virtueCost
plain-language theorem explainer
virtueCost supplies the J-cost incurred by a normalized action deviation within the virtue generator construction. Researchers on ethical sigma preservation in Recognition Science cite it when quantifying micro-move costs or certifying zero-cost alignment. The definition reduces directly to an application of the Jcost operator on the ratio of deviation to baseline.
Claim. The J-cost of a virtue move is given by $J(δ/β)$, where $δ$ denotes the action deviation and $β$ the baseline; the quantity equals zero precisely when the action is virtue-aligned.
background
The Virtue Generators from J-Cost module develops the ethical content of the J-cost function inside Recognition Science. It asserts a finite basis of 14 DREAM generators that span all sigma-preserving transformations, obtained from the Count Law at D=3 as 2*(2^3-1). The present definition supplies the concrete cost metric applied to each generator step. Module documentation states that the construction upgrades the scaffold tag in the pre-Big-Bang paper by furnishing the algebraic cost measure for the bidirectional F_2^3 structure.
proof idea
The definition is a one-line wrapper that applies the Jcost function directly to the ratio of the two real parameters.
why it matters
This definition populates the cost_perfect field of the VirtueGeneratorsCert structure and is invoked by the theorem virtueCost_perfect that records zero cost on perfect alignment. It supplies the missing cost function for the paper's virtue upgrade section, connecting J-uniqueness (T5) and the Recognition Composition Law to sigma-preserving ethical moves. The module documentation leaves open whether the 14 generators suffice for every sigma-preserving transformation.
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