A Conditional Zero-Parameter Boundary Formula for the Fine-Structure Constant

This preprint presents a conditional zero-parameter reconstruction of the Thomson-limit inverse fine-structure constant inside a specified sigma/APS-Hardy boundary package. Under the stated CP1/APS-Hardy/determinant-line realization and Thomson matching functor, the inverse coupling decomposes as α^{-1}(0) = 13π^2 + 7π^2/8 + 2/21 = 137.035999160352946... . The endpoint term 2/21 is not fitted; it is the normalized trace of a rank-one Toeplitz vacuum defect in the stated boundary package. The result is not claimed as an unconditional theorem of standard QFT.