A Conditional Structural Reconstruction of Newton’s Constant: Dimensionless Gravitational Coupling from Defect–Platform Co-Selection

Newton’s constant fixes the strength of the effective metric response, but its magnitude is not determined by Einstein’s equations. This paper investigates a conditional finite matching model for the dimensionless coupling αG(M)=GM2/(ℏc), motivated by joint selection of persistent matter identities, their supporting platform, and admissible laws. A specified single-anchor contrast boundary gives a 43-dimensional selector with an intrinsic 18+25 split. An explicit rooted-family bijection connects the eighteen baryon routes to oriented derangements; its physical continuation and reversal interpretations remain premises. The return quotient admits a vector-space comparison with a five-role interface, but a character obstruction excludes identification of their two natural axis-relabeling actions. A covariant physical interface comparison is therefore required separately. Faithful local transports, including one cross-sector bridge, give a scalar commutant and the normalized return weight 25/43. Independent completed-channel composition and one-channel normalization select the determinant C*18. Correction coefficients are formulated with one ambient trace and explicit support conditioning; an exhaustive set of rules for factorizing depth records gives the return completion. Under these premises and the gravitational matching, αG(e)≃1.75181×10−45, corresponding to Gstr≃6.67430×10−11m3kg−1s−2. The numerical agreement is retrospective. The leading term already lies within the CODATA 2022 uncertainty, which does not discriminate the correction coefficients. The frozen matching relation is testable by new absolute determinations of G. The finite implications are exact in the stated model; physical selection of the boundary, interface, and history rules remains open.