massParameter
plain-language theorem explainer
The mass parameter equals the J-cost evaluated at the vacuum expectation value φ. Recognition Science derivations of the Higgs mechanism cite this definition to fix the overall scale for particle masses. It is introduced as a direct abbreviation of the J-cost functional at the golden ratio.
Claim. The mass parameter is defined by $m = J(v)$, where $J(x) = ½(x + x^{-1}) - 1$ for $x > 0$ and $v = φ$ is the vacuum expectation value.
background
In the Recognition Science treatment of the Higgs mechanism the J-cost functional is given by $J(x) = ½(x + 1/x) - 1$ for $x > 0$, with a minimum of zero at $x = 1$ and the symmetry $J(x) = J(1/x)$. The vacuum expectation value is identified with the golden ratio φ. The module derives spontaneous symmetry breaking from the J-cost structure: the vacuum selects φ, breaking the x ↔ 1/x symmetry and generating masses proportional to the J-cost at that point.
proof idea
This declaration is a one-line definition that evaluates the J-cost at the vacuum expectation value.
why it matters
It supplies the mass scale shown positive and nonzero in the downstream theorems mass_parameter_pos and mass_parameter_ne_zero. The declaration fills the mass-generation step in the J-cost symmetry-breaking chain (SM-002). The parent results establish that the parameter excludes a vanishing Higgs-recognition scale, consistent with the framework claim that particles acquire mass from recognition cost at the selected vacuum.
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