= Solution
<Big Bang nucleosynthesis> is a kinetic process in an expanding universe. A common particle temperature does not imply chemical equilibrium for every nuclear reaction: reaction rates must also exceed the expansion rate and connect the required species efficiently. Around $10^9\,\mathrm K$, nuclear abundances retain the history of earlier freeze-out and cannot be inferred from equilibrium Boltzmann factors alone.
In particular, weak reactions cease to maintain <neutron-proton chemical equilibrium>. Subsequent <free-neutron decay after freeze-out> changes the surviving neutron inventory. The large photon-to-baryon ratio delays deuterium survival through photodissociation; once the <deuterium bottleneck> opens, reactions rapidly bind many surviving neutrons into helium-4. Coulomb barriers, decreasing density and further freeze-out prevent unrestricted equilibration of all nuclei. The final helium abundance therefore requires a reaction network and expansion history, not just the temperature and nuclear binding energies.
For illustration, if essentially all available neutrons end in helium-4 and the <neutron-to-proton ratio> at that stage is $r$, simple particle counting gives $Y_{\rm He}\simeq2r/(1+r)$. The crucial input $r$ is itself set by out-of-equilibrium history. Kinetic thermalization of the plasma can remain effective while these composition-changing processes are out of equilibrium.
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