IndisputableMonolith.CondensedMatter.SpinGlassFreezingRatio
The SpinGlassFreezingRatio module sets the freezing-to-Curie ratio for canonical 3D Heisenberg spin glasses to exactly 1/φ. Condensed-matter theorists modeling spin-glass transitions cite these definitions when mapping Recognition Science constants onto measured temperature ratios. The module is organized as a collection of ratio definitions for 3D and 2D cases plus supporting positivity and band lemmas.
claimThe freezing-to-Curie ratio equals $\phi^{-1}$ for canonical 3D Heisenberg spin glasses, where $\phi$ is the self-similar fixed point of the Recognition Composition Law.
background
Recognition Science obtains all constants from the forcing chain T0-T8 that terminates with D=3 and the phi-ladder. This module imports Constants, whose sole documented object is the fundamental time quantum $\tau_0=1$ tick. The central definition therefore expresses the 3D freezing ratio directly as $1/\phi$ and supplies auxiliary lemmas that locate the result inside the allowed band.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the numerical ratio required by SpinGlassFreezingCert and spin_glass_one_statement. It therefore inserts the phi fixed point (T6) into a concrete condensed-matter observable. No open questions are closed here.
scope and limits
- Does not derive the ratio from a microscopic Hamiltonian.
- Does not incorporate quantum corrections or finite-size effects.
- Does not treat non-Heisenberg spin glasses or higher-order interactions.
- Does not compute numerical values outside the exact $1/\phi$ expression.