{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LOD5FR7JXJQXGB26QWVIJ6XEO6","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":"dfd13533f1198add5f191502393d03ae197995586b95914bde8c5311724e04db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-01T14:01:02Z","title_canon_sha256":"4e2cd8f296855df950f7a06a0a7e1a15cc13134e6e69c8d271bb39826ba75c5a"},"schema_version":"1.0","source":{"id":"1608.00432","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00432","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00432v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00432","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"LOD5FR7JXJQX","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOD5FR7JXJQXGB26","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOD5FR7J","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:d98c5805c2ee43d2a75e521f2e0e275fdd768559dad1c3400c748af2bb9dbd46","target":"graph","created_at":"2026-05-18T00:46:49Z","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 a periodic Schr\\\"odinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean. We show in great generality that the bottom of the spectrum of the corresponding magnetic Schr\\\"odinger operator develops spectral islands separated by gaps, reminding of a Landau-level structure.\n  First, we construct an effective Hofstadter-like magnetic matrix which accurately describes the low lying spectrum of the full operator. The construction of this effective magnetic matrix does not require a gap in the spectrum of the non-magnetic o","authors_text":"Bernard Helffer, Horia D. Cornean, Radu Purice","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-01T14:01:02Z","title":"Low lying spectral gaps induced by slowly varying magnetic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00432","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:eae1b1509254806566cfaeed9067a09379b8f05d935e2386d2103c1ad8376380","target":"record","created_at":"2026-05-18T00:46:49Z","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":"dfd13533f1198add5f191502393d03ae197995586b95914bde8c5311724e04db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-01T14:01:02Z","title_canon_sha256":"4e2cd8f296855df950f7a06a0a7e1a15cc13134e6e69c8d271bb39826ba75c5a"},"schema_version":"1.0","source":{"id":"1608.00432","kind":"arxiv","version":2}},"canonical_sha256":"5b87d2c7e9ba6173075e85aa84fae477b755abadc05c4e1c7822ad1cf73c9cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b87d2c7e9ba6173075e85aa84fae477b755abadc05c4e1c7822ad1cf73c9cca","first_computed_at":"2026-05-18T00:46:49.232979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:49.232979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X5LMks1S3lYO7UfVlPQPNk70+m1s2MPkKBTMMzX0YADgqTVOzR/aomI5jBDELA+FoL7MrVdmZfb4sna/cwKcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:49.233560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00432","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eae1b1509254806566cfaeed9067a09379b8f05d935e2386d2103c1ad8376380","sha256:d98c5805c2ee43d2a75e521f2e0e275fdd768559dad1c3400c748af2bb9dbd46"],"state_sha256":"fa430d476babdb46f820c4230154b57d6027eaf3d66c2713247b29ddf56f279d"}