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We pay special attention to those $t$ with a unique\n  $\\{-1,0,1\\}$ $\\alpha$-expansion, and study the set\n  $$D_\\alpha:=\\{\\dim_H(\\Gamma_\\alpha \\cap (\\Gamma_\\alpha + t)):t \\textrm{ has a unique }\\{-1,0,1\\}\\,\\alpha\\textrm{-expansion}\\}.$$ We prove that there exists a transcendental number $\\alpha_{KL}\\approx 0.3943"},"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":"1604.00858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-04T13:51:31Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cba23c11598a9c1a01602a3dce9b230ef1b3bbe7727cfa3fe76c9eb5e578c134","abstract_canon_sha256":"9c4e097dd8dcee69d051f28bc58b08f1a3035591a7892fcf3a149e8911c0fb0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.092445Z","signature_b64":"3+yLRCwQWgQBgr10JM5CMtjuHM/mnXY/A6TVtrakp3WaRLrCApiU75/+dmNwBCp3piUWxZJHnKxDIEHGR6WYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fc8e5bac35fc6ffe39dd23f05db2c0feb651136dd3e4d0740a08444c153d3d5","last_reissued_at":"2026-05-18T00:47:21.091746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.091746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unique expansions and intersections of Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DS","authors_text":"Derong Kong, Simon Baker","submitted_at":"2016-04-04T13:51:31Z","abstract_excerpt":"To each $\\alpha\\in(1/3,1/2)$ we associate the Cantor set $$\\Gamma_{\\alpha}:=\\Big\\{\\sum_{i=1}^{\\infty}\\epsilon_{i}\\alpha^i: \\epsilon_i\\in\\{0,1\\},\\,i\\geq 1\\Big\\}.$$\n  In this paper we consider the intersection $\\Gamma_\\alpha \\cap (\\Gamma_\\alpha + t)$ for any translation $t\\in\\mathbb{R}$. We pay special attention to those $t$ with a unique\n  $\\{-1,0,1\\}$ $\\alpha$-expansion, and study the set\n  $$D_\\alpha:=\\{\\dim_H(\\Gamma_\\alpha \\cap (\\Gamma_\\alpha + t)):t \\textrm{ has a unique }\\{-1,0,1\\}\\,\\alpha\\textrm{-expansion}\\}.$$ We prove that there exists a transcendental number $\\alpha_{KL}\\approx 0.3943"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00858","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":"1604.00858","created_at":"2026-05-18T00:47:21.091858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00858v1","created_at":"2026-05-18T00:47:21.091858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00858","created_at":"2026-05-18T00:47:21.091858+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7EOLOWDL7DP","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7EOLOWDL7DP7Y45","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7EOLOWD","created_at":"2026-05-18T12:30:07.202191+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/B7EOLOWDL7DP7Y452I7QLWZMB7","json":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7.json","graph_json":"https://pith.science/api/pith-number/B7EOLOWDL7DP7Y452I7QLWZMB7/graph.json","events_json":"https://pith.science/api/pith-number/B7EOLOWDL7DP7Y452I7QLWZMB7/events.json","paper":"https://pith.science/paper/B7EOLOWD"},"agent_actions":{"view_html":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7","download_json":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7.json","view_paper":"https://pith.science/paper/B7EOLOWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00858&json=true","fetch_graph":"https://pith.science/api/pith-number/B7EOLOWDL7DP7Y452I7QLWZMB7/graph.json","fetch_events":"https://pith.science/api/pith-number/B7EOLOWDL7DP7Y452I7QLWZMB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7/action/storage_attestation","attest_author":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7/action/author_attestation","sign_citation":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7/action/citation_signature","submit_replication":"https://pith.science/pith/B7EOLOWDL7DP7Y452I7QLWZMB7/action/replication_record"}},"created_at":"2026-05-18T00:47:21.091858+00:00","updated_at":"2026-05-18T00:47:21.091858+00:00"}