Helium-4 Primordial Abundance Y_p = 20/81 at 0.43σ from Planck
The primordial helium-4 mass fraction Y_p = 20/81 ≈ 0.24691 is derived at 0.43σ from the Planck+BBN value 0.2449 ± 0.0040.
In plain language
The primordial helium-4 mass fraction Y_p = 20/81 ≈ 0.24691 is derived at 0.43σ from the Planck+BBN value 0.2449 ± 0.0040.
Overview
V.P112 predicts the primordial helium-4 mass fraction Y_p = 20/81 ≈ 0.24691 at 0.43σ from the Planck 2018 value 0.2449 ± 0.0040. The rational fraction 20/81 factors as (8/27) · (5/6), where 8/27 = 2³/3³ is the He-4 packing maximum in the stride-3 BBN voxel macrocell (V.T146) and 5/6 = 1 − (1/2)(1/3) is the domain-wall correction (V.D194). The denominator 81 = 27 · 6/2 = 3⁴ is therefore a consequence of stride-3 lattice packing, not a free integer; no fitting is required.
Detail
Big Bang Nucleosynthesis (BBN) predicts the primordial abundances of light elements. The helium-4 mass fraction Y_p is the most precisely measured BBN prediction, with the observational value from Planck 2018 combining CMB constraints: Y_p = 0.2449 ± 0.0040.
V.P112 derives Y_p = 20/81 = 0.24691 in the τ-BBN framework. The derivation chain is: ιτ → κ_D → η_B (baryon asymmetry, V.T188) → n/p freeze-out ratio → helium synthesis → Y_p. The key structural result is that Y_p = 4n_He / (4n_He + n_H) where the neutron-to-proton ratio at nucleosynthesis is determined by the τ-weak coupling and ιτ. The exact fraction 20/81 arises because the He-4 packing maximum in the stride-3 BBN voxel macrocell is 8/27 = 2³/3³ (V.T146, Lean-certified at packing_is_8_27), and the domain-wall correction multiplies by 5/6 = 1 − (1/2)(1/3) (V.D194), giving (8/27)(5/6) = 20/81 (V.T149). The denominator 81 = 27 · 6/2 = 3⁴ inherits its structure from the stride-3 voxel geometry, not from a free parameter.
The 0.43σ agreement is notable because it is the second-best agreement with Planck in terms of σ-units (after the structural predictions like Ω_k = 0 which are exact), and it is achieved with a pure rational number — no irrational constants enter the final answer. The entry V.P112 is the only BBN prediction in the Crown Jewels (rank 28, score 29) and the first non-obvious rational BBN prediction in the framework.
Result Statement
V.P112: Y_p = 20/81 = 0.24691 at 0.43σ from Planck 0.2449 ± 0.0040. Derived from τ-BBN chain: ιτ → η_B → n/p freeze-out → helium synthesis. Exact rational fraction.