{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KBDNHDCQPOHZGJDTGJDBSFWSSY","short_pith_number":"pith:KBDNHDCQ","canonical_record":{"source":{"id":"1109.6899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-30T17:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"8cbb07473b0c484b1410395df91f82309d14e885668af6385083857ad4f01d63","abstract_canon_sha256":"b70a7dafe101cb2fb67be248f8cb1405c5d9303a7bb6a9076c163ead8e27d755"},"schema_version":"1.0"},"canonical_sha256":"5046d38c507b8f93247332461916d296262cef737f1734ff587598ec4ca4b6ba","source":{"kind":"arxiv","id":"1109.6899","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6899","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6899v1","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6899","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"KBDNHDCQPOHZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KBDNHDCQPOHZGJDT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KBDNHDCQ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KBDNHDCQPOHZGJDTGJDBSFWSSY","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-30T17:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"8cbb07473b0c484b1410395df91f82309d14e885668af6385083857ad4f01d63","abstract_canon_sha256":"b70a7dafe101cb2fb67be248f8cb1405c5d9303a7bb6a9076c163ead8e27d755"},"schema_version":"1.0"},"canonical_sha256":"5046d38c507b8f93247332461916d296262cef737f1734ff587598ec4ca4b6ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:52.247733Z","signature_b64":"CGJxYYyIKsXzTvHrzQybhBYxeBuOLgupl2uLYM/HAKvQrFux81hVft/J06aGDn0iIhS3kx+2X5lTYYTyFVErBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5046d38c507b8f93247332461916d296262cef737f1734ff587598ec4ca4b6ba","last_reissued_at":"2026-05-18T04:11:52.247135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:52.247135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6899","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LD7gWy8CGfK9o0wjkgCZhu12RXbS0iEyZP/LyuzrdGOOQwuhqAIboNdDjf6xQOZcUXBuNGoZ1uI5viuJdripCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:33:49.422054Z"},"content_sha256":"e29eba41d59dc7f4646f86fa350dccd0a0bef79cf7ca2e1673718d7aa3e1966e","schema_version":"1.0","event_id":"sha256:e29eba41d59dc7f4646f86fa350dccd0a0bef79cf7ca2e1673718d7aa3e1966e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KBDNHDCQPOHZGJDTGJDBSFWSSY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the spectrum of stochastic perturbations of the shift and Julia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Messaoudi, E. H. El Abdalaoui","submitted_at":"2011-09-30T17:06:14Z","abstract_excerpt":"We extend the Killeen-Taylor study in \\cite{KT} by investigating in different Banach spaces ($\\ell^\\alpha(\\N), c_0(\\N),c_c(\\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectra involve the Julia set of an endomorphism of $\\C^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6899","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utrH97LSEk12RtOrJ5MHeetN5W9dEhrSGMeTD/28pAWHcqqoeAkFHnaKZ2u4R8NF8MaAerl86A1wwLAqqGoMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:33:49.422406Z"},"content_sha256":"994345a86fd212297bba0ef2ec96e21b924a772b27a2200a9e08c398ba684770","schema_version":"1.0","event_id":"sha256:994345a86fd212297bba0ef2ec96e21b924a772b27a2200a9e08c398ba684770"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/bundle.json","state_url":"https://pith.science/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T00:33:49Z","links":{"resolver":"https://pith.science/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY","bundle":"https://pith.science/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/bundle.json","state":"https://pith.science/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBDNHDCQPOHZGJDTGJDBSFWSSY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KBDNHDCQPOHZGJDTGJDBSFWSSY","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":"b70a7dafe101cb2fb67be248f8cb1405c5d9303a7bb6a9076c163ead8e27d755","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-30T17:06:14Z","title_canon_sha256":"8cbb07473b0c484b1410395df91f82309d14e885668af6385083857ad4f01d63"},"schema_version":"1.0","source":{"id":"1109.6899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6899","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6899v1","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6899","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"KBDNHDCQPOHZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KBDNHDCQPOHZGJDT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KBDNHDCQ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:994345a86fd212297bba0ef2ec96e21b924a772b27a2200a9e08c398ba684770","target":"graph","created_at":"2026-05-18T04:11:52Z","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 extend the Killeen-Taylor study in \\cite{KT} by investigating in different Banach spaces ($\\ell^\\alpha(\\N), c_0(\\N),c_c(\\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectra involve the Julia set of an endomorphism of $\\C^2$.","authors_text":"A. Messaoudi, E. H. El Abdalaoui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-30T17:06:14Z","title":"On the spectrum of stochastic perturbations of the shift and Julia sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6899","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:e29eba41d59dc7f4646f86fa350dccd0a0bef79cf7ca2e1673718d7aa3e1966e","target":"record","created_at":"2026-05-18T04:11:52Z","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":"b70a7dafe101cb2fb67be248f8cb1405c5d9303a7bb6a9076c163ead8e27d755","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-30T17:06:14Z","title_canon_sha256":"8cbb07473b0c484b1410395df91f82309d14e885668af6385083857ad4f01d63"},"schema_version":"1.0","source":{"id":"1109.6899","kind":"arxiv","version":1}},"canonical_sha256":"5046d38c507b8f93247332461916d296262cef737f1734ff587598ec4ca4b6ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5046d38c507b8f93247332461916d296262cef737f1734ff587598ec4ca4b6ba","first_computed_at":"2026-05-18T04:11:52.247135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:52.247135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGJxYYyIKsXzTvHrzQybhBYxeBuOLgupl2uLYM/HAKvQrFux81hVft/J06aGDn0iIhS3kx+2X5lTYYTyFVErBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:52.247733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e29eba41d59dc7f4646f86fa350dccd0a0bef79cf7ca2e1673718d7aa3e1966e","sha256:994345a86fd212297bba0ef2ec96e21b924a772b27a2200a9e08c398ba684770"],"state_sha256":"d8bc61fe7812181c0a44b6c1a7f0553adcdb2f39880a0dcf95370e98c92881bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zp4BAzS8Q69T1wi5sXVNz5eN0Q7bmKPY4/P7FzoMIMo3OUUP6rwEVbEstchdPXgJ4YZ23orhD1eThZbFgopJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:33:49.424445Z","bundle_sha256":"6654a23ba5084fe1f2efc5d74e2cc1475f63ec79e06cff759912b5f1a1250cfd"}}