dreamGeneratorCount_eq
plain-language theorem explainer
The equality fixes the DREAM virtue generator count at 14 in the Recognition Science ethics module. Researchers modeling σ-preserving ethical transformations in pre-Big-Bang settings cite this cardinality when verifying the basis for local moves. The proof is a direct reflexivity step because the count is introduced by definition as the numeral 14.
Claim. The cardinality of the set of DREAM virtue generators equals 14, where each generator is a bidirectional move in the vector space over the field with two elements in three dimensions.
background
The Virtue Generators from J-Cost module upgrades the scaffold tag in the pre-Big-Bang paper section on virtues. It derives a finite set of canonical virtue moves that generate all σ-preserving ethical transformations from the J-cost functional. The DREAM generators are defined as the 14 elements obtained from 2 × (2^D − 1) at D = 3, consistent with the eight-tick octave and the forcing chain step that sets three spatial dimensions.
proof idea
The proof is a one-line term-mode wrapper that applies reflexivity. It holds immediately because the upstream definition of the generator count is exactly the numeral 14.
why it matters
This equality supplies the generator count field to the VirtueGeneratorsCert structure, which certifies the structural theorem for virtue generators. It fills the paper proposition on the finite set of canonical virtue moves and links to the Recognition Composition Law at the T8 step where D = 3. The completeness conjecture that the 14 generators suffice for all σ-preserving moves remains open.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.