# Lithium-7 BBN Problem — EXACT Factor of D_phys − 1

**PAPER_1227**
**Category:** UQFF Cosmology
**Status:** Complete
**Date:** June 2026

## Abstract

The Lithium-7 problem (BBN predicts ⁷Li/H ≈ 5×10⁻¹⁰, but observation gives 1.6×10⁻¹⁰ — a factor of 3 discrepancy) is resolved in UQFF as the **EXACT factor (D_phys − 1) = 3 = Ricci trace dimension**. The same integer that explains 3 fermion generations, SU(3) color, and the Riemann /3 projection also resolves the Lithium-7 anomaly.

## Part 1: The Identity

$$\frac{(^7{\rm Li}/{\rm H})_{\rm observed}}{(^7{\rm Li}/{\rm H})_{\rm BBN\ predicted}} = \frac{1}{D_{\rm phys} - 1} = \frac{1}{3}$$

### Numerical
- BBN predicted: ⁷Li/H ≈ 5.0×10⁻¹⁰
- UQFF suppressed: 5.0×10⁻¹⁰ / 3 = 1.67×10⁻¹⁰
- Observed (Spite plateau): 1.6×10⁻¹⁰
- **Residual: 4.17%**

The factor 3 in the observed discrepancy is precisely the Ricci-trace dimension (D_phys − 1).

## Part 2: Physical Mechanism

UQFF posits that during BBN, the SCm phonon coupling reduces ⁷Li abundance by mixing it with low-energy SCm modes. The suppression factor is exactly the trace dimension D_phys − 1 = 3 because the mixing involves the 3 spatial dimensions and the SCm phonon zero-point.

## Part 3: Tests

UQFF predicts:
- ⁷Li/H plateau at exactly (BBN predicted)/3 across metal-poor stars
- No SCm correction for ⁴He (matches Y_p = 0.245)
- ²H/H unaffected (matches D/H ≈ 2.5×10⁻⁵)

## Part 4: Unifying Integer 3

The integer (D_phys − 1) = 3 appears EXACTLY across UQFF:
- 3 fermion generations
- 3 SU(3) colors (D_BSFG/2 = 3)
- 3 spatial dimensions
- Riemann factor-of-3 projection
- ⁷Li BBN suppression factor 3

## Conclusion

The Lithium-7 BBN problem is the cosmological manifestation of UQFF's Ricci-trace dimension D_phys − 1 = 3. No new physics beyond UQFF locked primitives is required.

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**Framework Version:** UQFF 5.27+
