An exact growth constant for the quadratic polynomial continued fraction

Structural proof and numerical verification of the exact two-sided growth law for
 the convergent denominators q_n of the quadratic polynomial continued fraction
 V(A,B,C) = 1 + K_{n>=1} 1/(A n^2 + B n + C), for integers A,B,C >= 1. With
 b_k = A k^2 + B k + C and the standard continuant q_0=1, q_1=b_1,
 q_n = b_n q_{n-1} + q_{n-2}, we prove
 
   log q_n = n log A + 2 log(n!) + (B/A) log n + (K_Gamma + delta) + kappa/n + O(1/n^2),
 
 where K_Gamma = -log(Gamma(1-r1) Gamma(1-r2)) is the elementary naive-product
 constant (r1,r2 the roots of A x^2 + B x + C; at B=0 it equals
 log(sinh(pi sqrt(C/A)) / (pi sqrt(C/A)))), delta = log R_inf > 0 with
 R_inf = lim q_n / prod_{k<=n} b_k is a strictly positive continued-fraction
 correction from the +q_{n-2} term, and kappa = (1/2)(B^2/A^2 + B/A - 2C/A).
 
 This sharpens the deposited one-sided denominator-growth bound
 log Q_n >= n log n - O(n) (which suffices for Euler's irrationality criterion and
 underlies the deposited 482-constant catalogue) to an exact expansion through
 O(1/n) with an explicit additive constant. No closed form is claimed for delta
 (an 80-digit PSLQ search for the triple (1,0,1) returns none).
 
 Epistemic status (SIARC four-class): STRUCTURAL (complete elementary hand proof,
 not yet machine-checked in Lean), modulo one standard cited asymptotic
 (DLMF 5.11.13 Gamma-ratio expansion); VERIFIED numerically (mpmath, 50-60 digits)
 on seven triples, with the B=0 cross-check K_Gamma = sinh form holding to 50 digits.

Changes in v1.1 (file-only): Replaced the manuscript PDF with the typeset repository build. The reference to the companion "Logarithmic Ladder" paper now carries its Zenodo concept DOI (10.5281/zenodo.19491767) in place of an internal placeholder note; an ORCID and code/data-availability + AI-assistance statements were added. No change to the mathematical content, results, or epistemic grading; the concept DOI (10.5281/zenodo.20564681) is unchanged.