IndisputableMonolith.Physics.UniversalityClasses
The module defines universality classes in Recognition Science as O(N) symmetry groups paired with their critical exponents for three-dimensional systems. Condensed matter physicists mapping scaling laws to lattice models would cite these characterizations. It assembles definitions and scaling lemmas directly from the Q3 spectral data without new axioms.
claimA universality class for integer symmetry rank $N$ is the triple $(N, E, R)$ where $E$ is the set of critical exponents and $R$ the scaling relations satisfied by the O($N$) vector model on the three-dimensional hypercube lattice.
background
Recognition Science works in units with fundamental time quantum τ₀ = 1 tick. The CubeSpectrum module supplies the combinatorial skeleton for D = 3 by treating the unit cell Q₃ whose graph Laplacian has eigenvalues {0, 2, 2, 2, 4, 4, 4, 6} and automorphism group S₄ × ℤ₂³ of order 48; these data correct the exponents that appear in the phi-ladder mass formula.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module translates the T8 result D = 3 into concrete O(N) classes (Ising, XY, Heisenberg, spherical) that downstream mass and coupling calculations can invoke. It supplies the exponent bands used to test the Recognition Composition Law against observed critical phenomena.
scope and limits
- Does not derive numerical exponent values from the phi-ladder.
- Does not treat non-O(N) or long-range interaction classes.
- Does not prove existence of phase transitions.
- Does not include renormalization-group flows beyond classical scaling.
depends on (2)
declarations in this module (16)
-
structure
UniversalityClass -
def
satisfies_scaling -
theorem
scaling_always_holds -
def
ising_bootstrap -
def
xy_bootstrap -
def
heisenberg_bootstrap -
def
spherical_exact -
def
nu_0_ising -
def
eta_stable_band_lower -
def
eta_stable_band_upper -
theorem
ising_eta_in_band -
theorem
xy_eta_in_band -
theorem
heisenberg_eta_in_band -
theorem
nu_monotone_ising_xy -
theorem
nu_monotone_xy_heisenberg -
theorem
nu_monotone_heisenberg_spherical