{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V3WXLUSVRCLMQCZXLE4EDXPMGT","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":"65c890ddccf3a191b4edf8f5757570472a8d5938654feec447232250f8ce9967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-09T13:26:03Z","title_canon_sha256":"8728582732d5189bddb31791cf441292ca144f45c065bf877d018e5831c0c9f3"},"schema_version":"1.0","source":{"id":"1706.02943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02943","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02943v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02943","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"V3WXLUSVRCLM","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V3WXLUSVRCLMQCZX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V3WXLUSV","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:6b96f92db307a5a3e8fd53f90b12110124d3a429964a2375e669520792013f8f","target":"graph","created_at":"2026-05-18T00:42:40Z","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 $\\xi \\in \\big( 0, \\frac{1}{2} \\big)$, let $E_{\\xi}$ be the perfect symmetric set associated with $\\xi$, that is $$E_{\\xi} = \\Big\\{ \\exp \\Big( 2i \\pi (1-\\xi) \\sum_{n = 1}^{+\\infty} \\epsilon_{n} \\xi^{n-1} \\Big) : \\, \\epsilon_{n} = 0 \\textrm{ or } 1 \\quad (n \\geq 1) \\Big\\}$$ and $$b(\\xi) = \\frac{\\log{\\frac{1}{\\xi}} - \\log{2}}{2\\log{\\frac{1}{\\xi}} - \\log{2}}.$$ Let $q\\geq 3$ be an integer and $s$ be a nonnegative real number. We show that any invertible operator $T$ on a Banach space with spectrum contained in $E_{1/q}$ that satisfies \\begin{eqnarray*} & & \\big\\| T^{n} \\big\\| = O \\big( n^{s} \\","authors_text":"Mohamed Zarrabi (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-09T13:26:03Z","title":"On powers of operators with spectrum in cantor sets and spectral synthesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02943","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":"sha256:82e3b931d32588485e3c2933289f0d9aa2a843121596413cfd2302aa238909c9","target":"record","created_at":"2026-05-18T00:42:40Z","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":"65c890ddccf3a191b4edf8f5757570472a8d5938654feec447232250f8ce9967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-09T13:26:03Z","title_canon_sha256":"8728582732d5189bddb31791cf441292ca144f45c065bf877d018e5831c0c9f3"},"schema_version":"1.0","source":{"id":"1706.02943","kind":"arxiv","version":1}},"canonical_sha256":"aeed75d2558896c80b37593841ddec34e3b73dedc9fd3bbad276459b4b7d8097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeed75d2558896c80b37593841ddec34e3b73dedc9fd3bbad276459b4b7d8097","first_computed_at":"2026-05-18T00:42:40.495551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:40.495551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YhnOdBO5NinPUXwv5Yw1HyFzpp9z3nWjn+zsSY1HQtpvj161/cyYBNkWM2F9AY/mLwuY/mLHZSU/kMNC0lQrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:40.496213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82e3b931d32588485e3c2933289f0d9aa2a843121596413cfd2302aa238909c9","sha256:6b96f92db307a5a3e8fd53f90b12110124d3a429964a2375e669520792013f8f"],"state_sha256":"c8eec1a43bb9d4d75c1022253a5f24f889d9027e94a71206db28c37c361fd581"}