{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6LWQ6UJAXEDBAZRDFLGUE4V3A7","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":"cc497a08e691300f46bf4b24d7b5a8c89dc6f1e9bec38615c495f94c553ef844","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-30T10:58:14Z","title_canon_sha256":"88e8acde8d9b3a0cdad24a4faf028fcbd4c0bf674c402a0b9b8790e35edc57ea"},"schema_version":"1.0","source":{"id":"1007.5412","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5412","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5412v4","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5412","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"6LWQ6UJAXEDB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6LWQ6UJAXEDBAZRD","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6LWQ6UJA","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:fa57d2a23e3ec358db842dc0ab57d24886300ffb017051dabf6540011792fd87","target":"graph","created_at":"2026-05-18T04:35:14Z","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":"For the periodic matrix-valued Jacobi operator $J$ we obtain the estimate of the Lebesgue measure of the spectrum $|\\s(J)|\\le4 \\min_n\\Tr(a_na_n^*)^\\frac12$, where $a_n$ are off-diagonal elements of $J$. Moreover estimates of width of spectral bands are obtained.","authors_text":"Anton A. Kutsenko","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-30T10:58:14Z","title":"Sharp spectral estimates for periodic matrix-valued Jacobi operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5412","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:dd2bca2b10c21784b2fcfb62e16c7bd4b1b1c5860361b764416103b5484ff0f5","target":"record","created_at":"2026-05-18T04:35:14Z","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":"cc497a08e691300f46bf4b24d7b5a8c89dc6f1e9bec38615c495f94c553ef844","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-30T10:58:14Z","title_canon_sha256":"88e8acde8d9b3a0cdad24a4faf028fcbd4c0bf674c402a0b9b8790e35edc57ea"},"schema_version":"1.0","source":{"id":"1007.5412","kind":"arxiv","version":4}},"canonical_sha256":"f2ed0f5120b9061066232acd4272bb07e4fc6fc95882bbc8fd3fd981a9cdd7b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2ed0f5120b9061066232acd4272bb07e4fc6fc95882bbc8fd3fd981a9cdd7b4","first_computed_at":"2026-05-18T04:35:14.646279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:14.646279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6gH4kiJCG2kPhe65uKLmYsNHF6TeOYnFoM5mOrcxDmpcYjlzdD2kcU008apIwGsQ05ncyHAXnDFcf+cCDqoHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:14.646967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5412","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd2bca2b10c21784b2fcfb62e16c7bd4b1b1c5860361b764416103b5484ff0f5","sha256:fa57d2a23e3ec358db842dc0ab57d24886300ffb017051dabf6540011792fd87"],"state_sha256":"6c5bf920b3946d7eada0136ea64349fc21648cd6017f194c52e12cc0f87cd972"}