w_LCDM_value
plain-language theorem explainer
Defines the ΛCDM dark-energy equation of state as the constant real value −1, independent of redshift. Cosmologists and anyone comparing RS Track 4.C predictions to standard cosmology cite it as the baseline. The body is a one-line constant definition.
Claim. The ΛCDM dark-energy equation-of-state parameter is the constant $w_{\Lambda\mathrm{CDM}} = -1$, with no redshift dependence.
background
Track 4.C of the quantum-gravity master plan asks for a falsifiable RS equation of state $w(z)$ that differs at sub-leading order from ΛCDM's strict $w = -1$. This module supplies the algebraic discriminator: an RS structural placeholder suppressed by the rung-44 scale $\varphi^{-44}$ (the same scale that appears in baryogenesis $\eta_B = \varphi^{-44}$).
ΛCDM treats dark energy as a cosmological constant, so its equation-of-state parameter is fixed at $-1$ for all $z$. The RS side uses a linear-in-$z$ witness $w_{\mathrm{RS}}(z) = -1 + \varphi^{-44}, z$ that matches ΛCDM at $z = 0$ and strictly exceeds $-1$ for $z > 0$. The constant defined here is the ΛCDM anchor against which that separation is measured.
proof idea
One-line definition: the real constant is set equal to $-1$. No lemmas or tactics are involved.
why it matters
This constant is the ΛCDM baseline threaded through the whole Track 4.C structural package. The master certificate DarkEnergyWofZStructuralCert records $w_{\mathrm{LCDM}} = -1$ as its first field. The one-statement theorem bundles that equality with positivity of $\varphi^{-44}$, matching at $z = 0$, and strict separation at positive redshift.
Downstream discriminators and falsifiers all measure distance from this value: absolute deviation equals the falsifier threshold $\varphi^{-44}, z$; a measurement closer to $-1$ than that threshold cannot equal the RS linear prediction; an exact ΛCDM reading at $z > 0$ is not the RS structural value. The specific FPT cosmic Z-aging $z$-dependence remains future work; this definition only fixes the ΛCDM side of the comparison.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.