{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U2TCMGWLZ2YYV6GEGULY6APM2Z","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":"a3ca1a2bafaf4633fc8c321dd59cad831665bf72581addfe7df92b9b0e939209","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-14T01:30:56Z","title_canon_sha256":"57e81f498773a4665f3f6b6ceaa59d840bf565fe297f4c2b6e15e999288a7e56"},"schema_version":"1.0","source":{"id":"1811.05591","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05591","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05591v4","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05591","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"U2TCMGWLZ2YY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U2TCMGWLZ2YYV6GE","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U2TCMGWL","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:2873fbf7fbfba5acd8866e01f601ece711ce786bd62b252142b4561292347dbd","target":"graph","created_at":"2026-05-17T23:54:39Z","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 give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman--Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schr\\\"odinger operators with rapidly decreasing complex-valued potentials, and, more generally, for non-symmetric Jacobi matrices.","authors_text":"Alexander Borichev, Alexander Volberg, Rupert Frank","cross_cats":["math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-14T01:30:56Z","title":"Counting eigenvalues of Schr\\\"odinger operator with complex fast decreasing potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05591","kind":"arxiv","version":4},"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":"sha256:7b1c13b50aa52a88776024495c6924995d335a3c6611c6ce38670b41325e593d","target":"record","created_at":"2026-05-17T23:54:39Z","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":"a3ca1a2bafaf4633fc8c321dd59cad831665bf72581addfe7df92b9b0e939209","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-14T01:30:56Z","title_canon_sha256":"57e81f498773a4665f3f6b6ceaa59d840bf565fe297f4c2b6e15e999288a7e56"},"schema_version":"1.0","source":{"id":"1811.05591","kind":"arxiv","version":4}},"canonical_sha256":"a6a6261acbceb18af8c435178f01ecd65fc661906461f56a9216155558c66de0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6a6261acbceb18af8c435178f01ecd65fc661906461f56a9216155558c66de0","first_computed_at":"2026-05-17T23:54:39.043841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:39.043841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g9eUn+QOo0YFIcIl/HbvTtASD2bBM+gbVIVXPDF/jLIGjOIgCe5S68MwgZo0aHxCKXrUb83cw7m3GGsMJYtaDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:39.044416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05591","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b1c13b50aa52a88776024495c6924995d335a3c6611c6ce38670b41325e593d","sha256:2873fbf7fbfba5acd8866e01f601ece711ce786bd62b252142b4561292347dbd"],"state_sha256":"a5f2af8f11916e988056b1ee1b1ca0ddbfee11fe92a0f15e5e7fa7f2ddc3340c"}