abundanceVsEta
plain-language theorem explainer
The definition enumerates how primordial light-element ratios vary with baryon-to-photon ratio η under Recognition Science constraints on BBN. A cosmologist fitting RS-derived η ≈ 6×10^{-10} to observed yields would cite these monotonicity relations when checking consistency with deuterium, helium, and lithium data. The body is a direct list of four trends taken from standard BBN calculations once RS fixes the reaction-rate parameters via the phi ladder.
Claim. The dependence of light-element abundances on baryon-to-photon ratio $η$ is: D/H decreases with $η$, $^4$He mass fraction slightly increases with $η$, $^3$He/H decreases with $η$, and $^7$Li/H is non-monotonic.
background
The module derives BBN yields from Recognition Science by fixing η near 10^{-10} via the self-similar fixed point phi and imposing eight-tick nuclear magic numbers on reaction rates. The shifted cost H(x) = J(x) + 1 converts the Recognition Composition Law into the d'Alembert equation H(xy) + H(x/y) = 2 H(x) H(y), which governs the underlying cost algebra. Nuclear densities sit on discrete phi-tiers, ρ_nuc ~ phi^{n_nuclear} × ρ_Planck, so abundances inherit the same discrete structure.
proof idea
The definition is a direct list literal that records the four monotonicity statements; no lemmas are applied beyond the upstream cost-algebra and phi-forcing structures already used to constrain η and the reaction rates.
why it matters
The list supplies the observational anchor for the RS derivation of η and flags the lithium discrepancy (predicted 5×10^{-10} versus observed 1.6×10^{-10}) that remains unresolved. It therefore sits downstream of the phi-forcing chain (T5–T8) and the eight-tick octave that sets nuclear reaction thresholds, while feeding the open question of whether stellar depletion or new physics closes the factor-of-three gap.
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