E_coh
plain-language theorem explainer
E_coh is defined as the real number phi raised to the power -5, supplying the base coherence energy scale of approximately 0.09 eV in RS units. Researchers deriving constants from the golden ratio in the Recognition framework cite this as the initial step in the chain leading to tau_0, c, hbar, G and alpha inverse. The implementation is a direct noncomputable power assignment on reals with no reduction steps.
Claim. The coherence energy is defined by $E_{coh} := phi^{-5}$, where $phi$ is the golden ratio.
background
The RRF Foundation module derives all physical constants from phi via gate identities. The explicit chain is phi to E_coh to tau_0 to c to hbar to G to alpha inverse. The IR Gate identity states hbar equals E_coh times tau_0, while the Planck Gate enforces (c cubed lambda_rec squared) over (hbar G) equals 1 over pi. Phi itself enters from the imported PhiLadder module as the self-similar fixed point.
proof idea
The definition is a direct assignment using the real power operation on phi to the integer exponent -5.
why it matters
This definition starts the constant derivation sequence in the RRF module and supplies the scale that later identities convert into hbar and G. It instantiates the framework landmark that hbar equals phi to the -5 in native units. No downstream theorems are recorded for this declaration, but it supports the broader claim that constants are derived rather than postulated.
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