{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MZDZNKHT2USKVZRXGRJ5JXXP3R","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":"acc1c136324950d4636b4bef10d1f74c89d1f7b583aa92a8a8f38fd4674a3821","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-30T10:57:36Z","title_canon_sha256":"5306659a67ed56c2a650a63b7f632d14f9ed4727e2e78a9387cc727621825a6a"},"schema_version":"1.0","source":{"id":"1108.0057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0057","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0057v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0057","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"MZDZNKHT2USK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MZDZNKHT2USKVZRX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MZDZNKHT","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b197d0437affd6413196f1f2910cf1bf1012e33c8eac6002b2b176f447a277d4","target":"graph","created_at":"2026-05-18T04:16:31Z","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 study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operators are perturbations of Laplace type operators either by random potentials or by random hopping terms, i.e., perturbations of the off-diagonal elements. We prove stability of arbitrary large parts of the absolutely continuous spectrum for sufficiently small but extensive disorder.","authors_text":"Daniel Lenz, Matthias Keller, Simone Warzel","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-30T10:57:36Z","title":"Absolutely continuous spectrum for random operators on trees of finite cone type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0057","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:f112ad5cf3142a6becf6156086eb52234ed788d50ecb4aa0db8724704810ab4d","target":"record","created_at":"2026-05-18T04:16:31Z","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":"acc1c136324950d4636b4bef10d1f74c89d1f7b583aa92a8a8f38fd4674a3821","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-30T10:57:36Z","title_canon_sha256":"5306659a67ed56c2a650a63b7f632d14f9ed4727e2e78a9387cc727621825a6a"},"schema_version":"1.0","source":{"id":"1108.0057","kind":"arxiv","version":1}},"canonical_sha256":"664796a8f3d524aae6373453d4deefdc69ddd1e645b02f4d7e32fa18c62336c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"664796a8f3d524aae6373453d4deefdc69ddd1e645b02f4d7e32fa18c62336c0","first_computed_at":"2026-05-18T04:16:31.758460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.758460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QokBDLPWesmsAeUCZChb4ezdujnS6ovLJQukTn8N3E0WZdTf3jZTFEu8Si6ewFsIuN4K9HY9Z9EN/eh30xU6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.758841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f112ad5cf3142a6becf6156086eb52234ed788d50ecb4aa0db8724704810ab4d","sha256:b197d0437affd6413196f1f2910cf1bf1012e33c8eac6002b2b176f447a277d4"],"state_sha256":"5f12a59236eabbc91bf044b19ff209b88a049a96cfc22e8ad74fa938c59e87c4"}