{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6YAR24VMVITJW3Y7SBZ2TFWISK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5cfa4dd5ecdc04c81c7a9146649b29dd5f5913c89eca4aebe9c2455a47f73d8c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T01:20:37Z","title_canon_sha256":"7296f6db21845079aeeefee7a7838d784be677a19b9507a9aa56180034754fed"},"schema_version":"1.0","source":{"id":"1204.4956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4956","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4956v1","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4956","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"6YAR24VMVITJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YAR24VMVITJW3Y7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YAR24VM","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:9186816397f0a9add31dfff99be425c81cbafc2fc9e7abc258ce8690d2917959","target":"graph","created_at":"2026-05-18T03:57:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\\aa)}$ be the $\\aa$-stable subordination of $L$ for $\\aa\\in (1,2).$ We found some classes $\\mathbb K_\\aa^{\\gg,\\bb} (\\bb,\\gg\\in [0,\\aa))$ of time-space functions containing the Kato class, such that for any measurable $b: [0,\\infty)\\times M\\to TM$ and $c: [0,\\infty)\\times M\\to M$ with $|b|, c\\in \\mathbb K_\\aa^{1,1},$ the operator $$L_{b,c}^{(\\aa)}(t,x):= L^{(\\aa)}(x)+  <b(t,x),\\nn \\c","authors_text":"Feng-Yu Wang, Xicheng Zhang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T01:20:37Z","title":"Heat Kernel for Fractional Diffusion Operators with Perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4956","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:96b38cf024d714714df68790b48b1482665eb49d1322490ec7f3de5226cd7165","target":"record","created_at":"2026-05-18T03:57:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5cfa4dd5ecdc04c81c7a9146649b29dd5f5913c89eca4aebe9c2455a47f73d8c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T01:20:37Z","title_canon_sha256":"7296f6db21845079aeeefee7a7838d784be677a19b9507a9aa56180034754fed"},"schema_version":"1.0","source":{"id":"1204.4956","kind":"arxiv","version":1}},"canonical_sha256":"f6011d72acaa269b6f1f9073a996c892bc26018eea88a84a54cd84172e52201b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6011d72acaa269b6f1f9073a996c892bc26018eea88a84a54cd84172e52201b","first_computed_at":"2026-05-18T03:57:15.092436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:15.092436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vUldMjTOtyA+LBHkTfdwOTGUVCEnHxiFOAYl35olRhmDsXpML25Zx1EJKGjI0vupQ1RVoCEidoH4ekMtd4q7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:15.093158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96b38cf024d714714df68790b48b1482665eb49d1322490ec7f3de5226cd7165","sha256:9186816397f0a9add31dfff99be425c81cbafc2fc9e7abc258ce8690d2917959"],"state_sha256":"a270f9dfd3f837a94b1a51514b846fcbcc1b784b0ec599df1cbef89383cce26d"}