PowerClass
plain-language theorem explainer
PowerClass is an inductive type that partitions superhuman powers into five epistemic categories according to their grounding in Recognition Science results. Researchers working on the σ-Resolution Superhero Thesis would cite this taxonomy when classifying capabilities by mechanism type. The definition proceeds by direct enumeration of five constructors with no proof obligations.
Claim. The inductive type $PowerClass$ is defined by the five constructors $DirectMechanism$, $Derivable$, $NautilusClass$, $Speculative$, and $Constrained$, each representing a distinct epistemic relationship to proved RS structure.
background
The Superhuman.Core module formalizes the σ-Resolution Superhero Thesis by classifying 27 canonical powers drawn from mythology, comics, and folklore. PowerClass supplies the five epistemic tiers: DirectMechanism for powers with existing Lean formalizations, Derivable for those following from RS results, NautilusClass for those requiring localized J-cost minimization, Speculative for cases consistent with RS but needing extension, and Constrained for those forbidden by conservation laws. Upstream foundations include the canonical arithmetic object from ArithmeticOf, the active edge count $A$ from IntegrationGap, and the cost function induced by multiplicative recognizers, all of which supply the RS mechanisms referenced in the classification.
proof idea
This is an inductive definition that introduces five constructors corresponding to the epistemic classes. No lemmas or tactics are applied; the structure is given directly by the enumeration.
why it matters
PowerClass serves as the foundational taxonomy for the power enumeration, feeding directly into the powerClass function that assigns each of the 27 powers to a class. It realizes the claim hygiene distinction between theorems, hypotheses, and models in the σ-Resolution framework. The classification extends Recognition Science structure to superhuman capabilities via the phi-ladder and J-cost mechanisms while preserving the separation of proved results from empirical claims.
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