Lambda_one_measured_input
plain-language theorem explainer
The RS dark-energy fraction equals exactly 11/16 minus α/π by definition, so the only external datum is the measured fine-structure constant. Cosmologists citing C-010.8 use this to separate structural content (mode count and correction shape) from the single boundary input α. The proof is pure reflexivity: the equality is definitional.
Claim. The Recognition Science prediction for the dark-energy density parameter satisfies $\Omega_\Lambda^{\mathrm{RS}} = \frac{11}{16} - \frac{\alpha}{\pi}$, where $\alpha$ is the measured fine-structure constant (the sole external input) and $\pi$ is the circle constant.
background
Module C-010 addresses the cosmological constant problem: QFT vacuum energy overshoots observation by ~10^120, while data give $\Omega_\Lambda \approx 0.7$. Recognition Science replaces that fine-tuning with a structural formula $\Omega_\Lambda = 11/16 - \alpha/\pi \approx 0.68$.
The geometric seed $11/16 = 0.6875$ comes from the D=3 ledger (eight-tick octave forced at T8, gap-45 synchronization, LCM structure). The correction $\alpha/\pi$ is an IR electromagnetic shift. In this module, $\alpha$ is pinned to the CODATA external anchor; it is the only measured input.
Omega_Lambda_RS is defined exactly as that difference. Calibration axioms elsewhere normalize the J-cost curvature so the cost functional is unique; here they only supply ambient context that vacuum energy is ledger J-cost of the empty configuration.
proof idea
One-line term proof by rfl. The left-hand side is the definition Omega_Lambda_RS := 11/16 - (alpha / Real.pi), so the stated equality is definitional and needs no lemmas, rewrites, or arithmetic.
why it matters
C-010.8 records the no-fine-tuning claim for the cosmological constant: the shape $11/16 - \alpha/\pi$ is structural; only $\alpha$ is a boundary datum. That separates RS from QFT vacuum counting, where both magnitude and shape are free.
Framework landmarks: T8 forces D=3 and the eight-tick octave that seed the $11/16$ mode fraction; $\alpha$ enters as the unique measured EM constant (with RS targeting $\alpha^{-1}$ near 137). Downstream narrative in the same file (C-010.9) ties a fixed $\Omega_\Lambda$ to $H_0$ via Friedmann equations and the Hubble tension. No used_by edges yet; the theorem is a citation anchor for the structural reading of the formula rather than a computational stepping stone.
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