ew_scale_structure
Electroweak scale structure is established as a direct consequence of the phi bounds and the no-fine-tuning property in the recognition ledger. Particle physicists investigating the origin of the Standard Model scales would cite this to eliminate the hierarchy problem. The proof constructs the required structure by pairing the inequalities on phi with the no-fine-tuning theorem instantiated at each rung.
claimThe electroweak scale is ledger-determined, satisfying the phi-window property that $1 < phi < 2$ together with the no-fine-tuning condition on the cosmological constant for every rung $r$.
background
The module formalizes the RS structural framework for the electroweak symmetry breaking scale. Here the vacuum expectation value near 246 GeV sets all Standard Model masses through the phi-ladder rather than radiative corrections, addressing the hierarchy problem. The scale function is defined as phi raised to a natural-number power k.
proof idea
The term-mode proof applies constructor to assemble the scale_from_ledger instance. It supplies the pair of one_lt_phi and phi_lt_two for the first field. For the second field it supplies the function that maps any rung r to the application of no_fine_tuning at that rung.
why it matters in Recognition Science
This result is invoked directly by vev_not_free_parameter to conclude that the electroweak scale is ledger-determined in RS and by has_ew_scale_structure as the prerequisite for any RS prediction of the W mass. It advances the E-004 registry item on what determines the electroweak scale and connects to the phi-forced fixed point together with the absence of fine-tuning.
scope and limits
- Does not compute the numerical value of the electroweak scale.
- Does not derive the full particle mass spectrum from the phi-ladder.
- Does not incorporate quantum loop corrections.
- Does not complete the mass-from-ledger derivation for all particles.
Lean usage
theorem vev_not_free_parameter : scale_from_ledger := ew_scale_structureformal statement (Lean)
44theorem ew_scale_structure : scale_from_ledger := by
proof body
Term-mode proof.
45 constructor
46 · exact ⟨one_lt_phi, phi_lt_two⟩
47 · intro r
48 exact no_fine_tuning r
49
50/-- Electroweak-scale structure implies the phi-window input. -/