rs_complexity_classes
plain-language theorem explainer
This definition enumerates six descriptive classes for the computational cost of Recognition Science processes, from O(1) ground-state checks to NP-hard global search. Modelers of ledger dynamics or phi-ladder mass computations would reference the list when estimating simulation resources. It is a direct list definition with no lemmas or computation.
Claim. The Recognition Science complexity classes are the list: ground state at ratio $x=1$ (unique zero of J-cost, $O(1)$ verification); local 8-tick updates ($O(1)$ per tick); balance verification (linear scan over $N$ bonds); J-cost minimization (convex, polynomial gradient descent); rung computation (EXPTIME, exponential in rung index); global configuration search (NP-hard analog over exponentially many states).
background
J-cost is the derived cost of a multiplicative recognizer comparator, equivalently the cost of any recognition event; it is strictly convex with unique minimum at ratio 1. Tick is the fundamental RS time quantum with one octave equal to eight ticks. Rung indexes the phi-ladder mass formula. The module IC-005 asks where RS physics sits in the complexity zoo and answers via J-cost convexity plus the eight-tick local dynamics.
proof idea
Direct definition that hard-codes the six string descriptions drawn from the module's summary of J-cost convexity, 8-tick locality, and phi-exponential growth.
why it matters
It condenses the complexity consequences of J-cost minimization and the eight-tick octave (T7) into a single reference list for the IC-005 question. No downstream theorems are recorded yet; the entry closes the module's complexity summary section.
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