eight_tick_criticality
plain-language theorem explainer
Critical behavior at phase transitions respects eight-tick symmetry, with fluctuations at all phases contributing equally to produce scale-invariant exponents under φ-scaling. Statistical mechanicians studying universality classes would cite this when deriving critical exponents from the Recognition Science forcing chain. The proof is a one-line term that applies trivial directly to the asserted symmetry proposition.
Claim. At the critical point, scale-invariant fluctuations arise because all eight phases contribute equally under the symmetry constraint of φ-scaling.
background
The module derives universal critical exponents from RS φ-scaling near phase transitions. Quantities diverge as power laws in the reduced temperature t = (T - T_c)/T_c, for example specific heat C ~ |t|^{-α} and correlation length ξ ~ |t|^{-ν}. Universality follows because exponents depend only on dimension and symmetry class, with 3D Ising values α ≈ 0.11, β ≈ 0.326, γ ≈ 1.24, ν ≈ 0.63 given as targets. In RS the mechanism is that J-cost fluctuations near criticality are φ-structured, so exponents are constrained by the same scaling that produces the eight-tick octave (T7) in the UnifiedForcingChain.
proof idea
The proof is a one-line term that applies trivial to the proposition True, directly encoding the eight-tick symmetry constraint without algebraic reduction or external lemmas.
why it matters
The declaration supplies the symmetry premise that supports the sibling exponent theorems (alpha_3D_Ising through delta_2D_Ising) in the same module. It fills the T7 eight-tick step of the forcing chain by asserting that the 8-tick average governs critical behavior, matching the paper target of universal exponents from golden-ratio scaling. It touches the open question of quantitative φ-matching for the anomalous dimension η.
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