physics_complexity_implies_limits
plain-language theorem explainer
Physics complexity from the ledger implies the computation limits from the ledger. Researchers analyzing RS placement in the complexity hierarchy would cite this when linking J-cost convexity to exponential costs in phi-rung spectra. The proof is a direct one-line wrapper applying the input hypothesis.
Claim. If the physics complexity structure derived from the J-cost ledger holds, then the computation limits from the ledger hold, namely that $phi$ is irrational.
background
The module IC-005 places physics in the complexity zoo via J-cost minimization. J(x) = (x + x^{-1})/2 - 1 is strictly convex with unique global minimum at x = 1. Local 8-tick dynamics keep per-step cost O(1), ground-state verification is linear in system size, yet phi-hierarchies in mass rungs drive exponential operation counts.
proof idea
This is a term-mode one-line wrapper that directly applies the hypothesis to obtain the target proposition.
why it matters
The declaration supplies the direct implication in IC-005.13, connecting the physics complexity structure to computation limits. It underpins the exponential-growth statement in the adjacent IC-005.14 for phi-rung hierarchies. In the framework it reinforces phi irrationality as the structural bound on exact RS representations, consistent with the self-similar fixed point.
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