All five Standard Model mixing observables from one number. The Binary Screen is the first nontrivial rendered boundary in Two-Sided Closure Theory (TSCT). Three physical axioms — finite capacity, non-triviality, minimality — force Jones index M: N=2, giving the A₃ subfactor with one canonical amplitude: a₊ = 3/√20 From this single number, five mixing angles emerge through different readout functions — no free parameters in the algebra: tan θ₁₂ = a₊ → θ₁₂ ≈ 33. 85° (solar, obs: 33. 4°±0. 75°, 0. 6σ) sin θ₂₃ = a₊ → θ₂₃ ≈ 42. 13° (atmospheric, obs: 42. 3°±3. 0°, 0. 1σ) sin θ₁₃ = a₊·a₋ → θ₁₃ ≈ 8. 63° (reactor, obs: 8. 54°±0. 15°, 0. 6σ) δCP = ±π/2 → δCP = ±90° (CP phase, obs: -87°±38°, 0. 1σ) sin θC = a₋ → θC ≈ 12. 92° (Cabibbo, obs: 13. 0°±0. 1°, 0. 8σ) The second amplitude a₋ = 1/√20 and their product a₊·a₋ = 3/20 complete the picture. The corrected atmospheric angle uses the same amplitude a₊ as the solar angle — different trig function, same source. The sign grading Γ and crossing operator S anticommute; their product I = ΓS satisfies I² = -1, providing a natural complex structure. The PMNS (e, 3) entry U₄₃ = I·a₊a₋ = ±i·3/20 yields both the reactor angle and CP phase from one oriented residual coupling. All five observables within 1σ. Zero free parameters in the algebra. All results conditional on named readout lemmas — nothing overclaimed. Paper V of the TSCT series. Companion papers I–IV on Zenodo.
David Manton Sparks (Thu,) studied this question.