cutoff_above_lhc
plain-language theorem explainer
The Recognition Science ultraviolet cutoff energy exceeds LHC energies by more than seven orders of magnitude. Particle physicists comparing natural regularization scales to collider reach would cite the bound when evaluating hierarchy between fundamental discreteness and accessible momenta. The verification reduces to unfolding the two energy definitions followed by direct numerical normalization.
Claim. The ratio of the Recognition Science ultraviolet cutoff energy (in GeV) to the LHC beam energy (in GeV) satisfies $E_{RS}/E_{LHC} > 10^{7}$.
background
Recognition Science treats spacetime as discrete at the voxel scale, the fundamental length quantum with $c=1$ in native units. This lattice structure bounds momenta by a Brillouin-zone maximum $p_{max}=πℏ/l_0$, supplying a natural ultraviolet cutoff that regularizes loop integrals in quantum field theory. The module QFT.UVCutoff derives the cutoff energy from this discreteness and places it relative to experimental scales.
proof idea
The proof is a one-line wrapper that unfolds the definitions of the RS cutoff energy and the LHC energy, then applies norm_num to discharge the numerical inequality.
why it matters
The result quantifies the scale separation that lets Recognition Science supply a first-principles UV regulator, directly supporting the module target of a paper on natural regularization from information-theoretic discreteness. It sits inside the QFT-013 development and inherits the discrete-lattice premise from the voxel definition and the forcing-chain discreteness. No downstream uses are yet recorded, leaving open its insertion into concrete renormalization-group calculations.
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