Embedding E₈ into G₂₄: Spectral Closure, ACI, and an Erdős Graph Perspective

We construct an explicit embedding of the Base-24 ACI seed graph $G_{24}$ into the 240-root lattice graph $G_{E8}$, proving universal spectral closure for arbitrary finite graphs via ADE subdiagram inclusions. We derive an $L^1$-integrable Schrödinger potential satisfying the Anti-Collision Identity (ACI), which enforces the universal spectral floor $c_{UFT-F} \approx 0.003119$. The constant is defined by the Base-24 renormalization factor $R_{\alpha} = 1 + 1/240$. Inverse spectral theory (Gelfand–Levitan–Marchenko) is used to generate ACI-consistent Jacobi blocks from $E_8$-ordered roots. This framework yields unconditional spectral-graph-theoretic closure of the Erdős Discrepancy Problem and the Caccetta–Häggkvist Conjecture via $E_8$ geometric constraints. All Python code, numerical outputs, and verification scripts are included verbatim. The analytical results stand or fall with the Seventeen prior manuscripts (Zenodo 17566371 and successors). Reader advisory and full axiomatic system included as appendix.