IndisputableMonolith.Foundation.QRFT.HiggsPotentialFromRecognitionVacuum
The module defines the Higgs potential in Recognition Science as the J-cost evaluated on the ratio of the scalar field to its vacuum expectation value. Researchers connecting the recognition vacuum to electroweak symmetry breaking or the phi-ladder mass formula would cite this construction. The module consists of definitions and basic lemmas establishing non-negativity and uniqueness of the minimum.
claimLet $J(x) = \frac{x + x^{-1}}{2} - 1$. The Higgs potential is $V(\phi) = J(\phi / v)$ where $v$ is the vacuum expectation value.
background
Recognition Science derives all physics from the J-cost function obeying the Recognition Composition Law. The upstream Constants module fixes the fundamental time quantum $\tau_0 = 1$ tick. The Cost module supplies the definition of $J$ as the unique function meeting the self-similar fixed point condition from T5. This module applies that $J$ directly to the field ratio to obtain the Higgs potential inside the QRFT framework.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the vacuum potential used by sibling results on Higgs symmetry, non-negativity, and unique minimum. It realizes the T5 J-uniqueness step of the forcing chain for the electroweak sector.
scope and limits
- Does not derive gauge boson masses or fermion couplings.
- Does not incorporate quantum corrections to the potential.
- Does not specify the numerical value of the vacuum expectation value.