PUH Theorem 393 — A Fixed Handedness Cannot Twist Light Evenly; a Half-Turn Step in Light's Topological Angle Would Twist the Oldest Light by α/2 = 0.209°, Within One Error of the Measured Twist

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. The microwave background's polarization arrives turned by a small angle, the same across the sky: 0.215 ± 0.074° from ACT DR6, 0.265 ± 0.058° with WMAP and Planck (T391's combination), consistent with no change across frequency (β ∝ ν^n, n = −0.35 +0.48/−0.47; Eskilt 2022). T391 showed that a twist the same in every direction needs something a mirror reverses, and that the archive's handedness has that shape, but found no coupling of it to light; T354 had said the framework contains no axion and no such coupling. Can this archive's handedness couple to light at all — through what, and how strongly? The author chose this as the next step after T391. RESULT 393.1 — A FIXED HANDEDNESS TWISTS NOTHING. In this archive's lattice the candidates close one by one: its bonds at the roots of E8 come in opposite pairs (T320) and its equations, second order in time (T175, as T381 notes), keep time reversal, so it gives light no handedness of its own (a handed medium would turn polarization as ν², 4.90 upper errors from Eskilt's fit); Faraday rotation goes as ν⁻² (3.51 lower errors) and T368 keeps the rebound's field out of space; turning gives at most 5.6e-9 rad (T391). With the Lorentz symmetry of the lattice's waves (T317), the only term left is electromagnetism's own handed term, θE·B, and while θ stays constant it does nothing: E·B is a total divergence. A handedness that never changes twists nothing. The twist measures how much θ changed along the light's path, β = αΔθ/2π, the same at every frequency (Eskilt's fit lies 0.73 of its error from no change). RESULT 393.2 — A HALF TURN TWISTS LIGHT BY α/2. If light keeps time-reversal symmetry, θ can be only 0 or π, so a change between two such phases is at least a half turn, which turns light by α/2 = 3.6487e-3 rad = 0.2091°, with nothing to adjust — the angle of one half-quantized Hall layer, one surface of a topological insulator (tan φ = α/(1 + n), n = 1). It lies 0.08 errors below ACT's value and 0.96 below the combined one, and within 1.5 errors of every measurement; a full turn, 0.4181°, lies 2.74 errors above ACT and 2.64 above the combined value, and the next odd step, 0.6272°, 6.24. RESULT 393.3 — WHEN THE STEP COULD COME: T369'S TRANSITION. The step must come after the light left, and the one change of phase the archive proposes in that interval is T369's: at once 10.5 to 11.4 billion years ago (z = 1.99 to 2.71), or region by region on its spread, a tenth of space changed by 12.6 and nine-tenths by 8.3 billion years ago (z = 4.92 and 1.09; width 0.406 e-folds, half changed at z = 2.52). Reionization, at z_re = 7.64 for τ = 0.054, came earlier. If the two phases differ by a half turn, every photon emitted before its region changed is turned by α/2 — all the light of last scattering, the same in every direction, since the turn depends only on θ where the light starts and ends; reionization's at once, or 0.9865 of it region by region (0.0135 of space having changed first) — and light from galaxies below z = 1, on average, almost not at all (0.017° at z = 1). Only something that CP reverses can choose the sign: T391's screw, or the weak handedness together with our matter excess, but not the weak handedness alone, which CP leaves unchanged; if nothing chooses, the sign is our own region's. RESULT 393.4 — WHAT WOULD SHOW IT. Every way to twist light uniformly and by the same angle at every frequency is a change in θ. A steady drift needs a rate the archive does not supply — 3.5451e-29 rad per metre of light path, 1.0811e-29 per comoving metre, or 0.03789° per e-fold — and gives the reionization signal (Sherwin and Namikawa 2021) 0.951, 0.650 or 0.308 of the recombination twist, and light from z = 1 0.153°, 0.065° or 0.026°. The half-turn step needs no rate, gives the reionization signal 1 at once or 0.9865 region by region, and leaves light from below z = 1 almost untouched on average. RESULT 393.5 — IF THE LATTICE CARRIES θ, THE COUPLING'S STRENGTH IS α. T354's 'no such coupling' narrowed: the coefficient of E·B in a medium is a property of its phase, not a new field with a particle of its own. If the lattice carries a θ, light couples to changes in it through electromagnetism's own handed term, with strength α, and no axion is needed. The handedness does not couple to light itself; at most a CP-odd handedness chooses the sign of a step. What the archive lacks is the lattice's θ in each phase. NOT CLAIMED: that the lattice carries a θ term, or that T369's transition changes it; that T369's transition happened; that the twist is cosmological, or evidence for this framework; that the weak handedness sets the sign; the sign; anything about axions. KILL-CONDITIONS: the twist shown to change with frequency; the twist of the reionization signal shown to differ clearly from that of last scattering (a single step after reionization fails); the uniform twist measured many errors from 0.2091° (the half-turn step fails, though a change in θ may remain); light emitted well after T369's transition shown to be turned, on average, by a comparable angle (the step's timing fails). OPEN: the lattice's θ in each of its phases, and whether T369's transition changes it by a half turn; time-reversal symmetry of light in both phases; the sign of the step, and which CP-odd object, if any, chooses it; the full-sky dipole — the dust, or a mechanism not yet found; the walls of a region-by-region transition.