phiLadderEnergy
plain-language theorem explainer
The definition supplies discrete energy levels on the Recognition Science phi-ladder as E_n equals E0 scaled by phi to the integer power n. Physicists constructing natural UV cutoffs for QFT loop integrals from spacetime discreteness would cite this when building the momentum ladder above the tau0 scale. It is realized by direct multiplication without further reduction steps.
Claim. $E_n = E_0 φ^n$, where $E_0$ is the fundamental energy scale and $φ$ is the self-similar fixed point.
background
The module derives a natural ultraviolet cutoff for quantum field theory from Recognition Science discreteness at the tau0 scale, with momenta bounded by p_max equal to hbar over tau0. The fundamental energy E0 is defined as hbar divided by tau0 and serves as the base for all higher scales. The phi-ladder then places discrete energies at successive rungs via multiplication by powers of the golden-ratio fixed point forced in the upstream phi-forcing chain.
proof idea
The definition is a one-line wrapper that directly multiplies the base energy E0 by phi raised to the rung index n.
why it matters
It supplies the energy values consumed by the adjacent-rung ratio theorem, which verifies that neighboring levels differ exactly by the factor phi. This step supports the QFT-013 program of regularizing UV divergences through tau0 discreteness and links to the phi-ladder structure used in mass formulas and the eight-tick octave.
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