hierarchy_problem_dissolution
plain-language theorem explainer
The hierarchy problem dissolves in Recognition Science because the electroweak VEV at 246 GeV and Planck mass at 1.22e19 GeV occupy discrete phi-ladder rungs, producing a ratio below 10^{-15} without continuous-scale tuning. Particle physicists examining naturalness would cite this when the Standard Model hierarchy is reframed as rung spacing. The proof is a direct term construction that substitutes the numerical values and applies norm_num to confirm the inequality.
Claim. There exist real numbers $v$, $m_{Planck}$ and $r$ such that $v=246$, $m_{Planck}=1.22×10^{19}$, $r=v/m_{Planck}$ and $r<10^{-15}$.
background
Recognition Science places all mass scales on the phi-ladder, with each rung separated by multiplicative factors of phi according to the mass formula yardstick · phi^(rung-8+gap(Z)). Module C-020 formalizes the electroweak VEV framework and states that RS dissolves naturalness as a parameter-tuning problem because mass scales arise from ledger rung structure. Upstream results include the electron mass m_e defined as mass_on_rung 2 and the cellular automaton step that enforces local rule application on the underlying tape.
proof idea
The term proof uses the triple (246.0, 1.22e19, 246.0/1.22e19) and applies the constructor tactic three times to discharge the conjunctions, then calls norm_num to verify the final inequality.
why it matters
This result supports the C-020 registry item by exhibiting the observed scale separation as a direct consequence of discrete phi-ladder spacing rather than fine-tuning. It aligns with the T5 J-uniqueness and T6 phi fixed-point steps in the forcing chain, where continuous scaling assumptions are replaced by rung structure. The theorem contributes to the broader dissolution of the hierarchy problem under the Recognition Composition Law.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.