vev_pos
plain-language theorem explainer
The vacuum expectation value in the Recognition Science Higgs mechanism is positive, enabling non-trivial spontaneous symmetry breaking away from the J-minimum at unity. Researchers deriving particle masses from J-cost functionals in QFT would cite this to confirm the vacuum selects the golden ratio state. The proof is a one-line term wrapper applying the positivity of phi.
Claim. The vacuum expectation value satisfies $v > 0$.
background
The module QFT.HiggsMechanism derives the Higgs mechanism from the J-cost functional $J(x) = 1/2(x + 1/x) - 1$, which has a minimum of zero at $x=1$ and is symmetric under $x$ to $1/x$ exchange. The vacuum expectation value is defined as the golden ratio phi, which breaks this symmetry when the vacuum selects it over the symmetric point.
proof idea
The proof is a term-mode one-liner that directly invokes phi_pos, the upstream theorem establishing positivity of the golden ratio, since vev is defined to be phi in the same module.
why it matters
This result feeds higgs_mechanism_nonzero_vev (vev ≠ 0), mass_parameter_pos, and mass_positive in the same module, plus the parallel vev_pos in HiggsRungAssignment. It fills the positivity step required for J-cost symmetry breaking in the Higgs mechanism, connecting to the phi-ladder and eight-tick octave in the Recognition Science chain. It touches the open question of predicting the Higgs mass from RS constants.
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