sigma_effect_well_defined
plain-language theorem explainer
Virtue sigma effects are well-defined by construction inside the VirtueSignature structure. Researchers modeling ethical decision processes in Recognition Science would cite this to anchor imbalance calculations before deriving love's unique effect or justice's preservation property. The proof is a direct reflexivity step on the structure field.
Claim. For any virtue signature $v$, the associated sigma effect satisfies $v.σ_{effect}=v.σ_{effect}$.
background
The VirtueSignature structure records a virtue's name, its loadings across four families, and a real-valued sigma effect that quantifies impact on global imbalance. Upstream, the sigma definition from the Abilene Paradox module computes σ as the signed gap between private preference and public vote (+1, -1, or 0 for truthful agents). The module sets the local context by associating each of the 14 DREAM virtues with a Born-profile signature whose sigma effect either changes total imbalance (love) or redistributes it without change (justice).
proof idea
The proof is a one-line term-mode wrapper that applies reflexivity (rfl) directly to the sigma_effect field of the input structure.
why it matters
This result supplies the well-definedness anchor for the virtue signatures in the Ethics module, enabling the sibling theorems that isolate love's unique sigma effect and confirm justice preserves sigma. It closes the definitional step in the Born-profile framework for DREAM virtues before any downstream use in mechanism design or decision models.
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