A Conditional Structural Reconstruction of Newton’s Constant: Dimensionless Quantum–Gravitational Coupling from Defect–Platform Co-Selection
Abstract
Newton’s constant G fixes the universal strength of the low-energy metric response, but the Einstein field equations do not determine its magnitude. At the interface of quantum theory and gravitation, the more appropriate structural target is the dimensionless coupling αG(M)=GM2/(ℏc), which compares the gravitational response of a mass anchor M with the quantum unit of action. We ask a deliberately limited question: can the normalization of this coupling be represented by a finite premetric selector while continuous Einstein and quantum-field dynamics remain downstream? Within a neutral-parent reconstruction framework, representative independence, cut independence, universality, and compositional consistency lead conditionally to a finite defect–platform module. An explicit boundary map gives dim Md=2d−d−1; for d=4, it splits intrinsically as 43=18+25. The eighteen-dimensional part matches an independently published light-baryon route count under a stated grade–role rule, while the twenty-five-dimensional part is an explicit ordered return module. Stated local cut transports generate M43(R), so a cut-independent scalar cannot assign unrelated weights to the two parts; the neutral projection is therefore 25/43. Basis invariance and multiplicative composition uniquely select the determinant, giving C*18, and finite symmetry projectors followed by a one-stratum return recurrence give the remaining correction. The finite theorems are exact inside the declared objects. Their use…
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