R26 closes a mathematical compatibility theorem, not an empirical physical selection theorem.

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Closed Mathematical Invariants

1. A convergent global Dirichlet refinement can co-exist with a fixed finite 5-regular Ramanujan internal fiber.
2. The combined operator is a tensor sum $L_n^{LG}=L_n^X\otimes I+{\mu }_F^{2}I\otimes L_F$ and inherits finite-fiber norm-resolvent convergence.
3. Its spectrum is the exact Minkowski sum of global spacetime and fiber spectra: $\mathrm{Spec}(L_n^{LG})=\{{\lambda }_{j,n}+{\mu }_F^2{\nu }_a\}$.
4. The $K_6$ profile provides an exact finite degree-five Ramanujan fiber with spectrum $\{0,6^{\times 5}\}$.
5. A $T_5$ / local-limit profile retains the Kesten–McKay law on $[1,9]$ internally without identifying its compact spectral support with the UV spacetime spectrum.

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Still Open Theoretical Gates

$$\boxed{{\displaystyle \text{Source selects split?}\mathbf{\text{NO CURRENT DERIVATION}}}}$$$$\boxed{{\displaystyle \text{Source derives }{\mu }_F?\mathbf{\text{OPEN DYNAMICAL GATE}}}}$$$$\boxed{{\displaystyle \text{Source derives cross-couplings/mixing?}\mathbf{\text{OPEN COUPLING GATE}}}}$$$$\boxed{{\displaystyle \text{Source derives global refinement compiler?}\mathbf{\text{OPEN COMPILER GATE}}}}$$

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Canonical Revision Firewall

The historical claim that the Ramanujan graph itself completes directly into $M_{D_H}$ is not silently rewritten. The R26 split is a proposed FQFT-v2 completion in which Ramanujan data and spacetime Dirichlet data have distinct typed roles.

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Brightest Next Gate: The Interaction Operator

The construction leaves one highly specific physical problem:

$$\boxed{{\displaystyle \text{Derive the coupling/gluing operator between }{\mathrm{\Delta }}_X\text{ and }{L}_F.}}$$

A pure tensor sum is the zero-mixing baseline (FQFT-MIX-26). Any nontrivial FQFT prediction must specify an admissible interaction operator

$$\mathcal{M}(X,F)$$

whose symmetry, dimensions, renormalization group flow, and observable consequences can be audited and falsified.