{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:46GD3A6MXMLDTXRRFXWIE6F7MJ","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":"09cec03b66f7a41c5688438c008f8d8c0b295b46069ee2ee8526522f85b58be9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-12T18:03:02Z","title_canon_sha256":"ab12c9a4af581d57882b67fbf04e81bbbcd02ebbef7f0223adbbb92c1ce71594"},"schema_version":"1.0","source":{"id":"1606.03745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03745","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03745v1","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03745","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"46GD3A6MXMLD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"46GD3A6MXMLDTXRR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"46GD3A6M","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:33f3450223a70f40ec4c8693b554d07dd2c03e88f38334dccb0c413406135f7c","target":"graph","created_at":"2026-05-18T01:12:33Z","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 investigate when the fundamental solution of the Schr\\\"odinger equation $\\partial_t=\\Delta+V$ posseses sharp Gaussian bounds global in space and time. We give a characterization for $V\\leq 0$ and a sufficient condition for general $V$.","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":"2016-06-12T18:03:02Z","title":"Characterization of sharp global Gaussian estimates for Schr\\\"odinger heat kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03745","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:aad42464518df184130f19e5b130b1dd06f6d2c227511124d49fea0a68abca1d","target":"record","created_at":"2026-05-18T01:12:33Z","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":"09cec03b66f7a41c5688438c008f8d8c0b295b46069ee2ee8526522f85b58be9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-12T18:03:02Z","title_canon_sha256":"ab12c9a4af581d57882b67fbf04e81bbbcd02ebbef7f0223adbbb92c1ce71594"},"schema_version":"1.0","source":{"id":"1606.03745","kind":"arxiv","version":1}},"canonical_sha256":"e78c3d83ccbb1639de312dec8278bf624b85e122c1879a9f9b8d0ba14db75bfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e78c3d83ccbb1639de312dec8278bf624b85e122c1879a9f9b8d0ba14db75bfe","first_computed_at":"2026-05-18T01:12:33.161228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:33.161228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E0KUq8Av6GGhCCpG6yeGBJJXL2KH8weSS8nOt+NidxeBsmE8Vh89hdKyVM2IKyegHOlxKsvTrxF4RlUniF9/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:33.161775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aad42464518df184130f19e5b130b1dd06f6d2c227511124d49fea0a68abca1d","sha256:33f3450223a70f40ec4c8693b554d07dd2c03e88f38334dccb0c413406135f7c"],"state_sha256":"eaa91d294bbe067caf710e5bc5cf24a479f20734f60073115226eaa185ac088b"}