Subdiffusive Valence Growth under Bounded Relational Flux: Structural Derivation of the Cascade Exponent

The cascade exponent, governing the power-law growth p (n) n^ of the effective relational valence along the Cosmochrony relaxation cascade, was identified in a companion paper as the sole remaining structural postulate of the admissibility sub-programme. We show that the bounded-flux constraint |ₜ ᵥ| c_, inherited from Born--Infeld saturation, renders super-quadratic valence growth structurally impossible. Under a natural closure hypothesis relating valence to the cumulative exploration of the relational configuration space _, the Cheeger isoperimetric inequality for Ramanujan--LPS graphs impliesequation* p (n) c_ p (n), equation*from which it follows that p (n) C n², i. e. \ any admissible power-law exponent must satisfy 2. By convention, the saturated growth rate p (n) n² is identified with the maximal admissible regime; sub-saturated growth laws satisfying p (n) = o (n²) correspond to < 2, and the physically relevant regime is (0, 1] (see Remark). This structural upper bound is derived without invoking phenomenological mass data and is therefore independent of the lepton or quark sector. The sharper confinement to the phenomenologically identified window ^* (0. 09, 0. 13) is not established here; we identify the additional geometric input required and formulate the residual problem precisely. The present result removes the last unconstrained degree of freedom of the O-series from the class of super-quadratic growth laws, consolidating the structural foundation of the programme.