vev_structure
The electroweak VEV satisfies the ledger-fixed scale hierarchy rather than acting as a free input. Model builders addressing naturalness in the Standard Model would cite this to replace tuning arguments with RS ladder structure. The proof is a direct term that invokes the prior result establishing the electroweak scale as ledger-determined.
claimThe electroweak vacuum expectation value satisfies the ledger-derived scale property, where mass scales arise as powers of the self-similar fixed point on the integer rung ladder.
background
The module addresses C-020 on the origin of the electroweak VEV near 246 GeV. Recognition Science treats mass scales as ledger-determined quantities generated by the phi-ladder, with the scale function defined as phi raised to an integer power. The upstream theorem vev_not_free_parameter shows the electroweak scale is ledger-determined via the electroweak scale structure result, while vev_from_ledger is the minimal placeholder Prop standing for that same ledger property.
proof idea
One-line term proof that applies the theorem vev_not_free_parameter to discharge the goal vev_from_ledger.
why it matters in Recognition Science
The declaration supplies the structural half of C-020, showing the VEV belongs to the same ledger hierarchy that dissolves the hierarchy problem. It sits inside the forcing chain after phi is fixed as the self-similar point and before numeric extraction of laboratory values. No downstream theorems yet reference it, leaving the full numeric derivation of v as an open step.
scope and limits
- Does not compute a numerical value for the VEV from the phi-ladder.
- Does not derive the full electroweak symmetry breaking dynamics.
- Does not address gauge coupling unification or running.
- Does not produce the Higgs boson mass.
formal statement (Lean)
36theorem vev_structure : vev_from_ledger := vev_not_free_parameter
proof body
Term-mode proof.
37
38/-- Electroweak-VEV structure implies electroweak-scale structural input. -/