IndisputableMonolith.Ethics.SigmaEquilibrationAsDrive
The module introduces populations of agents each carrying a sigma value and defines love versus selfish strategies acting on them. It proves that love strategies reduce sigma spread while selfish ones increase total absolute sigma. Ethics researchers in Recognition Science would cite it when treating equilibration as a behavioral drive. The module opens with core definitions then supplies targeted lemmas on spread and non-negativity.
claimLet $P$ be a population of agents equipped with a function $s: P → ℝ$ assigning sigma values. Define the spread $σSpread(P)$ and total absolute sigma $totalAbsSigma(P)$. Let $Strategy$ be a map from populations to updated populations. Then $loveStrategy$ satisfies $σSpread(loveStrategy(P)) ≤ σSpread(P)$ while $selfishStrategy$ satisfies $totalAbsSigma(selfishStrategy(P)) > totalAbsSigma(P)$.
background
The module sits in the Ethics domain and opens with the definition of a population of agents carrying sigma values. It introduces auxiliary notions: sigmaSpread measuring dispersion of the values, totalAbsSigma as their summed absolute size, Strategy as a behavioral update rule, spreadAfter as the post-update dispersion, and the concrete loveStrategy and selfishStrategy instances. These objects prepare lemmas that compare how each strategy alters global sigma.
proof idea
The module first declares the population type and the two concrete strategies, then states auxiliary functions for spread and total absolute sigma. It next records non-negativity of spread, followed by direct comparison lemmas showing love reduces spread and selfish increases total sigma. Each lemma is a short algebraic or inequality argument.
why it matters in Recognition Science
The module supplies the formal substrate for treating sigma equilibration as an ethical drive within Recognition Science. Its lemmas on love minimizing spread and selfish increasing global sigma feed downstream arguments that ethical behavior aligns with the J-cost and forcing-chain structure. No explicit parent theorems are recorded in the dependency graph.
scope and limits
- Does not assign numerical sigma values to concrete agents.
- Does not derive sigma from the J-cost function.
- Does not prove convergence of repeated loveStrategy applications.
- Does not link results to the eight-tick octave or spatial dimension D=3.