massGap
plain-language theorem explainer
The mass gap constant equals (√5 - 2)/2 exactly in RS units. It is the minimum non-zero value of the J-cost functional on the golden-ratio lattice. Researchers addressing the Yang-Mills mass gap problem cite this as the exact spectral gap forced by the recognition composition law. The definition is obtained by direct algebraic substitution of the golden ratio into J and simplification.
Claim. The Yang-Mills mass gap constant satisfies $Δ = (√5 - 2)/2$.
background
The J-cost functional is J(x) = ½(x + x^{-1}) - 1. The phi-lattice consists of points φ^n for n ∈ ℤ, where φ is the golden ratio fixed point. The module presents the mass gap as the exact minimum excitation cost above the vacuum on this lattice. Upstream results include the gap definition in Gap45.Derivation as the product of closure and Fibonacci factors, together with anchor gap functions that express residues as ln(1 + Z/φ)/ln(φ).
proof idea
The definition is a direct algebraic evaluation of J(φ) using the quadratic identity satisfied by the golden ratio, which simplifies to (√5 - 2)/2 with no lemmas applied.
why it matters
This supplies the exact value used by downstream theorems such as mass_gap_from_phi (equating it to J(φ)) and minimum_rest_mass_is_gap. It realizes the central claim of registry QG-005, the RS resolution of the Yang-Mills mass gap, emerging from J-uniqueness (T5) and the phi fixed point (T6) together with the recognition composition law. It leaves open the question of direct matching to observed hadron spectra on the phi-ladder.
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papers checked against this theorem (showing 1 of 1)
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Neural net reads a holographic metric off the lattice quark potential
"drag force, jet quenching parameter q̂, and diffusion coefficient computed via standard holographic formulas with the KAN-extracted w(r)"