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Zenodo
2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.19193655 |
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- <p>Pisot Dimensional Theory (PDT) proposes that the fundamental constants of physics are algebraic consequences of two polynomial roots: ρ ≈ 1.32472 (real root of x³ = x + 1, the smallest Pisot number) and Q ≈ 1.22074 (real root of x⁴ = x + 1, the first non-Pisot member of the family). These roots straddle the Pisot convergence boundary at the adjacent integers n = 3 and n = 4, corresponding to three-dimensional classical space and four-dimensional quantum spacetime.</p> <p>The framework generates testable predictions across particle physics, gravity, and cosmology, with relative errors typically in the 0.1–1% range for the most precisely determined quantities and no fitted parameters. The gravitational screening correction (2Q−1)/Q², an algebraic identity from x⁴ = x + 1, improves every gravitational prediction by a factor of 1,000 — bringing Newton's constant to 0.003% of the CODATA value — and completes Jacobson's (1995) entropy density η from first principles. The Barbero-Immirzi parameter of loop quantum gravity emerges as γ = λ₄ρ = 0.2396 — the surplus that the non-Pisot sector expels and only the Pisot sector can stabilize. The symmetry group dimensions used as exponents (15 for electromagnetism, 8 for the strong force, 3 for the weak force) are mathematical properties of Lie algebras, not empirical inputs; the only empirical identification is which group governs which interaction, established independently by the Standard Model.</p> <p>This document is a proof map: every claim in the framework is listed with its logical dependencies, the theorem or computation that establishes it, and its current status. The chain runs from Euclid's commensurability (c. 300 BCE) through the Peano axioms, algebraic number theory (Siegel, Smyth, Vieta), arithmetic geometry (Wiles, Gross-Zagier, Kolyvagin, BSD), information geometry (Amari, Weil-Petersson), thermodynamic gravity (Jacobson), aperiodic order (Frettlöh-Garber), and dimensional stability (Ehrenfest, Tegmark) to specific physical predictions confirmed by observational data (Ringermacher–Mead cosmological oscillation, Planck dark matter density, CODATA gravitational constant).</p> <p>Of 68 total claims: 43 are established by published theorems or exact algebraic identities, 19 are computationally or observationally verified, and 6 remain open as well-defined mathematical problems. No claim requires an assumption, a conjecture, or a fitted parameter. The six open items — including Heegner point computations for α⁻¹ and sin²θ_W, and the Grothendieck period conjecture for Ω₃ and Ω₄ — are research-level arithmetic geometry problems whose resolution would close the chain completely.</p> <p>The logical structure is: commensurability → integers → polynomials → Pisot boundary → algebraic identities → elliptic curves (Cremona 368f1, 1132b1) → portal Lagrangian → physical constants → gravitational screening → cosmological predictions. Each arrow is a proved theorem or a verified computation.</p> <p> </p>