lambda_exponent
plain-language theorem explainer
The definition supplies the integer exponent 583 for the phi-power suppression of the cosmological constant. Cosmologists examining the fine-tuning discrepancy would cite it when building the vacuum J-cost hypothesis. It is obtained by direct numerical evaluation of the logarithmic relation that matches the observed 10^{-122} factor using the golden ratio fixed point.
Claim. Let $n=583$ be the integer satisfying $n = 122 / (2.078 / 0.481)$ so that $phi^{-n} sim 10^{-122}$, where $phi$ is the self-similar fixed point.
background
The module COS-013 derives the cosmological constant from the J-cost ground state of the Recognition ledger. The observed vacuum energy is suppressed by roughly $10^{120}$ relative to naive QFT expectations, and the RS approach invokes phi-scaling of the vacuum J-cost to account for the small nonzero value. The supplied doc-comment states the explicit scaling hypothesis: Lambda proportional to phi to the minus n, with n chosen to bridge the gap.
proof idea
Direct numerical definition obtained by evaluating the logarithmic solution n = 122 times log(10) divided by log(phi) and rounding to the nearest integer.
why it matters
The exponent feeds directly into hypothesis3, which sets the vacuum scale to 1 over phi to the lambda_exponent. It realizes the phi-scaling route to the cosmological constant problem described in the module doc-comment and connects to the J-uniqueness and phi fixed-point steps of the forcing chain. The resulting prediction is numerically specific and therefore falsifiable against the measured dark-energy density.
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