hierarchyProblemDescription
The definition supplies a compact statement of the Standard Model hierarchy problem, expressing the Higgs-to-Planck mass ratio as approximately 10^(-17) and noting that Recognition Science accounts for it via a phi-cascade instead of parameter fine-tuning. QFT researchers examining naturalness and UV regularization would cite the entry when linking discrete spacetime to the absence of quadratic divergences. It is implemented as a direct string literal with no computation or external lemmas.
claimThe hierarchy problem is the observation that the Higgs mass satisfies $m_H / m_Planck sim 10^{-17}$, which Recognition Science resolves by a phi-cascade on the discrete lattice rather than fine-tuning of bare parameters.
background
Module QFT.UVCutoff derives the ultraviolet cutoff from Recognition Science discreteness. Spacetime is discrete at the tau_0 scale, so momenta are bounded by p_max = hbar / tau_0; this bound regularizes all loop integrals. The hierarchyProblemDescription sits inside that setting because the same discreteness that supplies the cutoff also converts the electroweak-Planck separation into a geometric phi-cascade on the ladder.
proof idea
The declaration is a definition realized by direct string assignment. No lemmas are invoked and no tactics are executed; the body is the literal text describing the mass ratio and its phi-cascade explanation.
why it matters in Recognition Science
The entry anchors the hierarchy problem inside the UV-cutoff derivation, showing how Recognition Science replaces fine-tuning with the phi-ladder structure already present in the forcing chain. It supports the module's claim of a natural regularization and connects to the broader program in which constants such as G and alpha arise from the same phi-forcing. No downstream theorems are recorded, leaving open how the cascade quantitatively reproduces the observed 10^{-17} ratio.
scope and limits
- Does not derive the numerical mass ratio from the phi-ladder.
- Does not specify the rung or gap values that produce 10^{-17}.
- Does not address renormalization-group evolution of the cutoff.
formal statement (Lean)
176def hierarchyProblemDescription : String :=
proof body
Definition body.
177 "m_H / m_Planck ~ 10^(-17), explained by φ-cascade"
178
179/-- Higgs mass in GeV. -/