module module moderate

`IndisputableMonolith.Physics.UniversalityClasses`

The module defines universality classes in Recognition Science, each specified by O(N) symmetry rank together with its critical exponents. Condensed-matter physicists mapping RS to known classes such as Ising or XY would cite these definitions. The module is built from imported constants and the Q3 cube spectrum, with no internal proofs.

claimA universality class is a pair $(N,\{\nu,\eta,\dots\})$ where $N$ is the rank of the orthogonal group O(N) and the exponents satisfy scaling relations derived from the Q_3 spectrum.

background

The module imports Constants, where the fundamental RS time quantum is defined by $\tau_0=1$ tick, and CubeSpectrum, which equips the 3-dimensional hypercube Q_3 with its graph Laplacian eigenvalues ${0,2,2,2,4,4,4,6}$ (multiplicities ${1,3,3,1}$) and automorphism group $S_4\times\mathbb{Z}_2^3$ of order 48. These spectral data supply the combinatorial corrections used for critical-exponent calculations. The module documentation states that each universality class is characterized by its O(N) symmetry rank and the corresponding critical exponents.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the UniversalityClass interface and scaling properties that support bootstrap constructions for concrete classes (Ising, XY, Heisenberg) and exponent bounds. It thereby links the Q_3 spectral formalism to critical phenomena within the Recognition Science derivation of physics.

scope and limits

Does not compute numerical values for any critical exponents.
Does not derive scaling relations from the J-cost or RCL.
Does not address the forcing chain T0-T8 or phi-ladder.
Does not prove existence or uniqueness of any specific universality class.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Physics.CubeSpectrum module_import

declarations in this module (16)

structure UniversalityClass L29
def satisfies_scaling L35
theorem scaling_always_holds L41
def ising_bootstrap L51
def xy_bootstrap L52
def heisenberg_bootstrap L53
def spherical_exact L54
def nu_0_ising L65
def eta_stable_band_lower L70
def eta_stable_band_upper L71
theorem ising_eta_in_band L73
theorem xy_eta_in_band L79
theorem heisenberg_eta_in_band L85
theorem nu_monotone_ising_xy L92
theorem nu_monotone_xy_heisenberg L96
theorem nu_monotone_heisenberg_spherical L100