The Higgs field interpretation of electroweak symmetry breaking is shown to be gravitationally impossible. A scalar condensate with vacuum expectation value of 246 GeV necessarily contributes an energy density of approximately 10^8 GeV^4 to the vacuum. The observed vacuum energy density is approximately 10^-47 GeV^4—a discrepancy of 55 orders of magnitude. The total energy required by the Higgs field (10^126 joules) exceeds the entire energy budget of the observable universe (10^71 joules) by a factor of 10^55. This "Incoherence Factor" constitutes a gravitational exclusion: the Higgs field cannot exist because it requires more energy than the universe contains. The geometric alternative—Kähler moduli stabilization in Type IIB string compactification—resolves all discrepancies. The cosmological modulus derives the observed vacuum energy to within approximately twenty-five percent, while the electroweak modulus produces a vacuum expectation value of 247 GeV and a scalar excitation near 125 GeV. The dark energy to matter ratio of 2.36 matches observation (2.13) within 11%. The electroweak parameters are derived from quantum group structure: the Higgs mass formula yields 123.5 GeV (observed: 125.25 GeV, 1.4% agreement). The quartic coupling is 0.125 (observed: 0.129, 3.1% agreement). The observed vacuum energy is not a substance requiring a source but the geometric eigenvalue of a stabilized manifold—the intrinsic tension required to prevent decompactification. The 125 GeV excitation discovered at the Large Hadron Collider is real; it is a modulus fluctuation, not a field condensate. The Higgs field is an ontological ghost—a mathematical error that has persisted for six decades.