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 spane₁, 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/so8ₛymboliccertificate. 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 (`so8closurefullₐppendix. pdf`) for the complete symbolic pipeline and generator listings. Keywords: so (8), Lie algebra closure, octonions, G₂, discrete null-lattice, phase-lift generator, symbolic certificate, Lean formal verification, Fano basis, triality.