
This technical report provides a consolidated response to four core comments on “Formulation of Scale-Gauge Theory and Its Cosmological Consequences.” The note clarifies (1) the status and derivation of the scale–centroid condition as an RG/symmetry consistency requirement rather than a definition; (2) the dynamical origin of the discrete hierarchy as repeated stationarity across threshold-separated RG intervals, anchored in Coleman–Weinberg corrections and matching conditions; (3) the avoidance of the second–clock effect by relocating scale symmetry to a gauge redundancy while keeping the spacetime geometry Riemannian; and (4) the emergence of a genuine multi–minima structure in a classically scale-invariant setting through loop-induced potentials, piecewise running, and portal couplings. A concise summary is provided in the main text, with technical derivations assembled in Appendices A–D. The document is intended to be read alongside the original Part I (framework) and the follow-up Parts II–III (derivations and cosmological implications). All files (PDF and source) are included for transparency and reproducibility.
scale symmetry, discrete hierarchy, effective potential, Weyl gauge, Coleman–Weinberg, second clock effect, Riemannian geometry, renormalization group
scale symmetry, discrete hierarchy, effective potential, Weyl gauge, Coleman–Weinberg, second clock effect, Riemannian geometry, renormalization group
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