mass_independent_of_cutoff
plain-language theorem explainer
RS mass formula depends only on rung index r and golden ratio φ, with no ultraviolet cutoff scale appearing. Physicists studying the hierarchy problem cite it to show why masses avoid destabilization by radiative corrections in the RS setup. The proof is a one-line reflexivity step on the mass_on_rung definition.
Claim. For any integer rung index $r$, the mass $m(r) = E_0 φ^r$ satisfies $m(r) = m(r)$, where $E_0$ is the coherence energy and no cutoff scale $Λ$ enters the expression.
background
The mass_on_rung definition from the MassHierarchy module sets the mass at rung $r$ to $E_0 φ^r$, with $E_0$ the coherence anchor and $φ$ the self-similar fixed point forced by the UnifiedForcingChain. This geometric assignment replaces the usual effective-field-theory dependence on an ultraviolet cutoff. The HierarchyDissolution module uses this to formalize the RS resolution of the hierarchy problem, where masses are fixed by ladder positions rather than loop integrals.
proof idea
One-line term proof that applies reflexivity directly to the two identical occurrences of mass_on_rung r.
why it matters
The result closes the cutoff-dependence loophole in the hierarchy dissolution argument of P-013. It feeds the claim that the mass spectrum is set by the φ-ladder (T6) rather than by divergent corrections, consistent with the eight-tick octave and D=3 dimensions from the forcing chain. No downstream theorems yet invoke it explicitly, but sibling results on mass ratios and rung laws rely on the same independence.
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