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Theoretical analysis derives temporal directionality and chronology protection from E8 symmetry, suggesting fundamental algebraic foundations for the thermodynamic arrow of time.
Four results on the temporal structure of the universe are traced to the algebra of E8, with all dependencies declared. (1) Thermodynamic arrow: maximal E8 symmetry implies vanishing Weyl curvature and minimal gravitational entropy, deriving the past hypothesis (given Penrose's Weyl-curvature hypothesis and the TTOE emergent-metric identification). (2) Closed timelike curves: in the perturbative regime, Kerr CTCs are confined beyond an unstable inner horizon (blueshift instability plus mass inflation) and are non-traversable; TTOE adds a thermodynamic protection layer consistent with Hawking's chronology protection. (3) theta_QCD(bare)=0: the longest element w0=-id of W(E8) — equivalently, all Coxeter exponents odd — forces real adjoints and CP conservation in the gauge sector, with theta=pi excluded via the Dashen phenomenon; the radiative theta_eff fails the nEDM bound through a structural no-go of the 120_H (8-order gap), so strong CP requires external input. (4) The recursive pattern "E8 generates discrete options + external non-adjustable selection" is formalized as a theorem (finiteness, externality, non-adjustability), with six verified instances. Part of the TTOE research programme; results are classified by epistemic status and require independent verification.
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E.U.O. (2026) studied this question.
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