rs_complexity_classes
plain-language theorem explainer
rs_complexity_classes enumerates six complexity classes for Recognition Science tasks. Complexity theorists classifying where physics sits relative to P, EXPTIME, and NP-hard analogs would cite the list. The definition is a direct literal construction of the string list with no computation or lemmas applied.
Claim. The Recognition Science complexity classes are the list: ground state verification at $x=1$ in $O(1)$ time; local dynamics via 8-tick updates in $O(1)$ per tick; balance verification in $O(N)$ linear time; J-cost minimization by convex optimization; rung computation in EXPTIME; global configuration search as an NP-hard analog.
background
The module IC-005 asks where physics sits in the complexity zoo and answers via J-cost structure. J-cost is the function $J(x)=(x+1/x)/2-1$, strictly convex with unique minimum at $x=1$. Local dynamics use the eight-tick octave (period $2^3$) with each tick updating at most eight neighbors. The phi-ladder enters via rung levels whose exponential growth drives EXPTIME behavior for high states.
proof idea
Direct definition as a list literal. No lemmas or tactics are applied; the body simply enumerates the six strings derived from the convexity of J-cost and the eight-tick structure.
why it matters
The definition supplies the summary certificate for the complexity analysis in IC-005. It places RS physics between linear-time verification and EXPTIME/NP-hard analogs, consistent with T7 (eight-tick octave) and the phi-ladder from the forcing chain. No downstream theorems reference it yet.
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