24 Dimensional Leech Lattice Kissing Number Projection Set and Additive Mirror Symmetry Network

Abstract

This work documents several number‑theoretic projection and additive mirror‑symmetry‑related observations for a finite integer set. The integer set K={12,23,34,39,141,171,182,268,273,329,376,403,453,487,697} is produced by means of a parameter‑free, pre‑specified sampling procedure, yielding a deterministic output set. Starting from this 15‑element set, three candidate vacant nodes {205,390,468} are selected according to pre‑defined projection constraints and interval‑based criteria to form an augmented 18‑element set. Numerical examinations suggest that this 18‑element set exhibits certain gcd(k,N)‑pro‑jection‑type relations with the kissing number of the 24‑dimensional Leech lattice, together with an internal additive mirror‑symmetry network. These reproducible numerical observations are presented for community inspection, independent verification, or potential falsification.