m_e_rs_eq
plain-language theorem explainer
The equality establishes that the Recognition Science electron mass equals the coherence energy scaled by phi squared. Researchers deriving lepton masses on the phi-ladder cite this when confirming the rung-2 placement for the electron. The proof is a direct simplification that substitutes the rung definition and anchor values, then closes by reflexivity.
Claim. The electron mass in RS units satisfies $m_e^{RS} = E_{coh} phi^2$.
background
In the Recognition Science framework, particle masses sit on a phi-ladder scaled from the coherence energy $E_{coh} = phi^{-5}$. The electron is assigned rung 2 via the lepton rung map. The upstream definition states the RS electron mass as $E_{coh}$ times phi raised to the electron rung. The rung theorem verifies that the electron rung equals 2, the muon rung equals 13, and the tau rung equals 19.
proof idea
The proof is a one-line wrapper that applies simplification to the electron-mass definition and the lepton-rung theorem, then closes by reflexivity.
why it matters
This declaration resolves registry item C-007 by confirming the electron mass formula with no free parameters. It is invoked directly by the downstream theorem that packages positivity and the equality to close the C-007 derivation. The result aligns with the phi-ladder mass formula and the eight-tick octave structure of the forcing chain.
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