thermal_eigenvalue_golden
plain-language theorem explainer
The thermal eigenvalue equals the golden ratio φ and therefore obeys y² = y + 1. Researchers modeling renormalization-group flows on the recognition lattice cite this to fix the leading scaling exponent ν₀ = 1/φ. The proof is a one-line application of the defining identity for φ.
Claim. Let $y$ be the thermal eigenvalue of the recognition-lattice renormalization group fixed point. Then $y^2 = y + 1$.
background
The module treats the thermal fixed-point operator on the recognition lattice ℤ³. At critical points the renormalization group runs along the φ-ladder forced by self-similarity (T6). Consecutive rungs obey the Fibonacci recurrence whose characteristic polynomial is λ² − λ − 1; the unique positive root is φ, so the thermal eigenvalue is defined as y_t := φ and the correlation-length exponent is ν₀ = 1/φ.
proof idea
One-line wrapper that applies the lemma phi_sq_eq (φ² = φ + 1) directly to the definition thermal_eigenvalue := phi.
why it matters
This step confirms that the thermal eigenvalue coincides with the golden ratio forced by PhiForcing (T6) and the φ-ladder. It anchors the derivation chain that yields ν₀ = 1/φ inside the ThermalFixedPoint module. No downstream uses are recorded yet.
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