IndisputableMonolith.CondensedMatter.SpinGlassFreezingRatio
The SpinGlassFreezingRatio module states that the freezing-to-Curie ratio for canonical 3D Heisenberg spin glasses equals 1/φ. Condensed matter researchers modeling spin glass transitions would cite the result when mapping RS constants onto measured ratios. The module is a definition module whose structure is carried by sibling lemmas on positivity, bands, and dimensional crossover.
claimThe freezing-to-Curie ratio for canonical 3D Heisenberg spin glasses equals $1/\phi$, where $\phi$ is the self-similar fixed point forced by the Recognition Composition Law.
background
The module belongs to the CondensedMatter domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants. It introduces sibling definitions that place the freezing ratio on the phi-ladder for both 3D and 2D cases. The local setting assumes the eight-tick octave and three spatial dimensions from the upstream forcing chain.
proof idea
This is a definition module, no proofs. The overall argument is carried by the sibling declarations freezingRatio3D, freezingRatio3D_pos, freezingRatio3D_band, freezingRatio2D, freezingRatio2D_pos, freezingRatio2D_band, dimensional_crossover, and the certification lemmas.
why it matters in Recognition Science
The module supplies a concrete condensed-matter application of the phi fixed point inside the Recognition Science framework. It fills the spin-glass sector of the unified forcing chain T0-T8 and states the ratio 1/φ directly from the module doc-comment. No downstream theorems are listed.
scope and limits
- Does not derive the ratio without the phi-ladder assumption.
- Does not treat quantum corrections outside RS-native units.
- Does not address non-Heisenberg spin glasses.
- Does not provide numerical fitting to specific experimental datasets.