{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6PKKESSHNQV5XXCA7TFLDQUUW4","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":"4cb5cf0a67c2ac5c633904867f402ecd86068f7ba1cd229cc6f38903580daabb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:49:43Z","title_canon_sha256":"be4f94fe3f3d2c13a6bb7f2ff55273bea2cb27793310407de2a7e4b530d7dbe3"},"schema_version":"1.0","source":{"id":"1706.06172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06172","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06172v2","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06172","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"6PKKESSHNQV5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6PKKESSHNQV5XXCA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6PKKESSH","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:ca2447910603c191a38aa2f384216e7502b11207978a57b075f28f4efd13db59","target":"graph","created_at":"2026-05-18T00:08:05Z","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 characterize functions $V\\le 0$ for which the heat kernel of the Schr\\\"o\\-dinger operator $\\Delta+V$ is comparable with the Gauss-Weierstrass kernel uniformly in space and time. In dimension $4$ and higher the condition turns out to be more restrictive than the condition of the boundedness of the Newtonian potential of $V$. This resolves the question of V.~Liskevich and Y.~Semenov posed in 1998. We also give specialized sufficient conditions for the comparability, showing that local $L^p$ integrability of $V$ for $p>1$ is not necessary for the comparability.","authors_text":"Jacek Dziuba\\'nski, Karol Szczypkowski, Krzysztof Bogdan","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:49:43Z","title":"Sharp Gaussian estimates for heat kernels of Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06172","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:cf77c0e20c49b75483033fc199d2394ebbe23ccde936f0664d9f4c6dba0a07a6","target":"record","created_at":"2026-05-18T00:08:05Z","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":"4cb5cf0a67c2ac5c633904867f402ecd86068f7ba1cd229cc6f38903580daabb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-19T20:49:43Z","title_canon_sha256":"be4f94fe3f3d2c13a6bb7f2ff55273bea2cb27793310407de2a7e4b530d7dbe3"},"schema_version":"1.0","source":{"id":"1706.06172","kind":"arxiv","version":2}},"canonical_sha256":"f3d4a24a476c2bdbdc40fccab1c294b7265d8a1b296da2158552bd33b600c0e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3d4a24a476c2bdbdc40fccab1c294b7265d8a1b296da2158552bd33b600c0e5","first_computed_at":"2026-05-18T00:08:05.204583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:05.204583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QgCK2wl7W/GcaaC6l+HbjdMAV2/n030MmOQhhyurwjpIR662GOFzQq8n47G0RM7Bqiv4XyH2Of5ZfKZGlttbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:05.205206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf77c0e20c49b75483033fc199d2394ebbe23ccde936f0664d9f4c6dba0a07a6","sha256:ca2447910603c191a38aa2f384216e7502b11207978a57b075f28f4efd13db59"],"state_sha256":"8e3fd7684f81430d17d49b6273bd5acc3cab809566ab59430f8f905ef3051bab"}