J
plain-language theorem explainer
The J-cost functional is defined by J(x) = ½(x + 1/x) - 1 for x > 0. Physicists deriving spontaneous symmetry breaking in the Standard Model from recognition cost would cite this as the potential whose minimum at unity selects the vacuum. The definition is a direct noncomputable alias to the upstream Jcost primitive.
Claim. $J(x) := ½(x + x^{-1}) - 1$ for $x > 0$.
background
The QFT.HiggsMechanism module derives the Higgs mechanism from J-cost symmetry breaking. The J-cost functional supplies the Mexican-hat potential: it attains its global minimum of zero at x = 1, obeys the reflection symmetry J(x) = J(1/x), and thereby encodes the gauge symmetry that is spontaneously broken when the vacuum expectation value settles at the golden-ratio fixed point φ. The module imports the Cost module (which supplies the primitive Jcost) together with Constants and the has class from AsteroidOreSpectroscopy that ranks spectral features on the phi-ladder.
proof idea
The declaration is a one-line wrapper that aliases Jcost x under the hypothesis x > 0.
why it matters
This definition supplies the potential used by every subsequent declaration in the module (J_min_at_one, vev, massParameter, YukawaCoupling, particleMass). It realizes the T5 J-uniqueness step of the forcing chain and directly supports the target PRL derivation of the Higgs mechanism from recognition cost. No open scaffolding remains inside the module.
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