E0
plain-language theorem explainer
E0 defines the fundamental energy scale as ħ divided by the fundamental tick duration τ₀. QFT researchers seeking a natural UV cutoff from spacetime discreteness would cite this as the base scale for regularizing divergences. The definition is a direct quotient using the imported constants hbar and tau0.
Claim. The fundamental energy scale is given by $E_0 = ħ / τ_0$, where ħ is the reduced Planck constant and τ₀ is the duration of one fundamental tick.
background
Recognition Science models spacetime as discrete with fundamental tick duration τ₀. The reduced Planck constant ħ equals φ^{-5} in RS units. The module derives a natural ultraviolet cutoff from this discreteness to address UV divergences in loop integrals, with p_max = ħ/τ₀ since c=1.
proof idea
The declaration is a direct definition of E0 as the quotient hbar / tau0. It applies no further lemmas or tactics beyond referencing the constants.
why it matters
This supplies the reference energy for the φ-ladder in phiLadderEnergy and the running coupling formula. It realizes the core claim of the QFT-013 paper on natural UV regularization from information-theoretic discreteness. The scale sets the point where the eight-tick octave and spatial discreteness cut off high momenta, enabling finite predictions for loop corrections.
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