The principal spectral constant \ (^-1\) (physically known as the inverse fine-structure constant) is derived from first principles. A circular Matrix Product State (MPS) with bond dimension \ (D=45\) yields the duality \^-1 = (_) -, \ (_\) is the dominant eigenvalue of the MPS transfer matrix. The same algebraic structure is isomorphic to the Fano 2-22 (Mori-Mukai ID-69), whose Minkowski period sequence encodes the parameters \ (D=45\), conformal weight \ (w=8\), and the integers \ (24\) and \ (25\). The unified 5D functional that generates the duality is₅₃ = 14\|F\|² + 12R + 12g^__ - ²2 (²- (⁴+1) ) ² + 12g^_ d\, _ d + ²|e^-i/6d - 43_|², \ (\|F\|² 12Tr (F_F^) \), \ (R\) is the Ricci scalar, and the spinorial holonomy term locks the boundary state \ (d\) to the bulk identity field \ (_\). The branching rules of the adjoint representation of \ (SO (15) SO (10) SO (5) \) determine the asymptotic spectral flow value\^-1 (₋₎ₖ₄ₑ) = 127. 982, \ (₋₎ₖ₄ₑ\) is the lower asymptotic boundary limit. The construction contains no free parameters and rests on a spectral rigidity conjecture: the bond dimension \ (D=45\) is the maximal rank compatible with the Fano moduli space.
Massimiliano Blandino (Sat,) studied this question.