PAPER-FBT02C: An S-Sector Maintenance Self-Energy Model of Effective Mass

This paper develops a conditional coarse-grained maintenance self-energy model for stable internal configurations in the Fracture–Berry–Tension framework, updated to the current single-carrier geometry of FBT0B and the affine-prequantum closure of FBT02A–FBT02B. The regular six-dimensional carrier is organised by the unique active relative-torus bundle Krel ↪→ X(6)Regπ −→ B(4)Reg, where Krel is an actual acting two-torus rather than the abstract contrast quotient Qrel = T3/ΔU(1). On the permutation-symmetric branch, Krel = KA2 = ker(z1z2z3). A primitive integral cycle in a local oriented cycle frame selects the residual circle ΣS ⊂ Krel that supports the loop algebra used by FBT02A. FBT02A constructs the strict affine central sector ˆ︂Lsu(2) = Lsu(2) ⊕ CKSwithρ(KS) = kaff id . FBT02B then uses the primitive first harmonic of the basic affine Cartan current to construct a positive prequantum line on the actual relative torus. On that branch, kpre = kaff = kS > 0. Thus the positive global normalisation used in the present paper is no longer introduced through a separate Berry–Affine matching hypothesis. FBT05A uses the tautological ray line and hence has the signed relation kBerry = −kS for the positively oriented primitive branch, while |kBerry| = kS. The maintenance self-energy constructed here is orientation-even at leading quadratic order and therefore depends on the positive capacity kS or equivalently on |kBerry|, not on the sign of kBerry. The geometric separation of FBT01A remains essential: ΩB ̸= A ̸= FA ̸= the affine-prequantum/Berry curvature layer. Since the relative orbit distribution is isotropic, ΩB|V ×V = 0, the central-response self-energy does not arise from a vertical restriction of the mother symplectic form.The local quantity entering this paper is not the global affine-prequantum level. We introduce a local central-response activity ϱS(x) =⟨︂Aˆ︁S(x)⟩︂, x ∈ B(4)Reg, or on a downstream Lorentzian/stable realisation of the same four-dimensional base. A finite-resolution field is then defined by ϕS(x) = Ccg[ϱS](x). A simple normalisation may use ϱS(x) = kSnS(x), with nS(x) a genuinely local dimensionless activity density. This does not localise the global integer kS. Let Cst ∈ Confst be a stable internal configuration carrying a nonnegative internal frequency operator ˆ︁Ω. Define ω2rms(Cst) = ⟨Cst, ˆ︁Ω2Cst⟩⟨Cst, Cst⟩.After unresolved central-response modes are integrated out, the leading positive local selfenergy is modelled by ΔES(Cst; x) = ζS(x) ϕS(x) ω2 rms(Cst), ζS(x) > 0. The corresponding effective rest-mass contribution is ΔmS(Cst; x) = ΔES(Cst; x)c20.The coefficient ζS is an effective constitutive response coefficient. It is not the affine level, the mixed two-form, the connection curvature, or a topological Chern integer. Geometry may dress ζS only through an explicitly defined response kernel. For a principal globally cycle-framed branch one may use connection components F(1)A , F(2)A . On an affine branch the cycle frame is local-system-valued, so the natural oriented curvature combination is the frame-covariant alternating pairing IF := 12εabFaA∧ FbA After a four-dimensional readout volume is chosen, IF = ρA volread4 may define an optional scalar dressing. Because εab is preserved by SL(2, Z), this formulation is compatible with the cycle-frame covariance of FBT0B. A QGT-compatible metric may alternatively define χη = ∥η∥2gread . Neither dressing is inserted without a separate response-kernel construction or a no-doublecounting audit.A Dirac-spectral realisation ˆ︁ΩD = cΣ|DΣ| gives ω2rms(χ) = c2Σ⟨χ,D2Σχ⟩⟨χ, χ⟩.The model is not claimed to provide the complete particle-mass spectrum. It supplies a conditional S-sector contribution to effective rest mass. A later inertial interpretation requires the same coefficient to appear in the worldline or kinetic action. The resulting dependency chain is FBT0B −→ Krel ↪→ X(6)Reg → B(4)Reg,FBT02A −→ KS, kaff,FBT02B −→ kS = kaff = kpre,FBT02C −→ ϱS(x) −→ ϕS(x) −→ ΔES −→ ΔmS..