{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BAE6ETBLG47H7UKZPP72VNM7FA","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":"24180b82f2391f0d3976d0a0855d6826ef7e975ec00efc3192b5215be38e192f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-07-13T22:46:48Z","title_canon_sha256":"a2a2d8438f4917e8c151ea9d33f608d736d3ab59846fdfb9b25eafb04ceec6dc"},"schema_version":"1.0","source":{"id":"1107.2692","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2692","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2692v1","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2692","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"BAE6ETBLG47H","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BAE6ETBLG47H7UKZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BAE6ETBL","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:995051c4af20945cdfbb105827c4eb921af2fde65485a1f25bd8a375cabd0610","target":"graph","created_at":"2026-05-18T04:18:15Z","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 consider the Schr\\\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics of the resonance counting function and show that, for sufficiently high energy, each non-degenerate gap contains exactly one eigenvalue or antibound state, giving asymptotics for their positions. Conversely, for any potential $q$ and for any sequences $(\\s_n)_{1}^\\iy, \\s_n\\in \\{0,1\\}$, and $(\\vk_n)_1^\\iy\\in \\ell^2, \\vk_n\\ge 0$, there exists a potential $p$ s","authors_text":"Evgeny L. Korotyaev, Karl Michael Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-07-13T22:46:48Z","title":"On the resonances and eigenvalues for a 1D half-crystal with localised impurity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2692","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":"sha256:497f0ffad28b09e6a643cd91680eec73de207cca2d44357b10a489edee75a5e2","target":"record","created_at":"2026-05-18T04:18:15Z","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":"24180b82f2391f0d3976d0a0855d6826ef7e975ec00efc3192b5215be38e192f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-07-13T22:46:48Z","title_canon_sha256":"a2a2d8438f4917e8c151ea9d33f608d736d3ab59846fdfb9b25eafb04ceec6dc"},"schema_version":"1.0","source":{"id":"1107.2692","kind":"arxiv","version":1}},"canonical_sha256":"0809e24c2b373e7fd1597bffaab59f283d29ae3c62dc7b3acb064661cc6e6d94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0809e24c2b373e7fd1597bffaab59f283d29ae3c62dc7b3acb064661cc6e6d94","first_computed_at":"2026-05-18T04:18:15.821765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:15.821765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qGxXxLh2yq88QfkV2ELCPDF2cHe3CwYdu9Pa2+Ej4lqh0Tp0O03HgkZhL4HmFE640cndyAPh1jcg0V6nRBj0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:15.822154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2692","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:497f0ffad28b09e6a643cd91680eec73de207cca2d44357b10a489edee75a5e2","sha256:995051c4af20945cdfbb105827c4eb921af2fde65485a1f25bd8a375cabd0610"],"state_sha256":"5a86126ddbc4539895b0fdeff3796838d4642f9ca560a328d9d3354e3f43df51"}