IndisputableMonolith.Sociology.PolarisationCheegerBound
The module defines the Cheeger threshold separating non-polarised and polarised regimes in Recognition Science sociology models as 1/φ lying in (0.617, 0.622). Researchers applying RS forcing chains to opinion dynamics or network structure would cite it to fix the transition point in discrete units. The module assembles supporting definitions and basic positivity lemmas around this constant.
claimThe non-polarisation Cheeger threshold equals $1/φ$ and satisfies $1/φ ∈ (0.617, 0.622)$, where $φ$ is the self-similar fixed point of the Recognition Composition Law.
background
Recognition Science obtains all structure from the T0-T8 forcing chain, with φ fixed by T6 as the unique positive solution to the self-similarity equation. This module imports the base time quantum τ₀ = 1 tick from Constants and adapts the classical Cheeger constant from graph theory to sociological polarisation. It introduces the predicates IsNonPolarised and IsPolarised together with the explicit threshold value cheegerThreshold, partitioning network regimes according to whether the Cheeger constant lies above or below 1/φ.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the concrete polarisation boundary that later sociology results in the Recognition framework use to classify social states. It translates the abstract φ fixed point from T6 directly into a sociological observable, providing the numerical interval that anchors discrete RS models of opinion dynamics.
scope and limits
- Does not derive the Cheeger bound from the forcing chain.
- Does not compute the threshold for any concrete network.
- Does not address continuous scaling limits or empirical fitting.