canonicalThreshold
plain-language theorem explainer
Defines the canonical CMB E/T polarization threshold as φ − 3/2, which equals the J-cost at the golden ratio. Cosmologists working the RS CMB polarization chain cite it as the predicted E-mode fraction (~11.8%). It is a bare real constant abbreviation, not a proved inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio. Equivalently it equals the J-cost $J(\varphi) = (\varphi + \varphi^{-1})/2 - 1 \approx 0.118$.
background
The module derives CMB E-mode polarization structure from the Recognition Science J-cost. The module status is a structural theorem (zero sorry, zero axiom). Observationally, E-mode polarization is roughly 10% of the temperature anisotropy; the RS claim is that the E/T ratio is set by $J(\varphi)$.
The cost functional is the unique $J$ forced by the Recognition Composition Law and the T5 uniqueness step: $J(x) = (x + x^{-1})/2 - 1$. At the self-similar fixed point $\varphi$ one has the elementary identity $J(\varphi) = \varphi - 3/2$. The constant $\varphi$ is imported from the RS Constants module.
Sibling definitions in the same file package a domain cost, non-negativity, positivity of this threshold, and a certificate structure for the polarization claim.
proof idea
There is no proof body. The declaration is a one-line real abbreviation: the right-hand side is the literal expression $\varphi - 3/2$. Algebraic equivalence to $J(\varphi)$ follows from the golden-ratio relation $\varphi^{-1} = \varphi - 1$ and is used implicitly by the surrounding polarization certificate, not discharged inside this def.
why it matters
Supplies the numerical RS prediction for the CMB E/T ratio inside the Cosmology.CMBPolarization3_FromJCost development. The module frames E-mode polarization as ~10% of temperature anisotropy and identifies the RS value with $J(\varphi) \approx 11.8%$. The threshold therefore sits at the interface between the T5/T6 forcing chain (unique J-cost and $\varphi$ as fixed point) and a concrete cosmological observable.
Downstream siblings such as the positivity lemma and the CMBPolar3Cert certificate package treat this constant as the reference scale. No open scaffold remains on the definition itself; any remaining tension is empirical (how tightly 11.8% matches the measured ~10% band).
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