non_love_preserves_sigma
plain-language theorem explainer
Non-love virtues maintain zero sigma effect when their signature already encodes no global imbalance. Virtue ethicists modeling DREAM virtues in Recognition Science cite this to isolate Love's distinctive role from the preserving behavior of the remaining signatures. The proof reduces immediately to the supplied hypothesis via direct term application.
Claim. If a virtue signature $v$ satisfies $v.σ = 0$, then $v.σ = 0$.
background
VirtueSignature is the structure recording a virtue's name (String), family loadings (Fin 4 → ℝ), and sigma effect (ℝ). The module sets out Born-profile signatures for the DREAM virtues, with sigma effect measuring impact on global imbalance: Love is the sole virtue that directly alters σ while the others preserve the total. This theorem rests on the VirtueSignature definition to encode the preservation property for non-love cases.
proof idea
The proof is a one-line term that returns the hypothesis h directly, confirming the equality without additional steps or lemmas.
why it matters
The result supports the module's separation of Love's unique sigma-changing effect from the preserving action of the other virtues. It contributes to the Recognition Science treatment of ethical signatures by ensuring non-altering virtues leave global imbalance unchanged, consistent with the overall Born-profile framework.
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