Papers · William Alexander Aldred

One Density, Two Tables: The Lithium Defect, Priced as a Closure Defect

by William Alexander Aldred — Independent Researcher

Published October 31, 2026 · Zenodo · 5 pp · DOI: 10.5281/zenodo.23851704

Abstract

Standard big bang nucleosynthesis has one free input, the baryon density. One input has to pay every table. Freeze the density at the cosmic microwave background's own value, ω_b = 0.02237 ± 0.00015 (Planck Collaboration 2020), and spend it, unfitted, on two tables. The deuterium table is paid: predicted D/H = (2.57 ± 0.13) × 10⁻⁵ (Fields, Olive, Yeh & Young 2020) against observed (2.527 ± 0.030) × 10⁻⁵ (Cooke, Pettini & Steidel 2018), a distance of 0.32σ. The lithium table is not paid. The same computation predicts ⁷Li/H = (4.72 ± 0.72) × 10⁻¹⁰; the Spite plateau measures (1.58 ± 0.31) × 10⁻¹⁰ (Sbordone et al. 2010). Stated as a closure defect, the miss is D_Li = _10( pred/ obs) = 0.475 dex, a factor of 2.987, at 4.01σ in linear propagation and 4.40σ in log propagation, with a Monte Carlo median of 0.475 dex and a 68% interval of [0.370, 0.588] dex. On the second named modern computation (Pitrou et al. 2018, PRIMAT) the defect is 0.551 dex: the price moves with the code, by 0.076 dex, and it does not close on either code. Each candidate door is priced at what it would have to deliver to close the defect exactly. Stellar depletion of the plateau must deliver 0.475 dex, a surviving fraction of 0.335; published diffusion models deliver 0.25 to 0.40 dex, which leaves 0.225 to 0.075 dex still owing. A revised ³He(α,γ)⁷Be rate must fall to a factor of 0.316 of its measured value, a cut of 68.4%, which sits 9.23σ from the rate's own published error, and the same rate sets the solar neutrino fluxes that already check it. New physics must destroy 66.5% of the primordial mass-7 yield after nucleosynthesis while moving the paid deuterium prediction by less than its joint 2σ slack of 10.4%. No door is endorsed. The arithmetic is the deliverable.

The result, in plain language

One density, two tables: Planck’s baryon density pays deuterium at 0.32σ and misses lithium by 0.475 dex. The paper prices the miss and bills each door: stellar depletion owes the full 0.475 dex and its models deliver 0.40 at best; the ³He(α,γ)⁷Be rate would have to fall to 0.316 of its measured value, 9.23σ inside its own error bar, with the Sun watching; new physics has to destroy 66.5% of the primordial mass-7 and keep deuterium inside 10.4%.

No door endorsed. The arithmetic is the paper.

Program note

Cube Campaign Batch 1, target C-10 — the BBN closure priced where it fails: lithium. Companion to One Density, Two Tables (the baryon closure, which closes at current precision), this paper takes the same frozen baryon density to the lithium table and prices the defect door by door. Its grades are printed on its face: the pricing is executed in the open — every input search-verified, the registered exclusion rule fired zero times — and discovery is explicitly barred by its registration: it prices the lithium problem as a closure defect and endorses no way out.

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