Equations actually solved
L_A = −¼FμνFμν + |DμΦ|² − λ(|Φ|² − v²/2)²
L_B = L_A + ½∂μχ ∂μχ − (κ/2)χ²|Φ|² − βJχ
χ̈ = ∇²χ − κχ|Φ|² − βJ
Φ̈ = DᵢDᵢΦ − 2λ(|Φ|² − v²/2)Φ − (κ/2)χ²Φ
βJ = source slider × zero-mean prescribed spatial Gaussian
EFMW root, when κ = 0:
∇²χ − ∂²ₜχ = βJ (c = 1)
Sign convention: metric ( + − − ), c = ℏ = 1. The full EFMW physical root identifies βJ = (4π/c²)(E + cP), but the definitions, units and physical generation of E and P are presently unresolved. Here βJ is only a transparent computational surrogate. The portal is a new hypothetical toy extension, not a consequence proven from EFMW.
The candidate scalar χ starts from a disclosed two-lobe pulse; the reference has no χ. Setting κ=0 makes it decouple from the Higgs–gauge sector. The source is static and mean-zero on the periodic grid, so it has a well-defined time-independent source potential.
Scope, provenance & falsification
- Reference: one classical U(1)-charged complex scalar, one U(1) gauge field, leapfrog/velocity-Verlet, gauge-covariant links, periodic space, temporal gauge A₀=0.
- Not simulated: SU(2), SU(3), fermion spinors, Yukawa dynamics, θ-QCD, quantum loops, gravity or a complete EFMW C1 11-sector theory.
- Energy: “Energy density” image excludes χ so that A and B are comparable; the total candidate Hamiltonian includes χ kinetic/gradient, portal potential and static-source potential.
- Numerical tests: Gauss law, energy drift, finite values and κ=0 decoupling; full convergence, independent verification and empirical agreement remain unperformed.
- Scientific next step: repeat at fixed physical L with resolutions 32, 64 and 128, compare convergent observables, and quantify the effect of κ with matched baseline data.
Source reference: EFMW frozen C1 audit and open physical obligations. These documents do not validate the coupling simulated here.