vev
plain-language theorem explainer
Recognition Science sets the vacuum expectation value to the golden ratio φ in its derivation of the Higgs mechanism. QFT researchers tracing mass generation to J-cost symmetry breaking reference this assignment to fix the scale of the broken vacuum. The declaration is a direct definition with no additional proof steps.
Claim. The vacuum expectation value $v$ equals the golden ratio $φ$.
background
The module derives spontaneous symmetry breaking from the J-cost functional $J(x) = ½(x + x^{-1}) - 1$, which attains its minimum of zero at $x = 1$ and is invariant under inversion. Symmetry breaking occurs when the vacuum selects the golden ratio φ instead of its inverse. This definition supplies the concrete numerical value for the vacuum expectation value that enters all mass formulas and positivity statements in the Higgs mechanism development.
proof idea
The declaration is a direct definition that sets the vacuum expectation value equal to the golden ratio φ.
why it matters
This definition provides the non-zero, non-unit vacuum value required for the symmetry-breaking theorems higgs_mechanism_nonzero_vev and symmetry_broken. It implements the selection of φ as the fixed point that breaks the x ↔ 1/x symmetry in the J-cost potential, enabling the mass parameter and particle mass constructions. The assignment aligns with the phi-ladder mass formula and the eight-tick structure of the Recognition Science forcing chain.
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