PowerClass
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not establish the existence of any superhuman power.
- Does not derive the 27-power count from RS axioms.
- Does not provide a mechanism for transitioning between classes.
- Does not address empirical verification of the classification.
formal statement (Lean)
32inductive PowerClass where
33 | DirectMechanism -- Class A: Lean module with formalization exists
34 | Derivable -- Class B: follows from existing RS results
35 | NautilusClass -- Class C: requires localized J-cost minimization technology
36 | Speculative -- Class D: consistent with RS but needs theoretical extension
37 | Constrained -- Class E: forbidden or constrained by conservation laws
38 deriving DecidableEq, Repr
39
40/-- Whether a power class represents an accessible (not forbidden) capability. -/
41def PowerClass.accessible : PowerClass → Bool
42 | .DirectMechanism => true
43 | .Derivable => true
44 | .NautilusClass => true
45 | .Speculative => true
46 | .Constrained => false
47
48/-! ## Power Enumeration -/
49
50/-- The 27 canonical superhuman powers from cross-cultural mythology, comics, and folklore. -/