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We certify a dimensionless spectral constant g arising from a self– adjoint anisotropic Laplace–Beltrami operator on a three–torus with golden– ratio anisotropy, using rational–interval arithmetic and explicit tail bounds. The constant is enclosed to forty digits with a provably valid rational in- terval and a cryptographic reproduction hash. We then state a single physics identification postulate: upon normal- ising the length scale by one low–energy atomic transition (measured to ∼12 digits), the same dimensionless constant coincides numerically with the inverse fine–structure constant α−1 to all digits currently measured. No claim is made that this constitutes a pure–mathematical proof of α. Instead, this work certifies a spectral invariant and isolates its physical identification as an explicit assumption. We also enumerate open assumptions regarding scheme–independence beyond 12 digits and the absence of hidden tuning. This manuscript provides (i) rigorous convergence and uniqueness re- sults, (ii) a certified rational interval for g accurate to 10−40, (iii) a proof of regulator equality (heat–kernel vs. zeta), and (iv) a numerical appendix including SHA-256 hashes for reproducibility.我们借助有理区间算术（rational–interval arithmetic）与显式尾界（explicit tail bounds），严格验证了带有黄金比例各向异性（golden–ratio anisotropy）的三维环面（three–torus）上，自伴各向异性拉普拉斯-贝尔特拉米算子（self–adjoint anisotropic Laplace–Beltrami operator）所导出的无量纲谱常数（dimensionless spectral constant）g。该常数通过可证明有效的有理区间与加密重现哈希（cryptographic reproduction hash），将精度限定至四十位有效数字。随后我们提出一项物理识别公设：以一个低能原子跃迁（测量精度约12位有效数字）归一化长度尺度后，该无量纲常数的数值与当前已测量的所有数位上的精细结构常数倒数（α⁻¹）完全吻合。本研究并未宣称这构成了精细结构常数的纯数学证明；相反，本工作仅验证了一个谱不变量，并将其物理识别作为一项明确假设。我们还枚举了关于12位有效数字以上方案独立性以及无隐式调谐的开放研究假设。本手稿包含以下内容：(i) 严格的收敛性与唯一性证明结果；(ii) 精度达10⁻⁴⁰的g的认证有理区间；(iii) 正则化等价性（热核（heat–kernel）与zeta函数（zeta））的证明；(iv) 包含用于重现性验证的SHA-256哈希（SHA-256 hashes）的数值附录。