hierarchy_problem_dissolves
Masses in Recognition Science sit on a geometric phi-ladder as E_coh times phi to the integer power r. Particle physicists examining naturalness would cite the result to observe how the hierarchy problem is removed by ledger geometry instead of renormalization. The proof is a one-line reflexivity that matches the definition of mass_on_rung exactly.
claimFor any integer rung index $r$, the mass at that rung equals $E_0 phi^r$, where $E_0$ is the coherence energy scale and $phi$ is the self-similar fixed point forced by the Recognition Composition Law.
background
The mass_on_rung definition supplies the geometric mass formula $E_coh * phi^r$ directly from the phi-ladder. Upstream rung definitions assign discrete integers to particles (electron at rung 2, top quark at rung 21) across lepton, quark, and boson sectors. The module localizes this to P-013, where the Standard Model hierarchy problem is declared dissolved because masses arise from ledger positions rather than divergent loop integrals.
proof idea
The proof is a one-line reflexivity that unfolds the definition of mass_on_rung in the MassHierarchy module and matches the right-hand side term by term.
why it matters in Recognition Science
The declaration supplies the explicit mass law that dissolves P-013 inside the Recognition framework. It rests on the phi fixed point (T6) and the eight-tick octave (T7) that fix the ladder spacing, with no free Yukawa parameters remaining. No downstream theorems depend on it yet; the equality closes the geometric assignment step without further scaffolding.
scope and limits
- Does not assign numerical rung values to specific particles.
- Does not incorporate radiative corrections or renormalization.
- Does not derive the coherence scale E_coh from more primitive constants.
- Does not address the dynamical origin of the rung assignments.
formal statement (Lean)
45theorem hierarchy_problem_dissolves (r : ℤ) :
46 Masses.MassHierarchy.mass_on_rung r = Masses.Anchor.E_coh * phi ^ r := rfl
proof body
Term-mode proof.
47
48/-- Hierarchy-dissolution structure implies the rung mass law. -/