The Fine-Structure Constant from the M→F-Theory Antisymmetric-Tensor Cascade: A Topological Conjecture on a Pascal Anti-Diagonal

Seven binomial coefficients along an anti-diagonal of Pascal's triangle, 28, 126, 210, 330, 165, 66, 13, all identified with canonical M-theory antisymmetric-tensor sectors, combine through endpoint subtraction (165 − 28 = 137) and a nested-reciprocal sum to yield α−1. To all digits computed, the inverse fine-structure constant equals the exact-rational sum: ^-1 = (V₅ - V₁) + ₊=₁^7 1V₁ V₂ Vₖ = 137. 035999086288 with the seven antisymmetric-tensor multiplicities V1, …, V7 on Pascal rows 8–13. Both the integer base and the residual ε emerge from the same combinatorial path. The base V5 − V1 = 137 connects two M-theory anchors: V5 = 165 = dim C3 (the 3-form gauge potential) and V1 = 28 = dim SO (8) (the Freund-Rubin gauge group of 11D-on-S7 KK reduction). The seven-term sum matches the 2018 CODATA recommended value α−1 = 137. 035999084 (21) at 0. 04σ. We explicitly anchor to the 2018 value (the experimental precision floor of ~2 × 10−9 drawn from Hanneke 2008's electron g−2 measurement) to isolate the derivation from the unresolved 5. 4σ Cs–Rb systematics that fractured the subsequent 2022 CODATA consensus, an issue developed in §6. 6 of the paper. The seven multiplicities are antisymmetric-tensor dimensions C (n, p) = dim Λp ℝn along the M→F-theory dimensional cascade (Cremmer-Julia-Scherk 1978, Vafa 1996), with E7 (7) U-duality of 4D N=8 supergravity framing the 4D corner. Two of the seven carry direct E7 (7) identifications: V1 = 28 (the rank-1 1/2-BPS small orbit) and V2 = 126 (E7 root count) ; the remaining five are antisymmetric form-content on Pascal rows 10–13. Unlike numerical-coincidence proposals (Eddington 1929, Wyler 1969), each Vk is identified with a canonical higher-dimensional-theory sector before α−1 is evaluated. The framework is a topological conjecture, with the candidate dynamical mechanism (iterated Atiyah-Bott-Berline-Vergne equivariant localization on a 7-fold BPS-moduli-space filtration over a G2-holonomy 7-manifold) left as the central open computational task. With seven integers and zero free parameters (verification code in Appendix C), it provides an immovable topological zero-point for α0, diagnosing the current 5. 4σ Cs–Rb inter-protocol tension as extraction-side systematics rather than instability of the underlying constant. Confirmation at sub-10−9 precision, once these systematics resolve, would constitute the first numerical prediction of M-theory's IR structure verified against precision metrology, directly addressing the critique that string theory makes no falsifiable predictions about fundamental constants. Falsifiable by confirmed α̇0 ≠ 0 at ≥5σ (after resolution of macroscopic systematics), or by any canonically-established higher-dimensional-theory object on Pascal rows ≤13 that the anti-diagonal misses.