Exact Closed Form Blind Prediction of the Quartic Higgs Self Coupling Parameter κ λ4

Following the analytical resolution of the trilinear Higgs self-coupling ratio κ_λ = 1 + |det(M)| / ℸ ≈ 1.002519, the complete reconstruction of the electroweak scalar potential requires isolating the quartic (hhhh) self-coupling vertex parameter λ4. In the continuous Standard Model, tree-level gauge invariance imposes λ4,SM ≡ λSM = mH² / (2v²) ≈ 0.129042, whereas current observational limits on triple-Higgs production (pp → hhh) at the Large Hadron Collider leave κ_λ4 ≡ λ4 / λ4,SM unconstrained by orders of magnitude. Within the discrete 5D cyclic complex Matrix M ∈ ℂ⁵ˣ⁵ framework governed by the quantum vacuum phase saturation bound ΦC = π / 4 and the coupling invariant ℸ ≡ e / (π α) ≈ 118.5712176, we derive the quartic Higgs self-coupling modification as a deterministic, second-order boundary projection: κ_λ4 = 1 + |det(M)|² / ℸ = 1 + (0.29867507)² / 118.5712176 ≈ 1.000752. This rigorously fixes the absolute quartic coupling to λ4 ≈ 0.129139, establishing an exact +0.0752% positive departure from tree-level symmetry. This monograph registers an a priori blind prediction securing absolute academic priority ahead of future 100 TeV hadron collider (FCC-hh) sensitivity reach.