dreamGeneratorCount
plain-language theorem explainer
The definition fixes the DREAM virtue generator count at 14, equal to twice the number of nonzero vectors in F₂³. Ethics researchers in the Recognition Science framework cite this constant when counting the basis for σ-preserving ethical transformations. It is introduced as a direct numeric assignment derived from the spatial dimension D=3.
Claim. The DREAM virtue generator count equals $14$, or equivalently $2(2^3-1)$.
background
In the Virtue Generators from J-Cost module the framework posits a finite set of canonical virtue moves that generate all σ-preserving ethical transformations. The DREAM generators arise from the consciousness modules and correspond to bidirectional moves in F₂³. The Count Law at D=3 yields 7 nonzero vectors, doubled to 14 for the bidirectional structure. J-cost is the cost function imported from the Cost module, and virtueCost vanishes for aligned actions. This definition upgrades the scaffold tag in the pre-Big-Bang paper §virtues section.
proof idea
The definition is a direct numeric assignment of the constant 14. No lemmas are applied; it serves as the base value for subsequent equalities such as dreamGeneratorCount_eq and positivity statements.
why it matters
This constant populates the VirtueGeneratorsCert structure and enables the dreamCount_from_countLaw theorem equating it to 2*(2^3-1). It fills the paper proposition on the cardinality of virtue generators. In the Recognition framework it connects to T8 fixing D=3, supplying the basis count for ethical transformations. The completeness conjecture that these 14 suffice for all σ-preserving moves remains open per the module documentation.
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