powerClass
plain-language theorem explainer
The powerClass definition maps each of the 27 canonical superhuman powers to one of five epistemic classes according to their grounding in Recognition Science mechanisms. Researchers formalizing the σ-Resolution Superhero Thesis would cite this classification when counting accessible powers or analyzing constraint reasons. The definition proceeds by exhaustive pattern matching over the Power inductive type.
Claim. The function $powerClass : Power → PowerClass$ is defined by cases on the 27 powers, sending the six direct-mechanism powers to DirectMechanism, the six derivable powers to Derivable, the six Nautilus-class powers to NautilusClass, the five speculative powers to Speculative, and the four constrained powers to Constrained.
background
In the Superhuman.Core module, the Power inductive enumerates 27 canonical superhuman powers drawn from mythology and folklore. PowerClass is the inductive type with five constructors: DirectMechanism for powers with direct RS formalization, Derivable for those following from existing results, NautilusClass for those requiring J-cost minimization technology, Speculative for those needing theoretical extension, and Constrained for those forbidden by conservation laws. The module formalizes the σ-Resolution Superhero Thesis power taxonomy, classifying powers by their relationship to proved RS structure. Upstream results include definitions such as the active edge count A from IntegrationGap and power spectrum from Cosmology, though the classification itself relies primarily on the inductive definitions of Power and PowerClass. The accessible predicate on PowerClass determines whether a power has an RS path, with 23 powers accessible and 4 constrained.
proof idea
The definition is implemented as exhaustive pattern matching on each constructor of the Power inductive type, directly assigning the corresponding PowerClass value in each case. No lemmas are applied; it is a pure definitional expansion.
why it matters
This classification underpins the count theorems for each class (classA_count through classE_count) and the constrained_has_reason theorem in the same module. It fills the structural role in the Superhuman taxonomy as described in the module documentation, separating powers with direct RS grounding from those that are speculative or constrained. In the broader Recognition Science framework, it connects to the forcing chain and J-uniqueness by categorizing capabilities according to their derivability from the core functional equation.
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