hierarchy_problem_dissolves
plain-language theorem explainer
The declaration establishes that mass at rung r equals the coherence energy times phi to the power r. Particle physicists examining naturalness would cite it to replace the Standard Model hierarchy problem with a geometric ladder. The proof is a one-line reflexivity that matches the mass function directly to its defining expression.
Claim. For every integer rung index $r$, the mass at that rung is $m(r) = E_0 phi^r$, where $E_0$ denotes the coherence energy scale.
background
The HierarchyDissolution module formalizes P-013, the claim that the Standard Model hierarchy problem dissolves in Recognition Science. Masses arise from ledger rung positions on the phi-ladder rather than from renormalization or divergent loop integrals. The upstream definition mass_on_rung states: 'Mass in RS units: E_coh · φ^r where r is the rung.' Multiple rung functions appear in the depends_on list, assigning integer positions to fermions, sectors, and ore classes, all feeding the same geometric law.
proof idea
The proof is a term-mode reflexivity that matches the left-hand side directly to the right-hand side by the definition of mass_on_rung.
why it matters
This theorem supplies the explicit mass law required by the P-013 resolution in the module doc-comment. It confirms that the spectrum is set by the phi-ladder (forced by dimension and phi-forcing) with no free Yukawa couplings and no radiative corrections to scalar masses. The result sits inside the foundation layer that eliminates the hierarchy problem by geometry rather than by dynamics.
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