StringTheoryVariant
StringTheoryVariant enumerates the five canonical superstring theories as an inductive type within the Recognition Science treatment of the string landscape. Physicists mapping the 10^500 vacua to J-cost minima would cite this enumeration when counting the discrete choices selected by the recognition vacuum at r=1. The definition is a direct listing of the variants with no proof body, deriving standard instances for decidability, equality, and finiteness automatically.
claimThe inductive type enumerating the five superstring theories: Type I, Type IIA, Type IIB, SO(32) Heterotic, and E8×E8 Heterotic.
background
The module treats the string theory landscape through the recognition cost J(r), where minima at J=0 select the recognition vacuum r=1. J is the cost function from the CanonicalJBand import, satisfying the Recognition Composition Law and fixing the self-similar point phi. The five variants listed here, together with M-theory, give configDim D=5 (+1 mother theory), matching the RS ledger count of 5 bulk dimensions plus 1 boundary.
proof idea
This is an enumerative definition with no proof body. The five constructors are listed directly, and the deriving clause automatically supplies DecidableEq, Repr, BEq, and Fintype instances.
why it matters in Recognition Science
This definition supplies the finite set of string theory variants used by StringTheoryCert to assert Fintype.card StringTheoryVariant = 5 together with J(1)=0. It fills the enumeration step in the Recognition Science framework, where the five variants plus M-theory correspond to configDim D=5 and unify at D+1=6. It touches the open question of how the full landscape of ~10^500 vacua reduces to these canonical forms under J-cost minimization.
scope and limits
- Does not derive J-cost values for each listed variant.
- Does not prove physical existence or stability of the theories.
- Does not address the full 10^500 vacua beyond these five canonical cases.
- Does not connect to the phi-ladder mass formula or Berry creation threshold.
formal statement (Lean)
23inductive StringTheoryVariant where
24 | typeI | typeIIA | typeIIB | so32Heterotic | e8e8Heterotic
25 deriving DecidableEq, Repr, BEq, Fintype
26