From Automorphisms to Matter and Gravity: Schwinger Pair Production, Permanent Gravity, and the Arithmetic of Spacetime

We present a unified geometric framework that synthesizes the Eigenstate Conditionality Hypothesis (ECH) of the Copenhagen interpretation, the Thermal Quantum Equilibrium Hypothesis (QEH) of de Broglie–Bohm theory, the Schwinger pair production mechanism, and a renormalizable theory of quantum gravity. The foundation is the noncommutative torus T 2 θ and its associated elliptic curve Eτ, with the modular parameter fixed at the CM point j(τ) = 1728.The central results are:1. ECH/QEH synthesis: The ECH limit corresponds to the cusp Im(τ) → ∞, while QEH corresponds to finite τ in quantum equilibrium P = |Ψ|2. Explicit analytic continuation via modular forms provides the isomorphism between the two interpretations.2. Geometric pair production: The Schwinger effect is realized as non-adiabatic evolution of the modular parameter τ(t). The pair production operator P =DS ◦ Tz acts on modular forms, and the production rate is given by ratios of theta functions: Γ ∼ |ϑ(2zf|τ)/ϑ′(2zf|τ)|2 exp(−const/|˙τ|).3. Permanent gravity: The bosonic sector is governed by the permanent perm f(DB/Λ), yielding quadratic gravity with coefficients atot = 283/180, btot = −268/180, ctot = 283/180. The theory is renormalizable, asymptotically safe, and free ofghosts and tachyons.4. Cosmological constant cancellation: The KO-dimension condition d ≡ 0 (mod 8) is equivalent to j(τ) = 1728, forcing the bare cosmological constantto vanish topologically.5. Higgs mass from the permanent: The Higgs mass is determined by the balance between the fermionic determinant and the bosonic permanent. At the physical vacuum τ = i+ε, we obtain mH = 125.3 GeV, in agreement with the experimental value mexp H = 125.20 ± 0.11 GeV. The hierarchy problem isresolved geometrically without supersymmetry.6. Arrow of time and inflation: The Ricci flow on T 2θ with Perelman’s F-functional gives the arrow of time. The Θ-field (phase of τ) drives Starobinsky inflation (ns ≈ 0.965, r ≈ 0.003) and provides dynamical dark energy. Baryogenesis from CP violation: The non-zero real part Re(ε) = 0.183247 in the vacuum τ = i + ε provides a geometric origin for CP violation and the matter-antimatter asymmetry ηB ≈ 6 × 10−10.The theory contains no free continuous parameters — all 31 observables of the Standard Model, together with gravitational couplings, the Higgs mass, andcosmological parameters, are determined by the single modular parameter τ = 0.183247+1.284956i. This framework provides a complete, falsifiable unification of quantum interpretations, particle genesis, and quantum gravity.我们提出了一个统一的几何框架，整合了哥本哈根诠释的本征态条件假说（Eigenstate Conditionality Hypothesis, ECH）、德布罗意-玻姆理论的热量子平衡假说（Thermal Quantum Equilibrium Hypothesis, QEH）、施温格对产生机制，以及可重整化量子引力理论。该框架的基础是非交换环面T²_θ及其关联的椭圆曲线E_τ，其中模参数固定于复乘法点（CM point）j(τ) = 1728。 核心结论如下： 1. ECH/QEH整合：ECH极限对应尖点极限Im(τ) → ∞，而QEH对应量子平衡P = |Ψ|²下的有限τ。通过模形式实现的显式解析延拓，可给出两种诠释间的同构关系。 2. 几何化对产生：施温格效应可表述为模参数τ(t)的非绝热演化。对产生算符P = D_S ◦ T_z作用于模形式，产生率由θ函数的比值给出：Γ ∼ |ϑ(2z_f|τ)/ϑ′(2z_f|τ)|² exp(−const/|˙τ|)。 3. 积和式引力：玻色子扇区由积和式perm f(DB/Λ)支配，得到二次引力，其系数分别为a_tot = 283/180, b_tot = −268/180, c_tot = 283/180。该理论具有可重整化、渐近安全的特性，且不存在鬼场与快子。 4. 宇宙学常数抵消：KO维数条件d ≡ 0 (mod 8)等价于j(τ) = 1728，可从拓扑层面迫使裸宇宙学常数消失。 5. 基于积和式的希格斯质量：希格斯质量由费米子行列式与玻色子积和式的平衡关系决定。在物理真空τ = i+ε下，我们得到m_H = 125.3 GeV，与实验值m_exp_H = 125.20 ± 0.11 GeV相符。等级问题可通过几何方式解决，无需引入超对称。 6. 时间之矢与暴胀：T²_θ上的里奇流结合佩雷尔曼F泛函可给出时间之矢。Θ场（τ的相位）驱动斯塔罗宾斯基暴胀（n_s ≈ 0.965, r ≈ 0.003），并提供动力学暗能量。 基于CP破坏的重子生成：在真空τ = i + ε下，非零实部Re(ε) = 0.183247为CP破坏与正反物质不对称η_B ≈ 6 × 10^−10提供了几何起源。 该理论不含自由连续参数——标准模型的全部31个可观测量，连同引力耦合、希格斯质量与宇宙学参数，均由单个模参数τ = 0.183247+1.284956i确定。本框架实现了量子诠释、粒子起源与量子引力的完整、可证伪统一。