falsifierThreshold
plain-language theorem explainer
Defines the Track 4.C structural falsifier threshold at redshift z as φ^{-44}·z, the absolute gap between the RS linear w(z) placeholder and ΛCDM's w=-1. Cosmologists and auditors of the dark-energy equation-of-state discriminator cite it when stating precision bands that would rule RS out. The body is a one-line product of the rung-44 scale with z.
Claim. For redshift $z \in \mathbb{R}$, the structural falsifier threshold is $T(z) := \varphi^{-44}\, z$, where $\varphi$ is the golden ratio and $\varphi^{-44}$ is the RS rung-44 forcing scale (the same scale as baryogenesis $\eta_B = \varphi^{-44}$).
background
Track 4.C of the quantum-gravity master plan asks for a falsifiable dark-energy equation of state $w(z)$ that differs at sub-leading order from ΛCDM's strict $w=-1$. This module ships the algebraic discriminator only: the RS deviation is suppressed by the rung-44 factor $\varphi^{-44}\approx 6.38\times 10^{-10}$, shared with baryogenesis via the $\varphi$-rung ladder value $-44$. The concrete FPT cosmic Z-aging $z$-dependence is deferred; a linear placeholder $w_{\mathrm{RS}}(z):=-1+\varphi^{-44},z$ stands in as a non-vacuous witness.
Upstream, phi_neg_44 is defined as $\mathrm{Constants.phi}^{(-44)}$, the positive rung-44 scale. ΛCDM is the constant $w=-1$. The absolute RS/ΛCDM separation at redshift $z$ is exactly $\varphi^{-44},z$, which this definition names as the falsifier threshold.
proof idea
Definition, not a proof. The body multiplies the already-defined rung-44 scale $\varphi^{-44}$ by the redshift argument $z$. Downstream positivity at $z>0$ is immediate from positivity of $\varphi^{-44}$ and of $z$ (via mul_pos). Specializations at $z=1/2$ and $z=1$ reduce by unfolding and ring.
why it matters
Names the precision band that turns the structural discriminator into an observational falsifier. The master-plan §7 band theorem states that a measurement of $w(z)$ at any $z>0$ equal to $-1$ within better than $T(z)=\varphi^{-44},z$ would falsify RS (which requires $w(z)-(-1)>0$); a detection of $w(z)>-1$ at that scale is consistent with the RS side. The threshold feeds the Track 4.C one-statement, the master cert structure, the absolute-deviation identity, the named bands at $z=0.5$ and $z=1$, and the near-ΛCDM-not-RS-linear comparison lemmas. It sits on the same $\varphi$-ladder scale as $\eta_B=\varphi^{-44}$; the open item remains the true FPT Z-aging $z$-shape beyond the linear placeholder.
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