Spinorial Entropic Gravity: Spacetime as a Real Spectral Triple over the Icosahedral Quasicrystal

Abstract Spinorial Entropic Gravity v2. 0 (SEG) reformulates the unification of gravity and quantum mechanics by replacing the Hadamard-functional axiom of v1. 5 with a single geometric axiom: spacetime is fundamentally a real spectral triple TSEG = (A, H, D) with KO-dimension 6 mod 8, where D = DSEG ⊗ 1 + gamma₅ ⊗ DF combines the icosahedral quasicrystal Dirac operator with a finite internal Dirac operator. In this framework, all derived quantities are observer-independent and regularisation-free. The spectral entropy Ssp = -zeta'D (0), equal to the log-determinant of D, replaces the Hadamard functional, while the spectral action Ssp = Trf (D²/Lambda²) + yields a single variational equation, delta Ssp / delta D = 0, from which the modified Einstein-Cartan equation, Yang-Mills equations, the Higgs mechanism, and Dirac equations follow simultaneously. This removes the conceptual loop of v1. 5, QFT -> S -> g -> QFT, because both the metric and the entropy are derived from the same fundamental operator D. Under standard noncommutative geometry assumptions, SEG v2. 0 derives the exact r = 1/2 theorem, shows that the icosahedral vacuum is a local minimiser of Fnorm, and establishes five of the seven Connes axioms for TSEG, with Axiom 5 reduced to explicit computation and Axiom 6 deferred to Appendix A. Conditional on completing Axiom 6, the Chamseddine-Connes-Marcolli uniqueness theorem implies AF = C ⊕ H ⊕ M3 (C), yielding the Standard Model gauge structure from KO-dimension 6. Its main falsifiable prediction is w (0. 5) ≈ -0. 85, testable by DESI, while preserving all predictions already obtained in v1. 5.