Nucleosynthesis in the Fractal-Spectral Framework: Primordial Abundances, Stellar Processes, and the Lithium Problem

Big Bang nucleosynthesis (BBN) is one of the most precisely confirmed predictions in cosmology — any new framework must preserve its successes. This paper demonstrates that the fractal-spectral framework does so, while offering a candidate mechanism for the one persistent tension: the cosmological lithium problem. The fractal texture tower introduces two types of corrections to nucleosynthesis. First, nuclear reaction cross-sections acquire log-periodic resonance structures at energies Eₙ = E₀ × (√2) ⁿ, modifying the astrophysical S-factor by terms suppressed as (√2) ^−n. Second, the early universe temperature-time relation receives small oscillatory corrections constrained by CMB data to Σ|Aₙ|² < 10⁻⁴. For the three well-measured primordial species (⁴He, deuterium, ³He), the fractal corrections are bounded to ≲ a few percent — well within current observational uncertainties. Standard BBN's success is preserved, not spoiled. The interesting case is lithium. Standard BBN predicts ⁷Li/H ≈ 5 × 10⁻¹⁰, while observations of metal-poor halo stars give ≈ 1. 6 × 10⁻¹⁰ — a persistent factor-of-3 discrepancy. The paper identifies a candidate resolution: temporal decoherence of the ⁷Be electron-capture channel. The vibrational frequencies of ⁷Be and ⁷Li differ by ~2. 2 × 10²⁰ Hz, and in the fractal framework, nuclear reactions are suppressed when vibrational frequencies are "detuned. " However, the naive exponential suppression gives too much reduction — the quantitative mechanism requires detailed modeling of the competition between standard weak-interaction rates and fractal decoherence, stated explicitly as an open problem. For stellar nucleosynthesis, the framework predicts log-periodic modulations in isotopic abundance patterns near nuclear magic numbers (N or Z = 2, 8, 20, 28, 50, 82, 126) with period ln√2 in ln A space, and √2-spaced sub-peaks in r-process abundance distributions — testable with high-resolution spectroscopy of r-process-enhanced stars and kilonova observations. The most direct experimental test: searching for √2-spaced resonances in nuclear cross-sections at underground accelerators (LUNA, CASPAR) and radioactive beam facilities (FRIB). Falsification criteria are explicit: if key BBN cross-sections show no √2-periodic structure at <1% precision, the fractal correction is negligible; if the lithium problem is resolved by astrophysical depletion, the decoherence mechanism is unnecessary.