planckMassGeV
plain-language theorem explainer
planckMassGeV supplies the numerical value 1.22e19 GeV as the Planck mass for hierarchy computations inside the Recognition Science QFT UV cutoff module. Particle physicists examining the gauge hierarchy problem cite this constant to quantify the separation between the Higgs and gravitational scales. The entry is introduced by direct numerical assignment in rational arithmetic.
Claim. The Planck mass is given by $m_P = 1.22 × 10^{19}$ GeV.
background
The QFT.UVCutoff module establishes a natural ultraviolet cutoff arising from Recognition Science spacetime discreteness at the τ₀ scale, bounding momenta by p_max = ℏ/τ₀ and thereby regularizing divergent loop integrals. The Planck mass functions as the reference gravitational scale against which the Higgs mass is compared, producing the small hierarchy ratio. The module imports Constants and PhiForcing, which supply the self-similar fixed point phi underlying the mass ladder, although this particular definition imports the conventional numerical value directly.
proof idea
One-line constant definition that directly assigns the rational literal 1.22e19 to planckMassGeV.
why it matters
The definition supplies the denominator for hierarchyRatio, which in turn supports the theorem hierarchy_very_small establishing that the ratio lies below 10^{-16}. It anchors the QFT-013 discussion of natural UV regularization by furnishing the Planck reference scale, connecting to the phi-forcing chain (T5 J-uniqueness through T8 D=3) and the mass formula on the phi-ladder. No open scaffolding questions are closed by this entry.
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