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Report . 2026
License: CC BY NC ND
Data sources: Datacite
ZENODO
Report . 2026
License: CC BY NC ND
Data sources: Datacite
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Consolidated Response to Reviewer's Comments on "Formulation of Scale-Gauge Theory and Its Cosmological Consequences" (with Appendices A–D)

Authors: Goto, Susumu;

Consolidated Response to Reviewer's Comments on "Formulation of Scale-Gauge Theory and Its Cosmological Consequences" (with Appendices A–D)

Abstract

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.

Keywords

scale symmetry, discrete hierarchy, effective potential, Weyl gauge, Coleman–Weinberg, second clock effect, Riemannian geometry, renormalization group

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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