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In this paper, we investigate the intersection of the unit circle $\\mathbb{S} \\subset \\mathbb{R}^2$ with the Cartesian product $K_{\\lambda} \\times K_{\\lambda}$. We prove that for $\\lambda \\in(0, 2 - \\sqrt{3}]$, the intersection is trivial, i.e., \\[ \\mathbb{S} \\cap (K_{\\lambda} \\times K_{\\lambda}) = \\{(0,1), (1,0)\\}. \\] If $\\lambda\\in [0.330384,1/2)$, then the intersection $\\mathbb{S} \\cap (K_{\\lambda} \\times K_{\\lambda})$"},"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":"2507.16510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-07-22T12:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"9bb2c460b1c0883593948d8038e070d46a9350c04bc36f077cc971be0e17d227","abstract_canon_sha256":"4011a8c577e8bfc29c48e22f1869c6afaaee963a34c1261c0bfa4c2f0b28163d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:11.253865Z","signature_b64":"92PILsc86dG0IfTsHWSMXAsqZI4bIuB+UsIBJ7qW8v/EKLDnjIgZFFtdsHmj1L//C5iZ9T2aaLnJuGJ5YzG+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb3a2b32d801c10b01b0d57f8a1564dcc3d6aca40fbe3d34c7dff6712f3bc8b","last_reissued_at":"2026-07-05T11:41:11.253368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:11.253368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the intersection of Cantor set with the unit circle and some sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Derong Kong, Kan Jiang, Wenxia Li, Zhiqiang Wang","submitted_at":"2025-07-22T12:16:02Z","abstract_excerpt":"For $\\lambda\\in(0,1/2)$ let $K_\\lambda$ be the self-similar set in $\\mathbb{R}$ generated by the iterated function system $\\{f_0(x)=\\lambda x, f_1(x)=\\lambda x+1-\\lambda \\}$. 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We prove that for $\\lambda \\in(0, 2 - \\sqrt{3}]$, the intersection is trivial, i.e., \\[ \\mathbb{S} \\cap (K_{\\lambda} \\times K_{\\lambda}) = \\{(0,1), (1,0)\\}. \\] If $\\lambda\\in [0.330384,1/2)$, then the intersection $\\mathbb{S} \\cap (K_{\\lambda} \\times K_{\\lambda})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16510","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.16510/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.16510","created_at":"2026-07-05T11:41:11.253431+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.16510v1","created_at":"2026-07-05T11:41:11.253431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16510","created_at":"2026-07-05T11:41:11.253431+00:00"},{"alias_kind":"pith_short_12","alias_value":"3WZ2FMZNQAOB","created_at":"2026-07-05T11:41:11.253431+00:00"},{"alias_kind":"pith_short_16","alias_value":"3WZ2FMZNQAOBBMA3","created_at":"2026-07-05T11:41:11.253431+00:00"},{"alias_kind":"pith_short_8","alias_value":"3WZ2FMZN","created_at":"2026-07-05T11:41:11.253431+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/3WZ2FMZNQAOBBMA3BVL7RIKWJX","json":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX.json","graph_json":"https://pith.science/api/pith-number/3WZ2FMZNQAOBBMA3BVL7RIKWJX/graph.json","events_json":"https://pith.science/api/pith-number/3WZ2FMZNQAOBBMA3BVL7RIKWJX/events.json","paper":"https://pith.science/paper/3WZ2FMZN"},"agent_actions":{"view_html":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX","download_json":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX.json","view_paper":"https://pith.science/paper/3WZ2FMZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.16510&json=true","fetch_graph":"https://pith.science/api/pith-number/3WZ2FMZNQAOBBMA3BVL7RIKWJX/graph.json","fetch_events":"https://pith.science/api/pith-number/3WZ2FMZNQAOBBMA3BVL7RIKWJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX/action/storage_attestation","attest_author":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX/action/author_attestation","sign_citation":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX/action/citation_signature","submit_replication":"https://pith.science/pith/3WZ2FMZNQAOBBMA3BVL7RIKWJX/action/replication_record"}},"created_at":"2026-07-05T11:41:11.253431+00:00","updated_at":"2026-07-05T11:41:11.253431+00:00"}