{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:R376A5DUYHDM4RKSTYL2GHGI4Z","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":"b0eb068bbc8c344ab9b3f99bfb03aa65479470b5a5283ef76d0170458e7af075","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-10T23:12:20Z","title_canon_sha256":"f5c40f11cdbd25729c1f5a430bd5c2384056e47def56962ac6d7ca7726ffba14"},"schema_version":"1.0","source":{"id":"1210.3084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3084","created_at":"2026-05-18T01:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3084v2","created_at":"2026-05-18T01:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3084","created_at":"2026-05-18T01:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"R376A5DUYHDM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"R376A5DUYHDM4RKS","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"R376A5DU","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:988162e0b1d7ab5ba8dffb5bcc6991b40f774e82135e82cc92e3cc0839e9384f","target":"graph","created_at":"2026-05-18T01:53:56Z","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 quasiperiodic Jacobi matrices of size N with analytic coefficients. We show that, in the positive Lyapunov exponent regime, after removing some small sets of energies and frequencies, any eigenvalue is separated from the rest of the spectrum by $N^{-1}(\\log N)^{-p}$, with p>15.","authors_text":"Ilia Binder, Mircea Voda","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-10T23:12:20Z","title":"On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3084","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":"sha256:70476b53b1bcf90bea67b0c03414f200ffccef7f07e635efdf8a6ad033e843ed","target":"record","created_at":"2026-05-18T01:53:56Z","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":"b0eb068bbc8c344ab9b3f99bfb03aa65479470b5a5283ef76d0170458e7af075","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-10T23:12:20Z","title_canon_sha256":"f5c40f11cdbd25729c1f5a430bd5c2384056e47def56962ac6d7ca7726ffba14"},"schema_version":"1.0","source":{"id":"1210.3084","kind":"arxiv","version":2}},"canonical_sha256":"8effe07474c1c6ce45529e17a31cc8e6719d0f0bc8aebf816d8c941eb5d9f3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8effe07474c1c6ce45529e17a31cc8e6719d0f0bc8aebf816d8c941eb5d9f3ea","first_computed_at":"2026-05-18T01:53:56.957489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:56.957489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5B9OhDnXk+LokpabXzyPCDQp1tbng39gbK/GKA7u+SmJt9BLzihdaoQzttq/ll803qGqCXEJq2xYes5p9pYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:56.957953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70476b53b1bcf90bea67b0c03414f200ffccef7f07e635efdf8a6ad033e843ed","sha256:988162e0b1d7ab5ba8dffb5bcc6991b40f774e82135e82cc92e3cc0839e9384f"],"state_sha256":"b06bf54b39be76025533a82dfd55efacab7308bfdbe127c0b1e3899af7207e63"}