HiggsBoson
plain-language theorem explainer
The HiggsBoson structure encodes the mass of the Higgs particle as a positive real number whose square is proportional to the second derivative of the J-cost functional at the vacuum expectation value. Researchers deriving spontaneous symmetry breaking and mass generation from recognition cost would cite this definition. It is introduced as a bare structure with no computational content beyond the positivity constraint.
Claim. The Higgs boson is a structure consisting of a positive real mass $m_H > 0$, where $m_H^2$ is proportional to the second derivative of $J$ at the vacuum expectation value, and $J(x) = 1/2(x + x^{-1}) - 1$ for $x > 0$.
background
In Recognition Science the J-cost functional is defined as $J(x) = 1/2(x + 1/x) - 1$ for $x > 0$, attaining its minimum value of zero at $x = 1$ with the symmetry $J(x) = J(1/x)$. The module QFT.HiggsMechanism derives the Higgs mechanism from this J-cost structure: the vacuum selects the golden-ratio fixed point, breaking the $x$ to $1/x$ symmetry and generating masses proportional to the curvature of $J$ at that point.
proof idea
This is a structure definition with no proof body. It directly encodes a real mass field together with the positivity hypothesis and the stated proportionality to $J''$ at the VEV.
why it matters
The definition supplies the Higgs boson object required by the SM-002 paper proposition on deriving the Higgs mechanism from recognition cost symmetry breaking. It sits inside the J-cost potential analysis of the module and supplies the type for any later mass-generation statements in the QFT domain. It leaves open the numerical calibration of the proportionality constant against the phi-ladder.
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