{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WFHR4GX3LFFKBWXNHN6R2RMTIF","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":"a6340a36bdb54c0d4d49f1daf79a9bacc8680e81a5dd201dfe974fc6b2bfeeb6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-09-30T01:41:36Z","title_canon_sha256":"1cf96533cd961abc5c9b13b7fff32551e26103159a461c38c9953fcda0f4c89a"},"schema_version":"1.0","source":{"id":"1609.09566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09566","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09566v2","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09566","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"WFHR4GX3LFFK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WFHR4GX3LFFKBWXN","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WFHR4GX3","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:0e7321bb26bdcbf8770df81e288d0a06aba521d825973cf0501bf401eb8ac987","target":"graph","created_at":"2026-05-18T00:34:35Z","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 establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class perturbations under very general assumptions. Our results apply, in particular, to perturbations of reflectionless Jacobi operators with finite gap and Cantor-type essential spectrum.","authors_text":"Jacob S. Christiansen, Maxim Zinchenko","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-09-30T01:41:36Z","title":"Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09566","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":"sha256:70abbe49e9e22fbf9fd3c3495205b2cd1934a81131d4b98f7786a1f7e3b71f53","target":"record","created_at":"2026-05-18T00:34:35Z","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":"a6340a36bdb54c0d4d49f1daf79a9bacc8680e81a5dd201dfe974fc6b2bfeeb6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-09-30T01:41:36Z","title_canon_sha256":"1cf96533cd961abc5c9b13b7fff32551e26103159a461c38c9953fcda0f4c89a"},"schema_version":"1.0","source":{"id":"1609.09566","kind":"arxiv","version":2}},"canonical_sha256":"b14f1e1afb594aa0daed3b7d1d4593417a95f2a5c01bb7c5743cb8441e544e0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b14f1e1afb594aa0daed3b7d1d4593417a95f2a5c01bb7c5743cb8441e544e0b","first_computed_at":"2026-05-18T00:34:35.303636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:35.303636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clm0aGWL9n3HgZJ777nCVcKEWMfD2Xcq0RN9eKQyV1QxIYrlIoZnwFgrGk9r12zEtRbd4ZJ9Hf+9TGadwa+uCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:35.304042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70abbe49e9e22fbf9fd3c3495205b2cd1934a81131d4b98f7786a1f7e3b71f53","sha256:0e7321bb26bdcbf8770df81e288d0a06aba521d825973cf0501bf401eb8ac987"],"state_sha256":"9d6262dcbb6d14d153dbb121e177fd7f39a2700185d9762e9054234ccdf2e2ba"}