The T3 Framework: Critical Vortex Universality from Nucleons to Quarks and QCD Emergence

摘要 本文将 T3 黑洞框架的涡旋束缚态图像推进到强相互作用尺度,发现临界速度 Vc = c√2 在核子尺度同样成立。基于 T3 结合子的 1-上闭链性质给出夸克线性禁闭势 V(r) = σr 的自洽性验证(非严格推导),弦张力估计 σT3 ≈ 0.13 GeV²(实验 0.18,同数量级)。 核心新结果一:数值求解核子涡旋场剖面,能量密度峰值 ρpeak ≈ 0.46 GeV/fm³,落入格点 QCD 典型范围 0.3–0.5 GeV/fm³;轴向压强呈现核心负压(弦张力)+ 外围衰减的定性正确图像,负压区域范围 ~0.8 fm 与格点一致。 核心新结果二:构造 T3 版本的三体 Mermin 不等式,发现 T3 的”非结合性 Tsirelson 上界”为 3√3/2 ≈ 2.598,严格落在经典界限 2 与量子界限 4 之间。这表明 T3 是一种中间非局域性理论——比经典实在论更非局域,但比量子纠缠更局域——为理解量子-经典过渡提供了新的代数视角。 建立有效色数跑动模型 Nc^eff(Q),使用两个拟合参数(Qtrans, ΔQ)匹配 7 个 PDG 数据点(χ²/ndof = 1.50)。提出 T3 的非结合性作为 QCD 非阿贝尔性的简化原型(非等价替代),三方向对应三色但承认色对称性截断。建立普朗克-核子恒等式 ρcore/ρPl = (Vc/c)⁹(mp/MPl)⁴ 作为数学恒等式(非物理预言)。诚实讨论所有循环论证、伪匹配和开放问题。 关键词:T3 代数,涡旋束缚态,夸克禁闭,QCD 原型,有效色数,格点 QCD 对照,Mermin 不等式,中间非局域性,黄金分割,诚实局限 Abstract This paper extends the vortex bound state picture of the T3 black hole framework to the scale of strong interactions, revealing that the critical velocity Vc = c√2 also holds at the nucleon scale. Based on the 1-upper-cocycle property of the T3 connector, we provide a consistency check (rather than a rigorous derivation) for the quark linear confinement potential V(r) = σr, yielding a string tension estimate σT3 ≈ 0.13 GeV² (experimental value: 0.18 GeV², same order of magnitude). Core New Result I: Numerical solution of the nucleon vortex field profile yields an energy density peak ρpeak ≈ 0.46 GeV/fm³, falling within the typical Lattice QCD range of 0.3–0.5 GeV/fm³. The axial pressure presents a qualitatively correct picture of core negative pressure (string tension) plus peripheral decay, with the negative pressure region spanning ~0.8 fm, consistent with Lattice QCD. Core New Result II: We construct the T3 version of the tripartite Mermin inequality and find that the “non-associative Tsirelson upper bound” in T3 is 3√3/2 ≈ 2.598, strictly lying between the classical bound of 2 and the quantum bound of 4. This indicates that T3 is an intermediate non-locality theory—more non-local than classical realism but more local than quantum entanglement—providing a new algebraic perspective on the quantum-classical transition. We establish an effective color number running model Nc^eff(Q), using two fitting parameters (Qtrans, ΔQ) to match seven PDG data points (χ²/ndof = 1.50). We propose the non-associativity of T3 as a simplified prototype (not an equivalent substitute) for the non-Abelian nature of QCD: three directions correspond to three colors, but we acknowledge the truncation of color symmetry. We establish the Planck-Nucleon identity ρcore/ρPl = (Vc/c)⁹(mp/MPl)⁴ as a mathematical identity (not a physical prediction). We honestly discuss all circular reasoning, pseudo-matches, and open issues. Keywords: T3 Algebra, Vortex Bound State, Quark Confinement, QCD Prototype, Effective Color Number, Lattice QCD Comparison, Mermin Inequality, Intermediate Non-locality, Golden Ratio, Honest Limitations