IndisputableMonolith.Materials.GlassTransitionFromJCost
This module establishes the connection between the J-cost functional and glass transition behavior in materials within Recognition Science. It defines key quantities such as the glass regime, fragility index, and transition certificates using the RS time quantum τ₀. The module consists entirely of definitions that build directly on the constants imported from IndisputableMonolith.Constants, providing the mathematical objects for subsequent analysis.
claimThe module defines the glass regime as the parameter range where J-cost induces vitrification, with fragility index $f = J(x)/x$ at the transition scale set by the time quantum τ₀, along with a certification predicate GlassTransitionCert for the transition point.
background
Recognition Science derives material properties from the J-cost J(x) = (x + x^{-1})/2 - 1, which quantifies deviation from multiplicative unity and appears in the forcing chain at T5. The module imports the fundamental RS time quantum τ₀ = 1 tick from Constants and operates in the materials domain. It introduces sibling definitions including GlassRegime, fragilityIndex, fragility_ratio, and GlassTransitionCert to model the liquid-to-glass transition via self-similar scaling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the core objects for glass transition modeling in RS, including GlassTransitionCert which certifies the transition point derived from J-cost. It positions glass phenomena as emergent from the J-uniqueness and phi-ladder in the forcing chain (T5-T6). No downstream uses are currently declared, indicating it serves as a foundational block for materials applications.
scope and limits
- Does not compute specific transition temperatures for real materials.
- Does not incorporate quantum or thermal fluctuation effects beyond J-cost.
- Does not address the Kauzmann paradox or other thermodynamic aspects.