{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VI4HGZ6REISJ2MYWGZC7UU5REA","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":"cb7e9f3e0644d459a26ee6421f26624cfb4198d290ca9602ef1b3134ce0b7513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-07T12:04:11Z","title_canon_sha256":"37a0257830ee52915bcc7ae9c5f35f655ebbda1f3ea915fcaa87888fe174cbe0"},"schema_version":"1.0","source":{"id":"1809.02425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02425","created_at":"2026-05-18T00:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02425v2","created_at":"2026-05-18T00:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02425","created_at":"2026-05-18T00:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"VI4HGZ6REISJ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VI4HGZ6REISJ2MYW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VI4HGZ6R","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:82fe7b725802253730c7f5ff49751ce3fbde682cf1f179a3f1995fcea9b4f694","target":"graph","created_at":"2026-05-18T00:05:36Z","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":"We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\\\"odinger operator with negative Hardy potential $$\\Delta^{\\alpha/2} -\\lambda |x|^{-\\alpha}$$ on $\\RR^d$, where $\\alpha\\in(0,d\\wedge 2)$ and $\\lambda>0$. The proof is purely analytical but elementary. In particular, for upper bounds of heat kernel we use the Chapman-Kolmogorov equation and adopt self-improving argument.","authors_text":"Jian Wang, Tomasz Jakubowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-07T12:04:11Z","title":"Heat kernel estimates of fractional Schr\\\"odinger operators with negative hardy potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02425","kind":"arxiv","version":2},"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:c39f9f17296729a40b8635a8d04983b16fb8f369c5e01d939d9329d74420b04b","target":"record","created_at":"2026-05-18T00:05:36Z","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":"cb7e9f3e0644d459a26ee6421f26624cfb4198d290ca9602ef1b3134ce0b7513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-07T12:04:11Z","title_canon_sha256":"37a0257830ee52915bcc7ae9c5f35f655ebbda1f3ea915fcaa87888fe174cbe0"},"schema_version":"1.0","source":{"id":"1809.02425","kind":"arxiv","version":2}},"canonical_sha256":"aa387367d122249d33163645fa53b1200f77a4d1a21987c7e7d8e40e8ba1dbfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa387367d122249d33163645fa53b1200f77a4d1a21987c7e7d8e40e8ba1dbfe","first_computed_at":"2026-05-18T00:05:36.820895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:36.820895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2pLAfJo3MNGVJrZYKER0/lSsltfkTfRiVMhu9GAb2cNVVVhJ9PisX+nSNawuvI2+zXgD3BeelWXHcI+ui0lDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:36.821373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c39f9f17296729a40b8635a8d04983b16fb8f369c5e01d939d9329d74420b04b","sha256:82fe7b725802253730c7f5ff49751ce3fbde682cf1f179a3f1995fcea9b4f694"],"state_sha256":"a39c09dd6c32cfcaa011f7091001702061dd6ab7937b3fb07ae01fa0950533e9"}