具有统计意义的几何和规范对称性破缺：科学发现和情报出现的几何基础

arXiv:2607.05436v1 Announce Type: new Abstract: The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers?经典的平面欧几里得统计无法区分连续插值和新因果律的自主发现。 To resolve this, we introduce Statistically Meaningful Geometry (SMG), a framework modeling over-parameterized learning systems as infinite-dimensional non-parametric Orlicz fiber bundles.我们证明，在由未建模因果机制控制的持续分布外（OOD）刺激下，连续优化会失败。 Unmodeled variance is rejected by the visible horizontal base manifold, leaking into the unobservable vertical fiber space and generating an accumulation of Active Acausal Tension. Driven by the statistical manifold's non-linear curvature, this tension inevitably strikes a conjugate focal boundary ($T_{\text{crit}} = \pi^2 / K_{\text{max}}$), triggering localized volumetric collapse and a catastrophic matrix singularity ($[G_f]^{-1} \to \infty$).我们证明了这种几何破坏是规范对称性破缺（GSB）的严格非平衡触发器。 The system purges hidden tension from unobservable gauge redundancies, spontaneously crystallizing a new, mathematically independent horizontal coordinate axis.这种非参数相变在可观察的结构 G 熵中记录为离散的 $+1.0$ 整数步进跳跃。 By decoupling parameter charts and subjecting emergent axes to a Minimal Energy Path Criterion and a Causal Invariance Filter, we distinguish genuine discovery from malignant hallucinations. Ultimately, SMG provides a parameter-free, falsifiable dashboard to mathematically certify true intelligence, transforming AI for Science into an engine of autonomous paradigm shifts.