A structural derivation of the parallel‑plate Casimir pressure is presented within the BRISM (BRane Interface Substrate Model) interface geometry. The π² numerator arises from the fixed interface scale ε = 1/π² set by phase neutrality, positivity, and σ‑additivity. The denominator 240 is obtained without mode summation or zeta regularization: in the ideal parallel‑plate limit, the dimensionless linear response factorizes as 𝒦 = 𝒫bulk ⊗ 𝒫brane, yielding tr (𝒦) = tr (𝒫bulk) ·tr (𝒫brane) = 24 × 10. The bulk count 24 follows from the minimal simple completion 𝔰𝔲 (5) of 𝔲 (1) ⊕ 𝔰𝔲 (2) ⊕ 𝔰𝔲 (3), while the brane count 10 combines six intrinsic metric modes with four orthogonal two‑sided transverse modes; isotropy enforces equal weighting. A one‑sided control gives 192, corroborating two‑sided completeness. The π² (from ε) and 240 (from channel counting) contributions are independent. No dynamical assumptions, fits, or regularization enter; the Casimir effect is interpreted as a local deformation of the interface geometry. All BRISM papers on Zenodo >> Searchlist
Swen Carlo Heinze (Sun,) studied this question.