Claims

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2020_01_08_cruz_lai_pramanik: An arXiv preprint claiming that every infinite set of reals is avoided by a compact set of positive measure, the full Erdős similarity conjecture, withdrawn by its authors three days later over a gap in Proposition 3.3.

2026_07_03_mora_cuellar_iosevich_kulkarni_rojas_aravena_yavicoli: An arXiv preprint asserting that the sum or difference of a geometric sequence, or of any set containing a lacunary sequence of at most exponential decay, and an arbitrary infinite set is never measure universal.

2026_09_03_iosevich_kulkarni_mora_cuellar_rojas_aravena_yavicoli: An arXiv preprint asserting that every set supporting a probability measure with Fourier-Stieltjes transform vanishing at infinity is avoided by a closed periodic set of relative measure at least 1 - epsilon.

2026_09_25_openai: A release manuscript proving that for every eta in (0,1) a compact subset of [0,1] of measure above 1-eta contains no affine copy of {2^{-n} : n >= 1} with nonzero dilation of either sign, accepted as a partial answer on the Lean declaration the corpus's verification built and audited.

2026_10_05_openai: A release manuscript claiming that for each fixed ratio q in (0,1) and each eta in (0,1) a compact subset of [0,1] of measure above 1-eta contains no affine copy of {q^n : n >= 1} with nonzero dilation; pending, with only the ratio q = 1/2 formally verified.

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