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April 18, 20260 citationsOpen Access

A minimal bi-scalar extension for decoupling morphology sourcing from metric response in the VFT programme

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JFJan-Frederik Flügge

Key Points

  • The central aim is to propose a minimal bi-scalar extension that resolves a no-go situation in the VFT programme.
  • Introduce a second scalar field sourced by a specific quasilocal source functional.
  • Maintain the original scalar field in relation to the Jordan metric.
  • Establish conditions for structural consistency, including design, stability, and Solar-System bounds.
  • Identified a two-range Yukawa eigenmode structure in metric-visible weak-field response.
  • Showed compatibility with the SPARC baseline as a potential empirical test.
  • Confirmed the preservation of the structural integrity of the VFT programme despite the extension.

Abstract

The Verarmungsfeldtheorie (VFT) programme has recently been shown to admit a struc- tural no-go for its single-eld, single-coupling dynamical subclass: one conformally coupled scalar eld with one universal coupling function cannot simultaneously sustain the galactic monopole response, an active morphology-sensitive non-monopolar source channel, and Solar- System consistency. The present paper does not contest this result. Instead, we identify a minimal post-no-go architecture that removes the specic bottleneck diagnosed by the no-go, while leaving the structural and empirical pillars of the programme intact. The construction introduces a second scalar eld σ that is sourced only by the monopole-nulled quasilocal source functional and does not couple directly to matter, while the original conformally coupled eld χ remains the unique metric-visible scalar entering the Jordan metric. The architecture preserves the no-slip property of the conformal backbone by construction and transfers the morphology-sensitive source burden out of the Solar-System screening chan- nel. We formulate three explicit structural consistency conditions of the extension a design condition on the covariant source functional, a mass-matrix stability condition, and a Solar-System mixing bound and identify a generic phenomenological consequence: the metric-visible weak-eld response acquires a two-range Yukawa eigenmode structure whose compatibility with the SPARC baseline becomes a direct empirical test. The paper does not claim closure of the VFT programme; it provides the rst constructive step beyond the audit phase that produced the single-eld no-go.

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Cite This Study

Jan-Frederik Flügge (2026) studied this question.

synapsesocial.com/papers/69e320af40886becb653fbd4https://doi.org/10.5281/zenodo.19612401
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