The Brody distribution, originally a phenomenological interpolation between Poisson and Wigner level-spacing statistics in quantum chaos, is calibrated here as a quantitative measure of short-range exclusion in 2D spatial point processes. Two results form the core. First, the 2D complete-spatial-randomness baseline is recalibrated to $β=0.96\pm0.15$, correcting the inappropriate 1D Poisson reference. Second, an empirical $β$--$r_{\text{excl}}$ calibration is validated against the effective hard-core radius with Spearman $ρ=0.988$. The framework is demonstrated on 58 manufactured surfaces (10 materials, 10 processes), phase-extracted interferometric profilometry of a certified roundness standard, and 2D binary embeddings of prime numbers. A sparse-integer control proves the prime $β=2.15$ signal is genuinely arithmetic ($Δβ=+0.68$ over random-integer control), while a Cantor-embedding null result ($β=1.40$, TOST $p<0.01$) demonstrates that 2D exclusion is embedding-created rather than intrinsic. Density-thinning experiments establish that $β$ captures exclusion strength rather than point density, while absolute values are density-dependent. A distinct CSR baseline for binary fields at low fill fraction is identified, with a decision table provided. The $β$--$r_{\text{excl}}$ calibration, the CSR baseline correction, and the control protocols together constitute a calibrated measurement framework for reproducible characterisation of short-range exclusion in 2D spatial point processes.

翻译：布罗迪分布最初是量子混沌中泊松统计与维格纳能级间距统计之间的唯象插值，本文将其标定为二维空间点过程中短程排斥的定量度量。核心包含两项成果：第一，将二维完全空间随机基线重新标定为 $β=0.96\pm0.15$，纠正了不恰当的二维泊松参照标准；第二，建立经验 $β$--$r_{\text{excl}}$ 标定关系，与有效硬核半径的斯皮尔曼相关系数达 $ρ=0.988$。该框架在58个人工表面（10种材料、10种工艺）、经认证圆度标准件的相位提取干涉轮廓仪测量数据以及质数的二维二进制嵌入中进行了验证。稀疏整数对照实验证明质数 $β=2.15$ 信号具有真正的算术特性（相较于随机整数对照 $Δβ=+0.68$），而康托尔嵌入的零结果（$β=1.40$，TOST $p<0.01$）表明二维排斥效应由嵌入过程产生而非内在属性。密度稀疏化实验证实 $β$ 捕捉的是排斥强度而非点密度，但绝对值具有密度依赖性。本文还识别了低填充率二值场的独特CSR基线，并提供了决策表。$β$--$r_{\text{excl}}$ 标定、CSR基线校正及对照协议共同构成可复现表征二维空间点过程中短程排斥的标定测量框架。