paper/PWBEZJP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.24685&json=true","fetch_graph":"https://pith.science/api/pith-number/PWBEZJP4H6T7VQMHLLEPIVFCXM/graph.json","fetch_events":"https://pith.science/api/pith-number/PWBEZJP4H6T7VQMHLLEPIVFCXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM/action/storage_attestation","attest_author":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM/action/author_attestation","sign_citation":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM/action/citation_signature","submit_replication":"https://pith.science/pith/PWBEZJP4H6T7VQMHLLEPIVFCXM/action/replication_record"}},"created_at":"2026-05-26T01:03:53.203004+00:00","updated_at":"2026-05-26T01:03:53.203004+00:00"}