omega_lambda_canonical_form
plain-language theorem explainer
The dark-energy density parameter equals the closed form 11/16 minus the CODATA fine-structure constant over π. Cosmologists and RS auditors cite it as the canonical expression for Ω_Λ with one measured input and purely combinatorial remainder. The proof rewrites via the one-measured-input decomposition, unfolds the mode counts 11 and 16, and finishes by arithmetic.
Claim. The RS dark-energy fraction equals $\Omega_\Lambda = \frac{11}{16} - \frac{\alpha_{\mathrm{CODATA}}}{\pi}$, where $\alpha_{\mathrm{CODATA}}$ is the CODATA 2022 fine-structure constant.
background
This module derives the cosmological constant fraction from phase saturation on the eight-tick ledger. The raw saturated fraction is the ratio of Q₃-saturated modes to the 8-tick addressing budget: 11 modes (from the [4,2,2] Gray-code plus gauge structure) over $2^4 = 16$ addressing bits, giving $11/16$. An electromagnetic one-loop correction then subtracts $\alpha/\pi$, the fraction of modes that are EM-active.
The local definition of $\Omega_\Lambda$ is raw fraction minus that EM correction. The upstream lemma omega_lambda_one_measured_input already packages the claim that this equals the integer ratio of saturated modes to tick addressing, minus the external CODATA anchor $\alpha$ over $\pi$. Early-universe and verification modules use the same closed form (sometimes with an RS-native $\alpha_{\mathrm{lock}}$), so the present statement pins the measured-input version used by the cosmology certificate stack.
Framework context: the eight-tick octave (forcing chain T7) supplies the $2^3$ cycle whose 4-bit addressing yields the denominator 16; the numerator 11 is the structural Q₃-mode count, not a fit parameter.
proof idea
One short tactic proof. Rewrite with the upstream equality that already decomposes $\Omega_\Lambda$ as saturated-mode count over tick-addressing bits, minus CODATA $\alpha/\pi$. Unfold the two natural-number definitions (saturated modes $= 11$, tick addressing $= 16$). Close by norm_num, which reduces $11/16$ to the rational literal in the goal.
why it matters
This is the citation form of the RS $\Omega_\Lambda$ prediction: integer combinatorics plus one external anchor. It feeds the module certificate omegaLambdaCert (raw fraction, correction bounds, Planck-consistent interval) and the vacuum-fluctuation structural track. Downstream, omega_lambda_independent_of_QFT_cutoff is literally exact this theorem for every hypothetical QFT UV cutoff, and vacuum_fluctuation_one_statement conjoins the canonical form, cutoff independence, and the numerical band $(0.683, 0.686)$ with Planck consistency. The structural certificate records it as the canonical field.
Relative to the primer, the $11/16$ piece is eight-tick (T7) addressing combinatorics; the $\alpha/\pi$ piece is the sole measured input after the module reverted an earlier zero-parameter claim that used a constructed $\alpha$ seed incompatible with data. The result therefore anchors Track 4.B: RS dark energy is not a QFT zero-point integral and carries no cutoff parameter in its signature.
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