关系型GNS融合与幂等规范-引力不动点
Relational GNS Fusion and an Idempotent Gauge-Gravity Fixed Point
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中文总结 AI 辅助
本文提出关系型非对易框架，构建归一化二次流算子的投影融合积，推导幂等紫外不动点，讨论几何、引力及标准模型相关结构的涌现，通过标准模型-帕蒂-萨拉姆重整化群分析检验其紫外 basin 的一致性。
中文摘要 AI 辅助
我们提出了一种关系型非对易框架，其中量子运动学、半经典几何、内部规范结构及紫外不动点行为，均作为配备正态及其Gelfand–Naimark–Segal（GNS）表示的公共*-代数的不同部分出现。核心构造是归一化二次流算子上的投影融合积。在闭合流部分中，$P_{\rm rel}(O_A^2)=2O_A$（忽略无关修正），且以$X_A\star X_A=X_A$（其中$X_A=r_AO_A$）形式表达的紫外自相似性，给出相互作用归一化不动点$r_A^*=1/2$。在由GNS Gram度量确定的保留算子基底下，针对规范部分的每代约化费米子流约定及规范玻色子正则归一化，给出了$(10/3)g_Y^2$、$2g_2^2$、$2g_3^2$和$32\pi G\mu^2$的公共代数值。我们讨论了洛伦兹几何与爱因斯坦引力的条件性涌现、类标准模型的内部代数、来自最小四次配对部分的三代通道、$3+1$维分支的最小选择，以及具有分支依赖记录箭头的关系型时间。标准模型-帕蒂-萨拉姆（Standard Model–Pati–Salam）重整化群分析为所提出的紫外 basin 提供了现象学一致性检验。
英文摘要
We propose a relational noncommutative framework in which quantum kinematics, semiclassical geometry, internal gauge structure, and ultraviolet fixed-point behaviour arise as sectors of a common $*$-algebra equipped with a positive state and its Gelfand--Naimark--Segal (GNS) representation. The central construction is a projected fusion product on normalized quadratic current operators. Within the closed current sector, $P_{\rm rel}(O_A^2)=2O_A$ up to irrelevant corrections, and ultraviolet self-similarity expressed as $X_A\star X_A=X_A$ with $X_A=r_AO_A$ yields the interacting normalized fixed point $r_A^*=1/2$. With the retained operator basis fixed by the GNS Gram metric, a reduced per-generation fermionic current convention for the gauge sectors and canonical graviton normalization give a common algebraic value for $(10/3)g_Y^2$, $2g_2^2$, $2g_3^2$, and $32πGμ^2$. We discuss conditional emergence of Lorentzian geometry and Einstein gravity, a Standard-Model-like internal algebra, three generation channels from a minimal quartic pairing sector, minimal selection of a $3+1$ dimensional branch, and relational time with a branch-dependent arrow of records. A Standard Model--Pati--Salam renormalization-group analysis provides a phenomenological consistency test of the proposed ultraviolet basin.
