This working note proposes a multi-sector extension of the Geometric Relay Theory framework through an n-branch transparency cascade. The source equation of the geometric relay \ (\) decomposes by linearity into sectoral branches \ (ᵢ\), each associated with an effective coupling \ (gᵢ=2/3\, mᵢ/M ₋\). Sub-Wronskians \ (W₈₉\) are introduced as structural detectors of dynamical separation between branches, while the index \ (Hᵢ=ᵢ/\) provides a formal bridge with Delayed Homeostasis: \ (Hᵢ>1\) corresponds to a living oscillatory branch, whereas \ (Hᵢ<1\) corresponds to a transparent branch. The note then develops the non-linear Padé/F⁴ regime, in which a smooth branch susceptibility \ (ᵢ (Hᵢ) \) replaces the sharp freezing cutoff. At the horizon, the radial transparency layers are spatially unobservable, but their integrated effect is formulated as a renormalisation of the effective matter Lagrangian, Wald entropy and quasi-normal-mode boundary conditions. The effective chain \ ᵢ ᵢ L₌, ₄₅₅ ₄₅₅ S ₄₅₅ ₐ₍₌ \ is thereby closed at the effective level, with \ (\) entering explicitly through the threshold \ (Hᵢ=Eᵢ/ () \), and with compositional dependence encoded through \ (fᵢ=xᵢ gᵢ²/ⱼ xⱼgⱼ²\). The document explicitly distinguishes two epistemic levels: results 1–8 are Level B, mathematically structured and reproducible; the horizon closure is Level C, coherent as an effective closure but still requiring a full covariant derivation from the action and systematic comparison with existing horizon-microstructure approaches. The proposal does not claim to demonstrate fundamental quantum gravity. It offers an effective candidate for horizon microstructure, thermodynamically active and potentially testable through QNM corrections in a primordial regime. The note stresses that the radial layers themselves are not directly observable; the relevant signature would be integrated, through effective entropy and QNM boundary conditions.
Olivier Lane-Larquey (2026) studied this question.