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We prove that $N>1$ points in the Minkowski plane $\\R^{1,1}$ generate $\\Omega(\\frac{N}{\\log{N}})$ distinct distances, or all the distances are zero. The proof follows the lines of the Elekes/Sharir/Guth/Katz approach to the Erd\\H os distance problem, analysing the 3D incidence problem, arising by considering the action of the Minkowski isometry group $ISO^*(1,1)$.\n  The signature of the metric creates an obstacle to applying t"},"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":"1203.6237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-28T11:45:14Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0ca675877ef676892e98ff380525ba2b7cc191b7e495efcb372adf4c82a7b3d0","abstract_canon_sha256":"192d105800edbda05c0c9f5e4f7979589ca24b78d7009a7cbe10f7d645523044"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:53.858978Z","signature_b64":"0k6I3gAobs4soaFGzbmrAj/ty4+T5XkLCBS+s0TLw/rnvXZp3vXSJuQ9a1vjL5LTIcxq4i4yyJpBwHDe5LIHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"757acb9fe189d82a265ef616a02bd71782cb247745c10fab2cb0a848d7670094","last_reissued_at":"2026-05-18T03:30:53.858339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:53.858339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Minkowski distances and products of sum sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Misha Rudnev, Oliver Roche-Newton","submitted_at":"2012-03-28T11:45:14Z","abstract_excerpt":"Given two points $p,q$ in the real plane, the signed area of the rectangle with the diagonal $[pq]$ equals the square of the Minkowski distance between the points $p,q$. 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