{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I4V4Z3HG3N7OEJT4RKL6CIRZQP","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":"ad843dee89cc7ba5344c94095e1152a19fa3ee9b627008c2b944f29f48fdc582","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-06-02T12:36:42Z","title_canon_sha256":"a5dabcd71ca0cb465c6b9229bc9f5fba7ae671f77c6e8ef86c9a88c1b42a01f4"},"schema_version":"1.0","source":{"id":"1606.00651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00651","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00651v1","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00651","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"I4V4Z3HG3N7O","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I4V4Z3HG3N7OEJT4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I4V4Z3HG","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:cb1301351e001ba5af268070ddaa59f3b4ae9c35fac8fc375b1cb4719ee91c19","target":"graph","created_at":"2026-05-18T01:13:03Z","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 consider a self-adjoint non-negative operator $H$ in a Hilbert space $\\mathsf{L}^2(X,{\\rm d}\\mu)$. We assume that the semigroup $(\\mathrm{e}^{-t H})_{t>0}$ is defined by an integral kernel, $p$, which allows an estimate of the form $p(t,x,x)\\le F_1(x)F_2(t)$ for all $(x,t)\\in X\\times\\mathbb{R_+}$; we refer to $F_1$ as the \\emph{control function}. We show that such an estimate leads to rather satisfying abstract results on relative compactness of perturbations of $H$ by potentials. It came as a surprise to us, however, that such an estimate holds for the Laplace-Beltrami operator on \\emph{an","authors_text":"Batu G\\\"uneysu, Jochen Br\\\"uning","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-06-02T12:36:42Z","title":"Heat kernel estimates and the relative compactness of perturbations by potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00651","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:f7b6dfdfcc6efdd179078ebf4dff8f750fa28e44fafc28e8f3d11547ef12b4f1","target":"record","created_at":"2026-05-18T01:13:03Z","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":"ad843dee89cc7ba5344c94095e1152a19fa3ee9b627008c2b944f29f48fdc582","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-06-02T12:36:42Z","title_canon_sha256":"a5dabcd71ca0cb465c6b9229bc9f5fba7ae671f77c6e8ef86c9a88c1b42a01f4"},"schema_version":"1.0","source":{"id":"1606.00651","kind":"arxiv","version":1}},"canonical_sha256":"472bccece6db7ee2267c8a97e1223983cd72444cb0af3b615098388af7933987","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"472bccece6db7ee2267c8a97e1223983cd72444cb0af3b615098388af7933987","first_computed_at":"2026-05-18T01:13:03.978466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:03.978466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"odsvI4UBL3cnJ1Q/FXh8QCRzt6s+P+LAPb1D+R3l184ktEBS5bCTJ5PX1rh+rCNCoQuT4IliGvxiiYMKicRyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:03.978800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7b6dfdfcc6efdd179078ebf4dff8f750fa28e44fafc28e8f3d11547ef12b4f1","sha256:cb1301351e001ba5af268070ddaa59f3b4ae9c35fac8fc375b1cb4719ee91c19"],"state_sha256":"d4c07c630787129da647266a86ed1326324a96d152f6e0bf722bccc9d1b7fad9"}