IndisputableMonolith.Physics.SymmetryBreakingFromRS
Defines spontaneous symmetry breaking structures from the Recognition Science cost: the SSB vacuum is the J-cost ground state J=0. Packages mechanism counts, ground-state and excitation data, and a certificate type. Physicists linking RS vacuum geometry to particle-physics SSB would cite it. Purely definitional; no theorems proved here.
claimThe module identifies the spontaneous-symmetry-breaking vacuum with the Recognition cost ground state $J=0$, and introduces mechanism data, excitation structure, and a certificate for SSB derived from the RS cost functional $J(x)=(x+x^{-1})/2-1$.
background
Recognition Science fixes a unique cost $J$ by the Recognition Composition Law, with closed form $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$). Its global minimum is $J=0$, attained at the self-dual point $x=1$. This module treats that minimum as the SSB vacuum.
It lives in the Physics domain and imports only the Cost module. Sibling definitions name the mechanism type, a count of mechanisms, explicit ground-state and excitation values, and a certificate wrapper that packages the identification for later use.
proof idea
This is a definition module, no proofs. It introduces named structures and values (mechanism type, mechanism count, ground state, excitation, certificate) that encode the identification of the $J=0$ vacuum with spontaneous symmetry breaking and expose them for downstream physics constructions.
why it matters in Recognition Science
Gives particle-physics language (SSB vacuum, excitations, certificates) to the RS cost minimum. Downstream work that needs an explicit vacuum or excitation spectrum rooted in $J$ can import these names rather than re-deriving the identification. No used-by edges are recorded yet; the module is infrastructure for later mass-ladder or forcing-chain applications that mention SSB. It does not itself touch T5--T8 or the alpha band.
scope and limits
- Does not prove the Standard Model Higgs mechanism emerges from J.
- Does not derive gauge-group breaking patterns or Goldstone spectra.
- Does not compute particle masses from the excitation data.
- Does not connect directly to eight-tick octave or D=3 forcing steps.
- Does not assert uniqueness of the SSB mechanism beyond the named count.