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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","authors_text":"Bochen Liu","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-18T16:01:45Z","title":"Hausdorff dimension of pinned distance sets and the $L^2$-method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08127","kind":"arxiv","version":3},"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":"sha256:652130e531d77d3e1519f5a60750c976cbd95ea6f8ef8c0531fba22878e0bfe5","target":"record","created_at":"2026-07-05T00:16:58Z","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":"96f81e71d6860f11eac8562c396f0b2ecddfde914b8dd60c52cc370f5b134acc","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-18T16:01:45Z","title_canon_sha256":"6a1167228342382a6a76be66a686f1d27291cbf34c23e4804f9775519703651b"},"schema_version":"1.0","source":{"id":"1810.08127","kind":"arxiv","version":3}},"canonical_sha256":"09139e3112d16ff444a523c6fa59b4f5598be7f384d801d50706f8100925e94a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09139e3112d16ff444a523c6fa59b4f5598be7f384d801d50706f8100925e94a","first_computed_at":"2026-07-05T00:16:58.835457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:58.835457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"++9/Q8CEmoHnc+mBbbowqpIt/i4xb7tRX+7LkTmZYF/ra5c3YxsiRPndfqn6eMUwt8uXNEF1LR2tvfgZ098NAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:58.835833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08127","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:652130e531d77d3e1519f5a60750c976cbd95ea6f8ef8c0531fba22878e0bfe5","sha256:8b9cd082f5213045f150053b984729bbfa7baad65b95c43de8babc8413f5c5bc"],"state_sha256":"70a5326b0d1a359e193019712e018b2f18da7c4df835b7fd93c0d91d63ae91b8"}