An Axion-like Higgs in the Absolute Frame Theory: Self-Couplings and a di-Higgs Signature

July 12th, 2026: updates following the development within the Absolute Frame Theory. In the Absolute Frame Theory (AFT) the Higgs is not a fundamental field: it is the chiral anisotropy of the background embedding X₀ of the observable four-dimensional manifold M into a flat fourteen-dimensional Euclidean substratum A (N=14=4+10), the neutral component of the electroweak bidoublet (1,2,2) in the 10 of the normal SO(10). We compute its effective potential, self-couplings, and unitarity, sorting every statement into what AFT derives and what it does not. The routing term of the AFT action evaluated on a single-plane-wave pilot wave—a theorem under substratum homogeneity—produces a bounded cosine potential V(φ) = −g_Ψ·cos(θ₀ + k_n·φ). Because the embedding field space is flat Cartesian ℝ⁴, the kinetic and gauge sector is Standard-Model-like, κ_V=1, in contrast with composite-Higgs constructions on a curved coset, where κ_V=√(1−ξ). The self-couplings follow from the cosine: the trilinear vanishes, κ_λ=0—a robust prediction, the only source able to switch it on being local spacetime curvature, suppressed by a factor ~10⁻⁵⁹ in canonical normalization with the embedding tension T_A canceling—while the quartic is negative, κ_4=−ξ/3, with a ~20% renormalization-group shift to the scale f. The resulting signature (κ_V, κ_λ, κ_4) ≈ (1, 0, −ξ/3) is a point inaccessible to curved-coset composite Higgs models, which correlate κ_V and κ_λ through a single parameter ξ. Tree-level perturbative unitarity is sound to the natural cutoff √s ~ f = v/√ξ, and one-loop vacuum stability is better than the Standard Model, a bounded cosine replacing a metastable quartic. The relation m_h² = g_Ψ/f² is dimensionally consistent. The prediction κ_λ=0 is testable at the high-luminosity LHC; the standard κ_V-driven compositeness bound is evaded because κ_V=1, leaving ξ largely unconstrained. AFT derives the form and the correlations among these couplings; the electroweak scale v, the phase θ₀, ξ, the amplitude g_Ψ, and the gauge-coupling values remain boundary data of A.