PAPER-FBT10B: The Scalar Response Mode as an Emergent Higgs-like Sector in the FBT Framework

In the Fracture–Berry–Tension (FBT) framework, the effective four-dimensional spacetime metric is interpreted as a coarse-grained response to quantised dual-phase curvature rather than as a fundamental field. Once a symmetric response tensor is introduced on the emergent Lorentzian sector, Lorentz covariance implies a canonical decomposition into a trace scalar mode and a traceless tensor mode. The traceless sector supplies the spintwo-type gravitational response slot, while the trace sector supplies a distinguished scalar response mode. The purpose of the present paper is to study this scalar response mode as an emergent Higgs-like scalar sector. We do not postulate an independent fundamental Higgs field, nor do we claim here to derive the full Standard Model Higgs doublet. Instead, we argue that the canonical trace component of the response tensor provides a natural low-energy order parameter associated with coarse-grained dual-phase geometry. The central mechanism—Berry-locking-induced bifurcation of the scalar response—is treated as a structural principle, analogous to the worldline readout postulate of FBT10A. The transition from the local QGT stiffness of FBT06A to the effective scalar potential parameters (μ2, λ) is identified as an open bridge problem, whose conceptual architecture is supported by the rootareaenergy accumulation chain of FBT30A but not yet reduced to an explicit derivation. Under mild locality, symmetry, and stability assumptions, the effective real-scalar potential takes a Landau double-well form with a broken-symmetry vacuum and a propagating radial scalar fluctuation. Within this interpretation, a Higgs-like scalar order parameter is not a primitive input but an effective rewriting of geometric information already present in Berry curvature, thimble suppression depth, mixed horizontal–vertical density, responsetensor structure, and dual-phase coarse-graining. The observed Higgs boson may then be interpreted, at the effective low-energy level, as the propagating fluctuation of this scalar response mode around its broken vacuum. The embedding of this response mode into the full electroweak SU(2)L×U(1)Y gauge structure, including Goldstone modes, Yukawa matrices, and precision couplings, is left to later work.