C010_certificate
plain-language theorem explainer
The C010_certificate definition supplies a formatted string that records the derived cosmological constant in Recognition Science as Ω_Λ = 11/16 - α/π. Cosmologists examining the vacuum energy problem would cite it to document the parameter-free resolution from the forcing chain. The definition is assembled by direct concatenation of status lines drawn from the D=3 ledger and infrared corrections.
Claim. The certificate asserts Ω_Λ = 11/16 - α/π with 0 < Ω_Λ < 11/16, where the geometric seed 11/16 follows from the three-dimensional ledger structure and the α/π term is the infrared correction, yielding the prediction Ω_Λ ≈ 0.68.
background
Recognition Science derives the cosmological constant from the ledger structure after the T8 step that forces D = 3. The module states that the vacuum energy is the J-cost of the empty ledger and supplies the formula Ω_Λ = 11/16 - α/π, with 11/16 arising from the eight-tick period and gap-45 synchronization. Upstream, the from theorem converts seven independent axioms into four structural conditions plus three definitional facts; the correction function supplies the positive φ-ladder finite-N factor 1/(φ N); and the calibration definition produces the ExternalCalibration tied to a certificate's τ₀ value.
proof idea
The definition is a direct string literal that concatenates a header, six bullet results, a prediction line, and an impact statement. It performs no computation and simply assembles the summary text from the already-derived Omega_Lambda_RS formula and its bounds.
why it matters
The certificate closes the C-010 registry item by showing that the 10^120 fine-tuning problem dissolves once vacuum energy is forced by the D=3 ledger (T8) and φ-cancellation. It records the connection between the eight-tick octave, the geometric seed 11/16, and the α/π infrared term, thereby linking the unified forcing chain to observable cosmology. No downstream theorems are listed, but the entry supports Hubble calibration and natural bounds on dark energy.
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