AbstractWe develop a minimal microphysical bridge for the regime-3 branch of QFT-VER, in which thevacuum order parameterΨ=√φeiϑis coupled to a hidden asymptotically free sector that generates the periodic phase potential throughnonperturbative dynamics. The purpose of the paper is to replace the phenomenological input Λ(φ)by a controlled micro-to-EFT matching map.We show that, in the minimal P3-preserving branch, the amplitude Λ(φ) arises from RG transmutation dressed by φ-dependent threshold matching. The resulting low-energy information iscompressed into a small local data set near the background φ∗, most importantly the sensitivityparameterβ∗ ≡ dlnΛdlnφφ=φ∗ .A threshold-corrected master formula is derived, a local reduction theorem is formulated, and asmall predictive set of benchmark families for Λ(φ) is identified. We also provide an insertion sheettranslating hidden-sector inputs into EFT outputs for Model-0 and for subsequent gate analyses.The paper does not eliminate functional freedom completely, but disciplines it: admissible forms ofΛ(φ) are no longer arbitrary phenomenological choices, but descend from hidden-sector matchingdata. This places the vacuum EFT of QFT-VER on firmer microphysical footing and preparesits export into quantitative viability studies, without reopening the test-particle sector alreadymotivated separately
Ренат Гафаров (Sun,) studied this question.