Anti-Derivative Reparameterization and Phenomenological Calibration of a Reduced Beryllium-7–Lithium-7 Network

The cosmological lithium problem is the disagreement between the standard big-bang nucleosynthesis (BBN) prediction for mass-seven and lithium abundances inferred from metal-poor stellar spectroscopy. Taking the 2026 Particle Data Group (PDG) review as benchmark, the predicted ⁷Li/H = (4.72 ± 0.70) × 10⁻¹⁰ exceeds the stellar-inferred (1.45 ± 0.25) × 10⁻¹⁰ by a factor of 3.255, corresponding to a required 69.28% reduction of the nominal terminal mass-seven abundance. We investigate whether an anti-derivative operator previously formulated by the author, A[f](u) = −∫ f′(u) du = C − f(u), can be consistently incorporated into a coupled two-species ⁷Be–⁷Li model and how phenomenological rate variations can reproduce the observational benchmark. The numerical system uses a normalized artificial production profile and dimensionless Gaussian transfer and destruction rates. The anti-derivative transformation is exactly invertible; numerical reconstruction agrees with the original trajectory at the level of 6.15 × 10⁻⁹ in units of 10⁻¹⁰ abundance, with the difference dependent on integration tolerance. A fit of the conversion-rate multiplier in the presence of lithium destruction gives 8.9955 and reproduces the central stellar-inferred lithium abundance. A distinct fitted beryllium-loss coefficient also matches the same target. This work thus demonstrates mathematical compatibility of the anti-derivative representation, transparent parameter calibration, a conservation-law diagnostic, and explicit numerical reproducibility. The artificial reaction network is not a thermally calibrated BBN calculation; no laboratory cross sections, full BBN evolution, or joint deuterium/helium fit were performed. The scope and reproducible boundaries of the phenomenological result are stated precisely.