{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:P7ILDAFHZXPRYEBDQZ352O3RAR","short_pith_number":"pith:P7ILDAFH","schema_version":"1.0","canonical_sha256":"7fd0b180a7cddf1c10238677dd3b71047e8c140318bc659fcc394d9a9c90bf17","source":{"kind":"arxiv","id":"2501.13771","version":2},"attestation_state":"computed","paper":{"title":"Pointwise upper bound for the fundamental solution of fractional Fokker-Planck equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haina Li, Yiran Xu","submitted_at":"2025-01-23T15:49:53Z","abstract_excerpt":"In this paper, we investigate the fundamental solution of the fractional Fokker-Planck equation. Utilizing the Littlewood-Paley decomposition technology, we present a concise proof of the pointwise estimate for the fundamental solution."},"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":"2501.13771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-23T15:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"c03d03c7d39f6f193d6b9c1c9bfe9bd2370a15a0b002fb4cf756d7f5652f976a","abstract_canon_sha256":"66f1d7b01232afd3794ab84e280a05974298945c66177ee8d6037f0a7563fd01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:42.433897Z","signature_b64":"Xb5/n1pkkem3VZzKO8BfrUqkqDM56fmn3ZmT5U+YPyINS/RxDn2gaMijWTTA9kZyHpwunUf6JGdOwPjmWwLMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd0b180a7cddf1c10238677dd3b71047e8c140318bc659fcc394d9a9c90bf17","last_reissued_at":"2026-07-05T10:04:42.433472Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:42.433472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise upper bound for the fundamental solution of fractional Fokker-Planck equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haina Li, Yiran Xu","submitted_at":"2025-01-23T15:49:53Z","abstract_excerpt":"In this paper, we investigate the fundamental solution of the fractional Fokker-Planck equation. Utilizing the Littlewood-Paley decomposition technology, we present a concise proof of the pointwise estimate for the fundamental solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13771","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.13771/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":"2501.13771","created_at":"2026-07-05T10:04:42.433535+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.13771v2","created_at":"2026-07-05T10:04:42.433535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13771","created_at":"2026-07-05T10:04:42.433535+00:00"},{"alias_kind":"pith_short_12","alias_value":"P7ILDAFHZXPR","created_at":"2026-07-05T10:04:42.433535+00:00"},{"alias_kind":"pith_short_16","alias_value":"P7ILDAFHZXPRYEBD","created_at":"2026-07-05T10:04:42.433535+00:00"},{"alias_kind":"pith_short_8","alias_value":"P7ILDAFH","created_at":"2026-07-05T10:04:42.433535+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/P7ILDAFHZXPRYEBDQZ352O3RAR","json":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR.json","graph_json":"https://pith.science/api/pith-number/P7ILDAFHZXPRYEBDQZ352O3RAR/graph.json","events_json":"https://pith.science/api/pith-number/P7ILDAFHZXPRYEBDQZ352O3RAR/events.json","paper":"https://pith.science/paper/P7ILDAFH"},"agent_actions":{"view_html":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR","download_json":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR.json","view_paper":"https://pith.science/paper/P7ILDAFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.13771&json=true","fetch_graph":"https://pith.science/api/pith-number/P7ILDAFHZXPRYEBDQZ352O3RAR/graph.json","fetch_events":"https://pith.science/api/pith-number/P7ILDAFHZXPRYEBDQZ352O3RAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR/action/storage_attestation","attest_author":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR/action/author_attestation","sign_citation":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR/action/citation_signature","submit_replication":"https://pith.science/pith/P7ILDAFHZXPRYEBDQZ352O3RAR/action/replication_record"}},"created_at":"2026-07-05T10:04:42.433535+00:00","updated_at":"2026-07-05T10:04:42.433535+00:00"}