physics_complexity_structure
plain-language theorem explainer
The declaration asserts that the physics complexity structure holds by equating it to computation limits derived from the ledger. Researchers classifying physical systems in the complexity zoo (P, EXPTIME) under Recognition Science would cite this to ground J-cost convexity in ledger properties. The proof is a one-line wrapper invoking the computation_limits_structure theorem.
Claim. The physics complexity structure holds: computation limits from the ledger are satisfied, where J-cost minimization is strictly convex with unique minimum at unity and local 8-tick dynamics remain O(1) per step.
background
The module IC-005 frames the computational complexity of physics via J-cost minimization on the ledger. J(x) = (x + x^{-1})/2 - 1 is strictly convex, attaining its global minimum only at x = 1, verifiable in constant time. Local updates affect at most eight neighbors per tick, while ground-state balance checks scale linearly with system size and phi-rung masses require exponential work.
proof idea
The proof is a one-line wrapper that applies computation_limits_structure, which itself reduces directly to phi_irrational.
why it matters
This establishes IC-005.12, confirming that physics complexity follows from ledger-derived computation limits. It sits downstream of the forcing chain (T5 J-uniqueness, T7 eight-tick octave) and supports the module's complexity summary: ground-state verification in P, phi-hierarchy in EXPTIME. No downstream uses are recorded yet.
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