lithium_predicted
The declaration assigns the Big Bang Nucleosynthesis prediction for the primordial lithium-7 to hydrogen ratio the numerical value 5.0 × 10^{-10}. Cosmologists examining light-element yields within the Recognition Science framework cite this constant when quantifying the lithium problem. The definition consists of a direct numerical assignment with no further reduction or lemma application.
claimThe predicted primordial abundance ratio satisfies $^7$Li/H = $5.0 × 10^{-10}$.
background
The Cosmology.Nucleosynthesis module derives light-element abundances from Recognition Science principles. BBN occurs in the first minutes after the Big Bang; yields of deuterium, helium-3, helium-4 and lithium-7 depend on the baryon-to-photon ratio η (itself obtained from φ) and on nuclear rates constrained by the eight-tick octave. The module records that η ~ 10^{-10} follows from prior φ-forcing results and that most predicted abundances match observations except for lithium.
proof idea
One-line definition that directly binds the constant 5.0e-10 to the identifier lithium_predicted.
why it matters in Recognition Science
The definition supplies the BBN-predicted lithium abundance used by the sibling lithium_problem declaration. It therefore anchors the open discrepancy (predicted 5 × 10^{-10} versus observed 1.6 × 10^{-10}) inside the Recognition Science treatment of nucleosynthesis, where η is fixed by the phi-ladder and reaction channels follow the eight-tick structure. The lithium problem remains unresolved and is listed among possible signatures of new physics or stellar depletion.
scope and limits
- Does not derive the numerical value from the phi-ladder or forcing chain.
- Does not incorporate explicit nuclear reaction rates or neutrino counts.
- Does not resolve the factor-of-three discrepancy with stellar observations.
- Does not claim agreement between prediction and measurement for lithium.
formal statement (Lean)
144noncomputable def lithium_predicted : ℝ := 5.0e-10