Paper H: Holosphere Recursion and the Free Energy Principle Toward a Predictive-Coding Universe

Paper H tests whether a recursion-critical regime in the Holosphere lattice supports a practical, falsifiable “plateau diagnostic” based on an operational free-energy reporting functional. We define F(R)=ϵ0Nvac(R)−TcohS(R)F(R)=\epsilon_0 N_{\mathrm{vac}}(R)-T_{\mathrm{coh}} S(R)F(R)=ϵ0Nvac(R)−TcohS(R) from the surface vacancy law and surface entropy law, using calibrated constants. The mathematical result is conditional: in the leading area-law regime, dF/dR=0dF/dR=0dF/dR=0 is equivalent to a calibration balance among constants, not to recursion criticality by itself. The core dynamical hypothesis is that near recursion criticality the flux–drift transport lane maintains bounded residual behavior and stabilizes a dynamic calibration ratio near unity across recursion depth, producing a weak-drift (plateau) trace in F(Rn)F(R_n)F(Rn). We test this hypothesis with numerical sweeps of a declared recursion update map, tracking the free-energy trace, residual variance, and the dynamic calibration ratio, and we provide clear failure modes. We then translate the plateau diagnostic into laboratory-oriented falsifiers in curved membranes, viral capsid assembly, and foam/porous media analogues. Finally, we compare the resulting error-bounded plateau behavior to the Free Energy Principle in neuroscience strictly as a structural analogy, without importing biological cognition claims.