The Bousso covariant entropy bound and the Randall–Sundrum II braneworld — both established physics — are evaluated on the S³/Z₂ orbifold geometry. The holographic encoding capacity condition forces the orbifold order to |Z₂| = 2 and the bulk dimension to |Z₂|^|Z₂| + 1 = 5, confirmed by 60 proofs across 19 mathematical domains. The resulting geometry with SU (5) gauge–Higgs unification via the Hosotani mechanism produces 52 physical quantities with zero adjustable parameters and zero open premises. Genesis freezing is a theorem (Proof 53, four independent routes from |Z₂| = 2) ; the microcanonical coupling theorem follows as the unique projection of the proven state. The single dimensionful anchor is the observer's own embedding scale ℓ ≈ 35 µm, self-consistently determined by Λ₄; all 49 dimensionless predictions are independent of this anchor. At every other orbifold order, all five benchmark quantities fail simultaneously. Every dimensionless observable is Tr (ρ · O) — a Born-rule expectation value on the genesis-frozen microcanonical state, with a different operator O for each sector. The gauge coupling, the cosmological constant, the CMB spectrum, and the dark matter ratio are not independent constructions: they are the same state measured with different projectors. The invariant is |Z₂| itself: every derived quantity is a tower address in the |Z₂| exponent tower (Proof 45), and the 52 predictions are 52 representations of this single generator. The encoding base of this tower is |Z₂|· (|Z₂|^|Z₂| + 1) = 10: every digit 0–9 is a tower address, and the gap between each prediction and observation is the measurement projector's traversal cost through the encoding geometry. The 52 quantities span the gauge couplings (g₂² = 4249/10000, α₃⁻¹ = 111229/13125), the electroweak scale (v = 246. 25 GeV), the Higgs and top-quark masses (with two-loop corrections on S³/Z₂ computed here for the first time in the gauge–Higgs unification literature), the CMB angular power spectrum (χ² = 0. 387 against Planck 2018), the cosmological constant, the dark matter ratio (ΩDM/Ωb = 59/11, confirmed at +0. 013%), and the fermion mass hierarchy. Of the 32 predictions, 26 are confirmed within 2σ; six are testable by near-term experiments (FCC-ee, sub-mm gravity, nEXO, DESI). The derivation chain is presented in sufficient detail for independent verification or falsification. Cross-sector rigidity is analytically derived: d (ln v) /d (ln η₃) = − (d+D) /d = −9/4, giving 278σ electroweak sensitivity per 0. 5% upstream perturbation with no correlated fitting corridor.
Alexander Humphrey (Thu,) studied this question.