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They described the set-valued bifurcation set\n  \\[\n  \\mathcal E_\\beta:=\\{t\\in[0, 1): K_\\beta(t')\\ne K_\\beta(t)~\\forall t'>t\\},\n  \\]\n  where $K_\\beta(t):=\\{x\\in[0, 1): T_\\beta^n(x)\\ge t~\\forall n\\ge 0\\}$ is the survivor set. In this paper we investigate the dimension bifurcation set\n  \\[\n  \\mathcal B_\\beta:=\\{t\\in[0, 1): \\dim_H K_\\beta(t')\\ne \\dim_H K_\\beta(t)~\\forall t'>t\\},\n  \\]\n  where $\\dim_H$ denotes the Hausdorff dimensio","authors_text":"Derong Kong, Simon Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-15T12:50:57Z","title":"Two bifurcation sets arising from the beta transformation with a hole at $0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07007","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:f8cf7c745d7a2a577056453f52b871fcd51d6bf6bc3dc9c4bd259ff13e490c93","target":"record","created_at":"2026-05-17T23:48:35Z","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":"5fb7823503e0b057c1657c643cb1555aa8f14f6bd309d9a3c0f070d5d02c07c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-15T12:50:57Z","title_canon_sha256":"c957992fe479c694f8bbe902ad8d1994d15f8d2f4804c7b6fb87fdf6e020949a"},"schema_version":"1.0","source":{"id":"1904.07007","kind":"arxiv","version":1}},"canonical_sha256":"0d4f438a411dfd9930b82cabbdaf06c5581ee53d3a6b53745d46b03b353777db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d4f438a411dfd9930b82cabbdaf06c5581ee53d3a6b53745d46b03b353777db","first_computed_at":"2026-05-17T23:48:35.490556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:35.490556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WacOrCwYs3ykswxl7Bp4FKEFMGAcHKnTCsHeOWhaFbFgkDSK7vNrfTnh1NPpvC7GSjBXYkTiGUOuBKSZ9ZFGCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:35.491032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8cf7c745d7a2a577056453f52b871fcd51d6bf6bc3dc9c4bd259ff13e490c93","sha256:878e20cf15b9f8acb845d1cb25b47f1afd9a05cc1c87b0afb99e5fe2ab82c2c7"],"state_sha256":"f82fd7c1fa01477052e105d7cac9a5ed22bfb3c8805d23ebab07309533c797be"}