Strong Bounds for 3-Progressions
summary
Proves a quantitative improvement showing dense A ⊂ {1..N} with size at least N/C must contain 3-term progressions until C reaches about 2^(log N)^(1/12), and gives a concrete count of solutions (roughly 2^{-d^{12}}·N^2 in the integer/cyclic setting, better exponents over F_q^n). Main engine is a dichotomy: either pnorm pseudorandomness holds or one gets a density increment onto a structured set; the proof uses spectral positivity, sifting via intersections of shifts, and bootstrapping to a subspace.
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