{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TJAPXE5LASPNTWFINJXUSOOLMW","short_pith_number":"pith:TJAPXE5L","schema_version":"1.0","canonical_sha256":"9a40fb93ab049ed9d8a86a6f4939cb65990aae2fbf51981113d2e427ef1fd882","source":{"kind":"arxiv","id":"2507.06237","version":2},"attestation_state":"computed","paper":{"title":"A Li-Yau gradient estimate for the Finslerian logarithmic Schr\\\"{o}dinger equation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Zisu Zhao","submitted_at":"2025-06-18T05:57:52Z","abstract_excerpt":"By leveraging a new Laplacian comparison theorem, we derive a Li-Yau type gradient estimate for a particular nonlinear parabolic equation, namely, the Finslerian logarithmic Schrodinger equation on a non-compact, complete Finsler manifold with mixed weighted Ricci curvature bounded from below. In our framework, all coefficients are time-dependent functions defined on the manifold. As applications, we establish both a Harnack inequality and an a priori estimate for the positive solutions of this specific 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":"2507.06237","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2025-06-18T05:57:52Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3a166120cd361bb27a2d57d5377c8c456a632b681cb71db2adc441ec9dd90f0a","abstract_canon_sha256":"2ae9abf5736446b3ca4db014807bfbb05442a1b927cb0b95f8e25313f30f758e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:37.417555Z","signature_b64":"hHV7qJwNpLXcy+aJHLSo05jz7r/01+tjwe/qY3+2AlkJzZ1pt3kL0g0q//LFDqui5vfMmNYtfOB4bgzqHml6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a40fb93ab049ed9d8a86a6f4939cb65990aae2fbf51981113d2e427ef1fd882","last_reissued_at":"2026-07-05T12:04:37.417024Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:37.417024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Li-Yau gradient estimate for the Finslerian logarithmic Schr\\\"{o}dinger equation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Zisu Zhao","submitted_at":"2025-06-18T05:57:52Z","abstract_excerpt":"By leveraging a new Laplacian comparison theorem, we derive a Li-Yau type gradient estimate for a particular nonlinear parabolic equation, namely, the Finslerian logarithmic Schrodinger equation on a non-compact, complete Finsler manifold with mixed weighted Ricci curvature bounded from below. In our framework, all coefficients are time-dependent functions defined on the manifold. As applications, we establish both a Harnack inequality and an a priori estimate for the positive solutions of this specific equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06237","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/2507.06237/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":"2507.06237","created_at":"2026-07-05T12:04:37.417095+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.06237v2","created_at":"2026-07-05T12:04:37.417095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06237","created_at":"2026-07-05T12:04:37.417095+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJAPXE5LASPN","created_at":"2026-07-05T12:04:37.417095+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJAPXE5LASPNTWFI","created_at":"2026-07-05T12:04:37.417095+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJAPXE5L","created_at":"2026-07-05T12:04:37.417095+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/TJAPXE5LASPNTWFINJXUSOOLMW","json":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW.json","graph_json":"https://pith.science/api/pith-number/TJAPXE5LASPNTWFINJXUSOOLMW/graph.json","events_json":"https://pith.science/api/pith-number/TJAPXE5LASPNTWFINJXUSOOLMW/events.json","paper":"https://pith.science/paper/TJAPXE5L"},"agent_actions":{"view_html":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW","download_json":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW.json","view_paper":"https://pith.science/paper/TJAPXE5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.06237&json=true","fetch_graph":"https://pith.science/api/pith-number/TJAPXE5LASPNTWFINJXUSOOLMW/graph.json","fetch_events":"https://pith.science/api/pith-number/TJAPXE5LASPNTWFINJXUSOOLMW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW/action/storage_attestation","attest_author":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW/action/author_attestation","sign_citation":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW/action/citation_signature","submit_replication":"https://pith.science/pith/TJAPXE5LASPNTWFINJXUSOOLMW/action/replication_record"}},"created_at":"2026-07-05T12:04:37.417095+00:00","updated_at":"2026-07-05T12:04:37.417095+00:00"}