Topological Origins of Cosmological Parity Violation: A Normalized Interface from Eleven Dimensions

We identify a top-down topological origin for four-dimensional gravitational parity violation within eleven-dimensional supergravity. In the product, block-diagonal limit (M11 = M4 × X7), the higher-derivative coupling C3 ∧ X8 contains a mixed component proportional to Tr (R4²) ∧ Tr (R7²). For an internal axion mode C3 = θ (x) ω3 (y), this sector reduces to a four-dimensional axion-Pontryagin interaction. The physical parity-violating source is not the bare topological coefficient (alphaₑff) alone, but the canonically normalized ratio g_θRR = alphaₑff / f_θ, where f_θ is fixed by the internal Hodge norm of the same axion mode. Thus, a phenomenological gravitational Chern-Simons parameter is reframed as a normalized compactification datum: a topological pairing divided by a dynamic, metric-dependent norm. We map the cosmological interface required to connect this geometric source to chiral tensor production, , anomaly transfer, washout, and baryogenesis. Furthermore, a companion C3 ∧ G4 ∧ G4 reduction can generate axion-gauge couplings when suitable smooth or localized gauge sectors are present, revealing that the ratio of gravitational to gauge-sector parity violation is constrained by internal compactification data. Ultimately, this framework does not merely complete a baryogenesis model; it translates gravitational-anomaly baryogenesis into a strict geometric target that can be computed, observationally constrained, and falsified.