IndisputableMonolith.Physics.HiggsFieldFromRecognitionVacuum
This module defines the Higgs vacuum in Recognition Science as the state where both potential V and J-cost equal zero at vacuum expectation value φ_H = v. It supplies the HiggsFieldSector and related objects for linking the abstract J formalism to the Standard Model Higgs. Physicists deriving masses via the phi-ladder would cite these definitions. The module is purely definitional and imports the J-cost from the Cost module.
claimHiggs vacuum condition: $V = J = 0$ at $\\_H = v$, where $J$ denotes the recognition cost function.
background
Recognition Science derives physics from the J-cost functional equation with J(x) = (x + x^{-1})/2 - 1. The module imports IndisputableMonolith.Cost to access this J function and places the Higgs sector inside the broader forcing chain that yields D = 3 and the phi-ladder mass formula. The module doc-comment states the core relation: Higgs vacuum: V = J = 0 at φ_H = v. Sibling declarations establish HiggsFieldSector, higgs_vacuum, higgs_symmetric, and the certificate HiggsFieldCert.
proof idea
This is a definition module, no proofs. It declares the Higgs vacuum objects and the certificate HiggsFieldCert without theorems.
why it matters in Recognition Science
The module supplies the Higgs vacuum definition that supports downstream mass-ladder constructions yardstick * phi^(rung - 8 + gap(Z)). It connects the recognition vacuum (J = 0) to the Standard Model Higgs field, consistent with T5 J-uniqueness and the phi self-similar fixed point from the unified forcing chain.
scope and limits
- Does not derive the numerical value of v.
- Does not address electroweak gauge boson masses.
- Does not treat fermion Yukawa couplings.
- Does not resolve the hierarchy problem.