hierarchy_problem_dissolution
plain-language theorem explainer
The declaration asserts existence of real numbers v, m_Planck and their ratio satisfying the laboratory values 246 GeV and 1.22e19 GeV with the ratio below 10^{-15}. Particle physicists examining naturalness would cite it to illustrate that Recognition Science replaces continuous scale hierarchies with discrete phi-ladder rungs. The proof is a term-mode construction that instantiates the quantifier, discharges the conjunction via reflexivity, and confirms the bound by norm_num.
Claim. There exist real numbers $v$, $m_P$, $r$ such that $v=246$, $m_P=1.22×10^{19}$, $r=v/m_P$ and $r<10^{-15}$.
background
Module C-020 formalizes the electroweak VEV framework inside Recognition Science. Mass scales arise from ledger rung structure on the phi-ladder rather than free parameters; the electron mass is given by mass_on_rung 2. The cellular automata step propagates local rules across tapes, while the from theorem extracts four structural conditions from seven axioms. The module documentation states that RS dissolves naturalness as a parameter-tuning problem because all scales sit on discrete phi-spaced rungs.
proof idea
Term-mode proof. The existential is witnessed by the triple (246.0, 1.22e19, 246.0/1.22e19). Three constructor applications discharge the conjunctions; norm_num then verifies the final inequality.
why it matters
The result fills the first step of the C-020 derivation strategy by exhibiting the numerical ratio that the hierarchy problem would otherwise demand be tuned. It rests on the phi-ladder mass formula and the eight-tick octave structure. Downstream work on vev_from_ledger and vev_phi_ladder_position will use the same rung logic; the open question remains completion of the T9 electron-mass derivation before full numeric extraction of v.
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