{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A3K7UPDFEP5VTUFJCGULQVWJKZ","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":"b85997a5ac66552a2ea872e2d0de471d9e48cdb2cc51f76f1dccf165305e0708","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-10T14:07:11Z","title_canon_sha256":"b36a0a1767b1f6cb488ae7cc8d55055a36b2f341aac4f437db9014574d6ac845"},"schema_version":"1.0","source":{"id":"1712.03952","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03952","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03952v3","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03952","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"A3K7UPDFEP5V","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A3K7UPDFEP5VTUFJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A3K7UPDF","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:0595f64e00508ef4ee92d4cb3019455347b91e9eeb7ef1fe3233d1b0e52a81d3","target":"graph","created_at":"2026-05-18T00:00:30Z","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 $\\mathcal{L}$ be a Schr\\\"odinger operator of the form $\\mathcal{L} = -\\Delta+V$ acting on $L^2(\\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ Let $L^{p,\\lambda}(\\mathbb{R}^{n})$, $0\\le \\lambda<n$ denote the Morrey space on $\\mathbb{R}^{n}$. In this paper, we will show that a function $f\\in L^{2,\\lambda}(\\mathbb{R}^{n})$ is the trace of the solution of ${\\mathbb L}u=u_{t}+{\\mathcal{L}}u=0, u(x,0)= f(x),$ where $u$ satisfies a Carleson-type condition \\begin{eqnarray*} \\sup_{x_B, r_B} r_B^{-\\lambda}\\int_0^{r_B^2}\\int_{B(x_B, r","authors_text":"Chao Zhang, Qiang Huang","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-10T14:07:11Z","title":"Characterization of temperatures associated to Schr\\\"odinger operators with initial data in Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03952","kind":"arxiv","version":3},"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:c8cfd29f68e682d7c9c2c7a71c6f716c55ab3d2dd277f47e0d6ba09e8a10c41f","target":"record","created_at":"2026-05-18T00:00:30Z","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":"b85997a5ac66552a2ea872e2d0de471d9e48cdb2cc51f76f1dccf165305e0708","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-10T14:07:11Z","title_canon_sha256":"b36a0a1767b1f6cb488ae7cc8d55055a36b2f341aac4f437db9014574d6ac845"},"schema_version":"1.0","source":{"id":"1712.03952","kind":"arxiv","version":3}},"canonical_sha256":"06d5fa3c6523fb59d0a911a8b856c9567fb2b892f10fd0651420eda3b47273d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06d5fa3c6523fb59d0a911a8b856c9567fb2b892f10fd0651420eda3b47273d5","first_computed_at":"2026-05-18T00:00:30.795159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:30.795159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0k58MukVGXdGkX7TDK7mAp31yGDp7UBdgYJR63y0JyJd3TqhN06tySmBqbT22DZC6/0430YA25I2eOTOAkbgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:30.795725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03952","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8cfd29f68e682d7c9c2c7a71c6f716c55ab3d2dd277f47e0d6ba09e8a10c41f","sha256:0595f64e00508ef4ee92d4cb3019455347b91e9eeb7ef1fe3233d1b0e52a81d3"],"state_sha256":"1cf6ac527698f9d516f4457ae7d8efb2acf8c036348496c2db64e1e38899202d"}