qSR: A Reproducible Dimensionless Structural Self-Regulation Constant for a 9+1 Closure Class — with Supplement v1.0

This release supplements qSR v1.4 with a unified account of ten-position internal closure. The qSR return invariant is the reciprocal Perron scale of a normalized positive cycle-with-retention operator and satisfies q^10 + q = 1. The supplement organizes C1–C5 as structural combinations with canonical readouts K, phi, e, pi and the Euler–Mascheroni constant, while C6–C10 provide a five-dimensional observation frame based on N_A, c, h, k_B and standard gravity. Internal K is a typed readout of the return structure; G and c enter only through an optional gravitational projection.The construction connects the d-indexed root family, finite return identities, continuous composition, cyclotomic phase and spectral-count compensation. An explicit dimensionless residual ledger establishes joint zero closure under the declared interfaces, supported by reproducible algebraic and numerical checks, negative controls and source hashes. The contribution lies in the organization and joint constraints of these interfaces, rather than the discovery of familiar constants or special functions. The original qSR v1.4 is retained, and the supplement separates exact internal relations from physical identification and external measurement.