Review: "From Discrete Null-Lattice Growth to so(8): Concrete Realization and Exact Lie Closure

We ask whether a discrete quadratic growth law on ℕ (motivated by null-shell counting on a discrete light-cone) can be chained through a divergent curvature channel and a normalized phase readout to an explicit exceptional Lie-algebra closure in eight dimensions. In the concrete Fano-basis octonion matrix realization, adjoining the antisymmetric phase-lift generator Δ (supported on the distinguished plane span{e₁, e₇}) to the 14-dimensional derivation algebra 𝔤₂ of the octonions generates — via iterated Lie brackets — the full 28-dimensional algebra 𝔰𝔬(8). The result is certified by:an exact symbolic proof object over ℚ (`artifacts/so8_symbolic_certificate.json` with rational structure constants),a compact pedagogical toy model so(3) + Δ₄ → so(4) with its own rational certificate,and full Lean 4 verification (HQIVPaperClaims lightweight target + HQIVSO8Closure heavyweight matrix closure). The construction is realization-specific to the octonionic carrier chosen to be compatible with triality and 3+1 null-lattice combinatorics. All reproducibility artifacts ( generator scripts, exact JSON certificates, Lean sources, low-memory build instructions, and the paper-reference bundle ) are included in the companion-code.zip archive. See the companion appendix (`so8_closure_full_appendix.pdf`) for the complete symbolic pipeline and generator listings.