falsifierThreshold_at_redshift_one

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 supplies the algebraic discriminator: the RS deviation is suppressed by the rung-44 factor $\varphi^{-44}\approx 6.38\times 10^{-10}$, the same scale that appears in baryogenesis as $\eta_B = \varphi^{-44}$.

The structural threshold at redshift $z$ is defined by $\mathrm{threshold}(z) := \varphi^{-44}\cdot z$. The named master-plan redshift $z = 1$ is the constant $1$. The linear placeholder $w_{\mathrm{RS}}(z) := -1 + \varphi^{-44}\cdot z$ then exceeds ΛCDM by exactly this threshold at every $z$. Full FPT cosmic Z-aging $z$-dependence remains future work; the linear form is a non-vacuous witness for the inequality.

One-line algebraic identity. Unfold the definitions $\mathrm{threshold}(z) = \varphi^{-44}\cdot z$ and $z_{1} = 1$, then apply ring to obtain $\varphi^{-44}\cdot 1 = \varphi^{-44}$. No external lemmas are required beyond the local defs.

Feeds the named-redshift falsifier bands theorem, which packages the $z = 1/2$ and $z = 1$ thresholds together with the corresponding $w_{\mathrm{RS}}$ values as Track 4.C's two master-plan bands. Also appears in the Track 4.C one-statement bundle (RS $w(z)$ suppressed by $\varphi^{-44}$, matching ΛCDM at $z = 0$ and strictly exceeding $-1$ at positive $z$) and in the gravity master-theorem handoff endpoint track4_dark_energy_falsifier_endpoint_holds.

Within the Recognition framework this pins the observational scale of the dark-energy discriminator to the same $\varphi$-ladder rung that forces baryon asymmetry. The specific dynamical $z$-shape from FPT cosmic Z-aging is still open; only the structural linear witness and its threshold identity are closed here.