A Parameter ASIP for the Quadratic Family

The paper proves an ASIP for the parameter process near a transversal Misiurewicz parameter by (i) constructing a positive-measure Cantor set Ω* via a polynomial Benedicks–Carleson exclusion with precise distortion/comparability bounds (Proposition 2.2; Lemma 2.4, incl. the new (2.31)) and (ii) transferring uniform exponential decorrelation and fractional response from phase to parameter space, then executing a block–martingale–Skorokhod scheme to obtain error exponents γ>2/5 (Theorem 1.1; Section 4) . The candidate outline matches the high-level scaffolding but incorrectly asserts uniform L^p bounds for block-level martingale differences and invokes a reverse-martingale strong invariance principle without verifying its hypotheses; in the paper, fourth moments of the block martingale terms grow like j^{4/3+ι} and are handled via tailored LLN and Skorokhod time-change, not by a uniform-moment ASIP for reverse MDs (see (4.20), (4.25)–(4.31)) .