Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

===== Figure X (extended). =====
The figure depicts a projection of a four-dimensional deterministic structure with coordinates (p,τ0,n,τ)(p,\tau_0,n,\tau)(p,τ0,n,τ), where ppp is the precision index, τ0\tau_0τ0 the initial structural tolerance, nnn the cumulative experiment count, and τ\tauτ the induced tolerance. Each translucent surface corresponds to a fixed experiment count nnn under logarithmic experiment accumulation, τnaive(p,τ0,n)=τ02−pκ(n)\tau_{\mathrm{naive}}(p,\tau_0,n)=\tau_0 2^{-p}\kappa(n)τnaive(p,τ0,n)=τ02−pκ(n). Increasing nnn monotonically lowers the surface, reducing the viable precision horizon. The horizontal plane τ=∣r∣max⁡\tau=|r|_{\max}τ=∣r∣max defines an absorbing collapse boundary; intersection with this plane induces collapse deterministically. The infrared fixed-point surface τIR(p,τ0)\tau_{\mathrm{IR}}(p,\tau_0)τIR(p,τ0) is independent of nnn and forms a time-invariant foliation that never intersects the collapse boundary, illustrating robustness to unlimited experiment accumulation.