First-crossing composition at resonant integer thresholds

A vanishing clock error can persist after first-crossing indices are composed. For harmonic returns, the inverse-digamma flow approaches its centered affine asymptote from above, eventually selecting strict rounding at affine ties. Every fixed positive-time cascade transfers to that rule outside a density-zero set, and its defect law is expressed as a Haar pushforward retaining resonant face values. At time log(3), the two-step harmonic defect is exactly 3 for every starting index n ≥ 1, whereas ordinary affine ceilings give 0. A signed criterion extends the transfer to logarithmic clocks. Positive truncations converge uniformly to log(2n+1) and admit arbitrarily high fixed-order flow approximations, yet all retain defect 3 while the limit has defect 0. Rational splitting also retains an explicit positive defect along every subsequence whose total overshoot satisfies nR_n → 0; both defects 1 and 2 occur with positive overshoot tending to zero at quadratic scale. This deposit contains the main preprint, a mathematical supplement with arithmetic classifications and finite-sample certificates, editable sources, and reproducibility files. External human mathematical review and the complete priority comparison remain pending. The DOI identifies this deposited version; it does not certify mathematical correctness or novelty.