{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MS3YXVRRJVLDAZ6JNE2TT22BNR","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":"2b9dce72da0b00f8014ee0a48ea14c7cb57a16f46f1e095930413f2759bfb4ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-02-01T14:01:59Z","title_canon_sha256":"71f004a398aaeedb363e3ea813f70c06dbabfaed3cbf3f88e64a0287d4bd1a17"},"schema_version":"1.0","source":{"id":"1902.00335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00335","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00335v1","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00335","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"MS3YXVRRJVLD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MS3YXVRRJVLDAZ6J","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MS3YXVRR","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:64390026b7a1792987d82132f2df4a2f6abe2fd766a1f47d86c8cc284f871fd9","target":"graph","created_at":"2026-05-17T23:54:57Z","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":"Under certain assumptions (including $d\\ge 2)$ we prove that the spectrum of a scalar operator in $\\mathscr{L}^2(\\mathbb{R}^d)$ \\begin{equation*} A_\\varepsilon (x,hD)= A^0(hD) + \\varepsilon B(x,hD), \\end{equation*} covers interval $(\\tau-\\epsilon,\\tau+\\epsilon)$, where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic perturbation, $\\varepsilon=O(h^\\varkappa)$, $\\varkappa>0$.\n  Further, we consider generalizations.","authors_text":"Victor Ivrii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-02-01T14:01:59Z","title":"Bethe-Sommerfeld conjecture in semiclassical settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00335","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:fd311d5bf6b62f5825aacf93aab93a7673b3b2809e40135d485bcc5d7966b412","target":"record","created_at":"2026-05-17T23:54:57Z","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":"2b9dce72da0b00f8014ee0a48ea14c7cb57a16f46f1e095930413f2759bfb4ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-02-01T14:01:59Z","title_canon_sha256":"71f004a398aaeedb363e3ea813f70c06dbabfaed3cbf3f88e64a0287d4bd1a17"},"schema_version":"1.0","source":{"id":"1902.00335","kind":"arxiv","version":1}},"canonical_sha256":"64b78bd6314d563067c9693539eb416c7ff009bde921f656128bdbe7915b93cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64b78bd6314d563067c9693539eb416c7ff009bde921f656128bdbe7915b93cb","first_computed_at":"2026-05-17T23:54:57.752560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:57.752560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+6mW7ihjJ355QZqik0mfD7DMchtfyTPvojJgoTfs3YC3gZ573tZc754HkuNroCPxVPcpkKll6LEURULG0dDEBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:57.753026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd311d5bf6b62f5825aacf93aab93a7673b3b2809e40135d485bcc5d7966b412","sha256:64390026b7a1792987d82132f2df4a2f6abe2fd766a1f47d86c8cc284f871fd9"],"state_sha256":"1bd55d72d6c71b13872018ea367acd2cda964ba0f2c1a26c7e06d6456e7f4810"}