Tail-Index Renormalization after Posts in Classical Sequential Growth

Classical sequential-growth models of causal sets transform their projective coupling sequences after a post by a known binomial map. This preprint proves a uniform adjacent-ratio theorem for sequences whose ratios are eventually positive, eventually nonincreasing, and regularly varying with index −α < 0. The effective power index is −α/(α+1) throughout every subscale precursor window. When the precursor size is proportional to the balance scale, the normalized response instead approaches the unique positive solution of x(c+x)^α = 1. Constant-ratio, slowly varying, finite-support, and sparse boundaries delimit the result. The proof uses regular variation and geometric localization of positive triangular sums. The theorem is conditional on a supplied algebraic coupling tail and does not select a CSG law, establish post occurrence or recurrence, recover a continuum, or predict a physical parameter.Version 0.2.1 is a typesetting-only correction. It adds a properly rendered PDF and buildable TeX source because Zenodo's Markdown preview did not render the mathematics or tables in v0.2.0. The scientific claims, hypotheses, proofs, evidence, and reproducibility archive are unchanged.