Omega_Lambda_lt_069

This module identifies the cosmological dark-energy fraction with the equilibrium vacuum share of a discrete ledger under phase saturation. The explicit RS formula is $\Omega_\Lambda = 11/16 - \alpha/\pi$: the combinatorial seed $11/16$ comes from passive-mode counting on the $Q_3$ cube geometry, and $\alpha/\pi$ is the electromagnetic correction using the measured CODATA fine-structure constant as the sole external input.

The sibling theorem Omega_Lambda_lt_seed already shows $\Omega_\Lambda < 11/16$ by unfolding the definition and using positivity of $\alpha/\pi$. The present result only tightens that rational upper bound to the decimal threshold $0.69$ used in the module's unconditional precision band. Module status marks the formula and basic bounds as proved; the bridge from ledger saturation to cosmology remains a named hypothesis elsewhere in the file.

Two-step calc chain. First apply Omega_Lambda_lt_seed, which gives $\Omega_\Lambda < 11/16$. Then close $11/16 < 0.69$ by norm_num. No unfolding of $\alpha$ or $\pi$ is needed at this step; the seed inequality already absorbs the positive correction term.

Feeds directly into Omega_Lambda_band_unconditional, which packages $\Omega_\Lambda \in (0.5, 0.69)$ as the unconditional precision band for the phase-saturation prediction. That band is the numeric face of the module claim $\Omega_\Lambda \approx 0.6852$ against observational dark-energy fractions near $0.69$.

In the broader RS chain the seed $11/16$ is geometric (mode counting on the cube, tied to the $D=3$ forcing landmark), while $\alpha$ is the measured EM input. This upper bound is therefore pure arithmetic once the formula and $\alpha/\pi > 0$ are in hand; it does not touch the still-open CosmicPhaseEquilibrium or vacuum_fraction_bridge hypotheses that would identify the ledger vacuum share with cosmological $\Omega_\Lambda$.