IndisputableMonolith.Sociology.PolarisationFromSigmaCascade
The module defines how social polarisation arises from sigma cascades in the recognition cost framework. It sets consensus as the equilibrium state where the recognition cost J vanishes. The module provides definitions establishing that polarisation states carry positive cost and exhibit symmetry.
claimThe consensus equilibrium is the state in which the recognition cost $J$ equals zero. Polarisation from sigma cascade is a configuration with associated positive cost and symmetry properties.
background
Recognition Science models social phenomena using the J-cost function imported from the Cost module. The module doc-comment identifies consensus with the recognition equilibrium where this cost is zero. It develops the idea of polarisation emerging from sigma cascades as a departure from this equilibrium, with associated cost and symmetry features.
proof idea
This is a definition module with no complex proofs. It introduces the consensus equilibrium directly as J equal to zero and then defines polarisation properties in terms of cost and symmetry using the imported cost definitions.
why it matters in Recognition Science
The module applies the recognition framework to sociology, providing tools to analyze social polarisation as a cost-driven process from sigma cascades. It serves as a foundation for further sociological extensions within the framework, though it has no listed downstream dependencies at present.