{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D7TS55IB3DJIJD4TDR4RLQCMU4","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":"a5feca66c83e7ffaff5e2491e39edf6e0c0152c379b4a790441863fd56fa4c87","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T19:57:01Z","title_canon_sha256":"84b3d9809c872a3ce891a14bd6cca85859cc3cd1cc1f563a21e1e8fd3420bcbc"},"schema_version":"1.0","source":{"id":"1207.3782","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3782","created_at":"2026-05-18T03:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3782v2","created_at":"2026-05-18T03:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3782","created_at":"2026-05-18T03:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"D7TS55IB3DJI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D7TS55IB3DJIJD4T","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D7TS55IB","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:c94f3ce098cadc3ce1207ccbe8235ebcd14ab822261214d32aef192ddd73d273","target":"graph","created_at":"2026-05-18T03:02:47Z","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":"In the present paper, we prove an improved Combes-Thomas estimate, i.e., the Combes-Thomas estimate in trace-class norms, for magnetic Schr\\\"{o}dinger operators under general assumptions. In particular, we allow unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.","authors_text":"Zhongwei Shen","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T19:57:01Z","title":"An Improved Combes-Thomas Estimate of Magnetic Schr\\\"{o}dinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3782","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:aae225d07c017539b0f251f9a2754662e562b0a222e9d0b1929777446f59a53b","target":"record","created_at":"2026-05-18T03:02:47Z","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":"a5feca66c83e7ffaff5e2491e39edf6e0c0152c379b4a790441863fd56fa4c87","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T19:57:01Z","title_canon_sha256":"84b3d9809c872a3ce891a14bd6cca85859cc3cd1cc1f563a21e1e8fd3420bcbc"},"schema_version":"1.0","source":{"id":"1207.3782","kind":"arxiv","version":2}},"canonical_sha256":"1fe72ef501d8d2848f931c7915c04ca737cab552e4885243e120fc4953604244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fe72ef501d8d2848f931c7915c04ca737cab552e4885243e120fc4953604244","first_computed_at":"2026-05-18T03:02:47.252114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:47.252114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/J8v4/7tpC9KZ/QgWLhRBfmZLw6H51QzAHGobW1qsohh2AmiS/GNabqV3PwN3wHsDewQWs3qTswLIWV6+7t4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:47.252680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3782","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aae225d07c017539b0f251f9a2754662e562b0a222e9d0b1929777446f59a53b","sha256:c94f3ce098cadc3ce1207ccbe8235ebcd14ab822261214d32aef192ddd73d273"],"state_sha256":"65f956e9d373e493e70df5667e31b05bc1b410fac71e89283c94bd0c954d02ac"}