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This answers a question recently raised by Guth, Iosevich, Ou and Wang, as well as improves results of Keleti and Shmerkin.\n  (This version is already published on Proceeding AMS so I would like to leave it unchanged. However the statement in the abstract, which is the second part of Theorem 1.1, should be weakened a bi"},"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":"1810.08127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-18T16:01:45Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"6a1167228342382a6a76be66a686f1d27291cbf34c23e4804f9775519703651b","abstract_canon_sha256":"96f81e71d6860f11eac8562c396f0b2ecddfde914b8dd60c52cc370f5b134acc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:16:58.835833Z","signature_b64":"++9/Q8CEmoHnc+mBbbowqpIt/i4xb7tRX+7LkTmZYF/ra5c3YxsiRPndfqn6eMUwt8uXNEF1LR2tvfgZ098NAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09139e3112d16ff444a523c6fa59b4f5598be7f384d801d50706f8100925e94a","last_reissued_at":"2026-07-05T00:16:58.835457Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:16:58.835457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hausdorff dimension of pinned distance sets and the $L^2$-method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.CA","authors_text":"Bochen Liu","submitted_at":"2018-10-18T16:01:45Z","abstract_excerpt":"We prove that for any $E\\subset{\\Bbb R}^2$, $\\dim_{\\mathcal{H}}(E)>1$, there exists $x\\in E$ such that the Hausdorff dimension of the pinned distance set\n  $$\\Delta_x(E)=\\{|x-y|: y \\in E\\}$$\n  is no less than $\\min\\left\\{\\frac{4}{3}\\dim_{\\mathcal{H}}(E)-\\frac{2}{3}, 1\\right\\}$. This answers a question recently raised by Guth, Iosevich, Ou and Wang, as well as improves results of Keleti and Shmerkin.\n  (This version is already published on Proceeding AMS so I would like to leave it unchanged. 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