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Geometric Resolution of the 7Li Cosmological Problem: A 3.998D Fractional Manifold Perspective

Submitted:

13 June 2026

Posted:

15 June 2026

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Abstract
We present a novel geometric resolution to the Lithium-7 (7Li) cosmological mass problem using a discrete 4-simplex lattice with a spectral dimension of 3.998. The framework relies exclusively on a rigid set of boundary conditions intrinsic to the model, including a combinatorial invariants of the 4-simplex primitive unit cell, four open degrees of freedom per simplex, a base vacuum anchor equal to the electron rest mass energy MeV, and hyperspherical normalisation, with no free thermodynamic parameters, baryonic density term nor references to fluid-dynamical nucleosynthesis. The local field saturation is governed by a master action density derived from the lattice geometry. The production efficiency of stable 7Li topological nodes and its structural abundance ratio are obtained from topological entropy, volumetric projection, and lattice friction. The predicted lithium-to-hydrogen ratio is determined to be ~1.3671715 x 10-10 , in excellent agreement with observations. An accompanying polytopic-tiling analysis demonstrates that the full light-element hierarchy (Protium, Deuterium, Helium-3, and Helium-4) can emerge as a geometric inevitability of exposed-surface ratios and topological stability. Helium-4 appears as the lowest-friction closed tetrahedral configuration, naturally accounting for its ~25% mass fraction without acoustic tuning. We argue that the apparent Lithium Problem may be a mathematical artefact of imposing a continuous fluid approximation on a space that is structurally saturated by discrete 4-simplex spatial geometry. This work offers a radically more efficient description of nucleosynthesis, free from ΛCDM baggage.
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