HQIV is an axiom-free, knob-free theory with one meaningful combinatorial postulate: transverseDim = 3 and discrete null-shell growth. The HQIV Spine forces (α, γ) = (3/5, 2/5), the orientation carrier 2³ = 8, seven imaginary directions and Fano incidence, then the octonions and g2∪Δ⇒so (8) as gauge completion. Every downstream result (including this chemistry stack) is derived from this spine with no tunable constants beyond a single proton-scale witness. This Tier-2 working paper presents HQIV light-cone chemistry as a discrete electronic-structure substrate: machine-checked Lean 4 lemmas plus downstream Python witnesses for spectroscopy, packing, bands, SCF/Fock/KS, AO integrals, and core XPS. It follows the Tier-0/1 light-cone, closure, lattice-growth, octonionic-action, Kirchhoff, and thermodynamic-arrow records and the published Tier-2 nucleon-binding/BBN layers. The finite quantum bookkeeping and sparse-update interpretation of the octonionic carrier are developed in the companion light-cone/OSH-oracle record; this manuscript uses that substrate. From the discrete light cone the chemistry stack proves electron counting, octet capacity, VSEPR contact geometry, dipole cancellation, bond-order bookkeeping, hydrogenic line spectra, stoichiometry and Hess-law thermochemistry, finite-site energy traces, phase-geometry density, molecular concentration, discrete Fick diffusion, Nernst–Einstein-style carrier slots, and transported reaction-gate rates. The binding layer adds an algebraic second-order architecture: preferred-axis spectral gap, continuous selection weights, an n-body envelope, a five-channel outside-contact Geff ledger, and a six-route voltage-generation ledger. Each recovering the proved base readout when unstressed. Condensed packing splits Lindemann lattice density from optical number density; steric, pack-open, ionic-character, period-channel, and Madelung d-shell dresses follow from the log-linear constraint system on quarantined observables. On the fourteen-species condensed panel the mean density comparison error is ≈0. 37% (data/hqivₗabwitnesses. json). On the same Morse spine the discrete electronic stack now includes activation/KIE, two-band and multi-orbital bands, SCF, Fock, local-XC Kohn–Sham, EH AO integrals, and core XPS — a first-principles discrete alternative to fitted XC for closed-shell solids and molecular ices, with continuum GTO/STO libraries kept as optional comparison layers. All load-bearing claims are carried by Lean theorems with zero sorry and no bespoke mathematical axioms beyond the standard logical core. The bundled reproducibility scripts (scripts. zip) generate every quoted numerical readout directly from the proved slots; comparison data (NIST/CRC, GMTKN, W4, etc. ) remain quarantined outside the derivation path. Residual-correlation audits identify formal targets for future second-order terms (coupled relaxation, concentration flow, curvature propagation) without introducing fitted coefficients. This work supplies a practical, auditable discrete electronic-structure workflow that a chemist can run today from the public HQIV Lean repository without trusting an unproved chemistry oracle or choosing an XC functional.
Steven Jr Ettinger (Fri,) studied this question.