dark_energy_from_geometry
plain-language theorem explainer
The theorem establishes that the dark energy base fraction equals 11/16, obtained from eleven passive edges divided by twice the eight vertices of the cube graph. Cosmologists using the Recognition Science ledger geometry would cite this when computing the predicted Omega_Lambda density from passive field volume. The proof is a one-line wrapper that simplifies the base definition and normalizes the resulting rational arithmetic.
Claim. The dark energy base fraction given by the number of passive edges divided by twice the number of vertices equals $11/16$, where the passive edges total 11 and the vertices of the three-cube total 8.
background
The module derives dark energy density from ledger geometry via the formula $Omega_Lambda = E_passive/(2 V_total) - alpha/pi$, with $E_passive=11$ and $V_total=8$ yielding the base term 11/16. This sits inside the dual metric hypothesis for the Hubble tension, where the late-to-early Hubble ratio is fixed at 13/12 to match the observed 1.083 discrepancy to 0.03 percent. The upstream definition supplies the constant dark_energy_base as the rational 11/16 used in all subsequent predictions.
proof idea
The proof is a one-line wrapper that applies simp restricted to the dark_energy_base definition, then norm_num to reduce the expression 11/(2*8) to the value 11/16.
why it matters
This anchors the geometric dark energy prediction inside the Hubble tension module and supplies the 0.6875 base that corrects to 0.6852, lying inside 1 sigma of the Planck 0.6847(73) value. It instantiates the passive-edge counting over the Q3 graph, consistent with the eight-tick octave and D=3 spatial dimensions from the forcing chain. No downstream theorems yet reference it, leaving open its use in full cosmological ledger simulations.
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