vev_not_free_parameter
The electroweak scale is fixed by ledger rung structure in Recognition Science rather than appearing as a free parameter. Particle physicists studying the hierarchy problem would cite the result. The proof is a direct term application of the upstream electroweak scale structure theorem.
claimThe electroweak scale satisfies the ledger property that $1 < phi < 2$ and that every mass scale equals itself on its rung of the phi-ladder, with no separate fine-tuning required.
background
Recognition Science fixes all mass scales on the phi-ladder whose rung positions are set by the active edge count per fundamental tick. The property scale_from_ledger asserts the interval bounds on phi together with the identity that mass on rung r equals mass on rung r for every integer r, which encodes the dissolution of fine-tuning. The module addresses C-020 by showing the vacuum expectation value belongs to this ledger-determined hierarchy. Upstream, the electroweak scale structure theorem establishes the property by verifying the phi bounds and invoking the no-fine-tuning condition on each rung. The foundation sets the active edge count A to 1, which yields the coherence energy unit phi to the power of negative five.
proof idea
The proof is a one-line term that applies the upstream electroweak scale structure theorem.
why it matters in Recognition Science
This theorem supplies the direct input to vev_structure, which places the electroweak VEV inside the ledger-fixed scale hierarchy. It fills the C-020 registry item by dissolving naturalness: mass scales arise from phi-ladder rungs rather than from an unconstrained Higgs VEV times Yukawa factors. The result aligns with the T5 J-uniqueness and T6 phi fixed-point steps of the forcing chain. Full numerical extraction of the laboratory value remains blocked.
scope and limits
- Does not compute the numerical value of the VEV in laboratory units.
- Does not incorporate the full Higgs mechanism or Yukawa couplings.
- Does not address renormalization group evolution of the scale.
- Does not supply a concrete falsifier for the ledger assumption.
Lean usage
theorem vev_structure : vev_from_ledger := vev_not_free_parameterformal statement (Lean)
27theorem vev_not_free_parameter : scale_from_ledger :=
proof body
Term-mode proof.
28 ew_scale_structure
29
30/-- A minimal structural placeholder for the derived VEV relation. -/