Primordial Helium-4 Mass Fraction Y_p

τ-Formula

Y_p = (8/27) × (5/6) = 20/81 = 0.2469

Derivation

The rational fraction $20/81$ factors as $(8/27) · (5/6)$ where $8/27 = 2^3/3^3$ is the He-4 packing maximum (a $2^3$ tetrahedron of nucleons inside the stride-3 macrocell $3^3$ of the BBN voxel lattice, V.T146), and $5/6 = 1 - (1/2)(1/3)$ is the domain-wall correction (V.D194). So $27 = 3^3 = (stride)^3$ and $81 = 27 · 6/2 = 3^4$ are both traceable to the stride-3 lattice (no free integers).

The fiber suppression is selective: it affects only $A ≥ 7$ nuclei (those requiring EM radiative capture across the full $τ^3$ geometry). Light nuclei with $A ≤ 4$ fit the stride-3 macrocell and are unaffected:

• $Y_p$ ($^4He$): unchanged (voxel packing geometry, independent of $^7Be$ production).
• $D/H$: unchanged (set by deuterium bottleneck, not by $^7Be$ channel).
• $^3He/H$: unchanged ($A = (τ^3) = 3$, fits macrocell).

No BBN products have $5 ≤ A ≤ 6$ (the mass gaps at $A = 5$ and $A = 8$ in nuclear physics prevent their formation). The $τ$ framework therefore resolves the lithium problem selectively—without disturbing the other successful BBN predictions. (Registry: V.T245, V.T246, Wave 25.)

Source

This prediction is derived in the Numerical Physics Ledger (Chapter 62 — inflation-cmb-bbn), Books IV–V of Panta Rhei.