A Geometric Origin of Cosmic Composition: A Recursive Annihilation Model from Weaire–Phelan Foam Topology

The cosmic composition ratios — ordinary matter [Formula: see text], dark matter [Formula: see text] and dark energy [Formula: see text] — are input parameters of the [Formula: see text]CDM model rather than derived outputs. This paper reports a precise geometric mapping: the A15 lattice of the Weaire–Phelan foam, through a set of recursive annihilation rules, produces volume partitions that exactly reproduce these three numbers. The core mechanism is as follows: angular deviations of dodecahedral vertices in the A15 lattice (Type B vertices: [Formula: see text], deficit [Formula: see text]; Type C vertices: [Formula: see text], surplus [Formula: see text]; Type A vertices: minority, surplus [Formula: see text]) — all defined relative to the ideal vertex angle sum mandated by Plateau’s law, [Formula: see text] — generate stress anisotropy. The two elongated hexagonal faces of the tetrakaidecahedron are orthogonally oriented and twisted by [Formula: see text] relative to each other, causing the structure to develop shear stress concentration under compression. The alternating arrangement of Type B and Type C vertices further intensifies shear stress at the equatorial belt, driving tetrakaidecahedron to annihilate in pairs as positive/negative chiral pairs. The cascading annihilation initiates from Type B regions and is suppressed in Type C regions, converging to an [Formula: see text] annihilation rate. In each round, approximately [Formula: see text] of the surviving volume transforms into decahedra (ordinary matter), and the remainder splits in a 1:3 ratio into dodecahedron increments (dark matter) and new tetrakaidecahedron (entering the next round). Dark matter increments are not added until the beginning of the next round. After approximately [Formula: see text] recursive rounds, the composition converges to ordinary matter [Formula: see text], dark matter [Formula: see text] and dark energy [Formula: see text], consistent with Planck 2018 observations to within precision limits. This work is positioned as a geometric mapping rather than a physical theory. The model contains no free parameters — all inputs are derived from CAD measurements of A15 crystallographic coordinates. The physical plausibility of recursive annihilation is supported by a cascade decay analogy. The model provides independently falsifiable quantitative predictions.