The Riemann Hypothesis as a Corollary of the Granger Representation Theorem: ARIMA(35,1,∞) from the Standard Model Algebra A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ)
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We prove that the Riemann Hypothesis follows from the physical reality of the Standard Model algebra A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) via a six-step chain of published theorems. (1) The ascending superoperator of A_F on End(ℂ⁶) has eigenvalues {1, ½, ⅓, ⅙} with degeneracies {1, 3, 8, 24} by Schur's lemma. (2) These eigenvalues at KMS inverse temperature β = 2π produce 18 physical constants matching observation with zero free parameters (companion paper, DOI 10.5281/zenodo.18913234); the probability of accidental agreement is less than 10⁻³⁶, establishing the algebra as physically real. (3) The fermionic partition function factorises as L(s) = A(s) × ζ(s) × ζ(s−1) with A(1) = 0. (4) The prime counting function admits an ARIMA(35,1,∞) representation: unit root λ=1 carries the Li(x) trend; 35 autoregressive modes at {½(×3), ⅓(×8), ⅙(×24)} provide mean reversion; MA roots are the nontrivial zeros of ζ(s). (5) The Granger Representation Theorem (Engle–Granger 1987, Nobel Prize 2003) guarantees that if all AR roots are strictly inside the unit disk, no MA root can be explosive. (6) Since ½, ⅓, ⅙ < 1, no zeta zero can leave the critical line Re(s) = ½. This is the Riemann Hypothesis. Every step is either a computation, a published theorem, or an empirical fact at odds of 10⁻³⁶. No new mathematics is required. Companion papers: DOI 10.5281/zenodo.18913234 (physics), DOI 10.5281/zenodo.18919654 (mathematics).
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Related works
- Is supplement to
- Working paper: 10.5281/zenodo.18913234 (DOI)
- Working paper: 10.5281/zenodo.18919654 (DOI)
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2026-03-14