Conditional Scale Selection and Curvature Normalization in the Axis Model

We separate a microscopic scale benchmark from the finite normalization of the Einstein–Hilbert operator. A positive quadratic response with a supplied scalar source gives an exact reduced binding term. For fixed coefficients, the scale functional B ell^(-4) − A_bind ell^(-3) + C_wall ell^2 has a unique global minimum on ell > 0 when A_bind >= 0 and B, C_wall > 0. We prove this result, its joint field–scale stability criterion, and the derivative corrections needed when the coefficients vary. A specified response reader and an independent energy unit then convert dimensionless coordinates to a length. The gravitational reference coefficient remains finite matching data. For a declared normalized Gaussian theory with two real neutral scalar blocks, one photon, and a screened Abelian vector complex, the signed minimal curvature sum is S_min = −5/6 − xi_1 − xi_2. It enters a loop contribution, while the total coefficient obeys A_EH = A_* + [f C_loop − f_* C_loop,*] + Delta A_loc. The familiar area normalization and rational response are explicit specializations. A published numerical example is retained as a conditional benchmark with its reader, units and reference condition exposed. The construction establishes neither an absolute physical Newton constant nor a universal replacement for the coupled metric and source equations. Version v2 corrects the scale-selection and gravitational-normalization claim scope of the historical v1 record (DOI: 10.5281/zenodo.20611626), which remains preserved under the same Zenodo concept. The historical numerical output is retained as a benchmark, not a physical Newton-constant prediction. Curvature matching is imported from F5's conditional H1 effective theory; source normalization and ultraviolet transport retain their originating Action-Level and UV Matching authority. The present conditional construction does not use measured gravitational quantities to set the displayed inputs; this does not certify their independent historical selection. No physical parent selection or H2 completion is asserted. The accompanying source, notebook, manifests and clean-execution receipt form the v2 reproducibility release. The computational artifact is version 2.0.0, with notebook Axis_F13_Conditional_Normalization_Reproducibility_v2.0.0.ipynb and package Axis_F13_v2_Source_and_Reproducibility.zip. The original notebooks remain separate historical provenance. No experimental dataset was generated or used to select the revised calculation.