physics_complexity_from_ledger
plain-language theorem explainer
The declaration equates the physics complexity structure to the proposition that phi is irrational. Researchers studying computational complexity classes for physical simulations in Recognition Science cite this as the bridge from J-cost convexity to exponential hierarchies. The definition is a direct alias requiring no additional steps beyond the upstream irrationality result.
Claim. The physics complexity structure is the proposition that the golden ratio phi is irrational.
background
The module IC-005 examines where physics sits in the complexity zoo (BQP, QMA, PSPACE) under Recognition Science. J-cost minimization is strictly convex with unique minimum at x=1, local 8-tick dynamics are O(1) per step, ground-state verification is linear time, and phi-rung mass computations are exponential. The upstream result states: 'THEOREM IC-002.4: φ is irrational. This is the core structural constraint on RS computation: exact representation of RS constants requires transcendental arithmetic.'
proof idea
The definition is a one-line alias to computation_limits_from_ledger, which asserts Irrational phi. No lemmas or tactics are invoked beyond the direct equality.
why it matters
This definition supplies the core claim for THEOREM IC-005.12. It feeds directly into physics_complexity_implies_limits, which derives computation limits from the structure, and into physics_complexity_structure. In the framework it anchors the phi-hierarchy exponential growth (phi^n rungs) and the eight-tick local dynamics that keep verification in P while higher rungs enter EXPTIME.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.