{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EWJ55ZRKQJ5XZOGHER2VPXYOAW","short_pith_number":"pith:EWJ55ZRK","schema_version":"1.0","canonical_sha256":"2593dee62a827b7cb8c7247557df0e05956ffd8acd21c8051d5d14f10f55bbbd","source":{"kind":"arxiv","id":"1101.2975","version":1},"attestation_state":"computed","paper":{"title":"On the spectral theory of operators on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Matthias Keller","submitted_at":"2011-01-15T11:34:25Z","abstract_excerpt":"We study a class of rooted trees with a substitution type structure. These trees are not necessarily regular, but exhibit a lot of symmetries. We consider nearest neighbor operators which reflect the symmetries of the trees. The spectrum of such operators is proven to be purely absolutely continuous and to consist of finitely many intervals. We further investigate stability of the absolutely continuous spectrum under perturbations by sufficiently small potentials. On the one hand, we look at a class of deterministic potentials which include radial symmetric ones. The absolutely continuous spec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.2975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-15T11:34:25Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"387b8acb5045b7532b7f151b56b6d95dc99b9439043df00a49b7285163482e8b","abstract_canon_sha256":"f3b6b7338a1a36578df4bb8ec493d3e395d213b45a1b5b35a663a85c7d7f5bf2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:57.197861Z","signature_b64":"dB12WZrelob4OwJTz8P5rIo/s9L+Fbh8ZyFAPaDD+uPQUzHYb1TDCUaAwjcLOJUuakOa+nbiiMaKnGbLWWQPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2593dee62a827b7cb8c7247557df0e05956ffd8acd21c8051d5d14f10f55bbbd","last_reissued_at":"2026-05-18T02:22:57.197220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:57.197220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the spectral theory of operators on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Matthias Keller","submitted_at":"2011-01-15T11:34:25Z","abstract_excerpt":"We study a class of rooted trees with a substitution type structure. These trees are not necessarily regular, but exhibit a lot of symmetries. We consider nearest neighbor operators which reflect the symmetries of the trees. The spectrum of such operators is proven to be purely absolutely continuous and to consist of finitely many intervals. We further investigate stability of the absolutely continuous spectrum under perturbations by sufficiently small potentials. On the one hand, we look at a class of deterministic potentials which include radial symmetric ones. The absolutely continuous spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2975","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.2975","created_at":"2026-05-18T02:22:57.197300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.2975v1","created_at":"2026-05-18T02:22:57.197300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2975","created_at":"2026-05-18T02:22:57.197300+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWJ55ZRKQJ5X","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWJ55ZRKQJ5XZOGH","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWJ55ZRK","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW","json":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW.json","graph_json":"https://pith.science/api/pith-number/EWJ55ZRKQJ5XZOGHER2VPXYOAW/graph.json","events_json":"https://pith.science/api/pith-number/EWJ55ZRKQJ5XZOGHER2VPXYOAW/events.json","paper":"https://pith.science/paper/EWJ55ZRK"},"agent_actions":{"view_html":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW","download_json":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW.json","view_paper":"https://pith.science/paper/EWJ55ZRK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.2975&json=true","fetch_graph":"https://pith.science/api/pith-number/EWJ55ZRKQJ5XZOGHER2VPXYOAW/graph.json","fetch_events":"https://pith.science/api/pith-number/EWJ55ZRKQJ5XZOGHER2VPXYOAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW/action/storage_attestation","attest_author":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW/action/author_attestation","sign_citation":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW/action/citation_signature","submit_replication":"https://pith.science/pith/EWJ55ZRKQJ5XZOGHER2VPXYOAW/action/replication_record"}},"created_at":"2026-05-18T02:22:57.197300+00:00","updated_at":"2026-05-18T02:22:57.197300+00:00"}