We derive the explicit Hamiltonian for the Fano 7-QD network introduced in Paper CXCVII, in which the 7 nodes of the Fano plane are physical orbital quan- tum dot modes of the Transdimensional Anomalous Hall Effect (TDAHE) ground state in rhombohedral graphene. The Hamiltonian has three terms: onsite energies set by the Klein ladder eigenvalues (εi = λkJ), antisymmetric pairwise hopping re- stricted to Fano lines (tij = tφijk, where t/J = fbulk = 3.6917%), and a three-body non-associative interaction (K/J = n · fbulk = 1.255%, n = 0.34 from G2 non- associativity). The three-body term H3body = K P lines φijk(ni −1 2)(nj −1 2)(nk −1 2) is the Hamiltonian realisation of non-associativity: it energetically selects Fano-line correlated states as the ground state, providing the physical explanation for why the Fano-Toffoli gate satisfies FT = 0 if and only if the input lies on a Fano line (proved in Paper CXCVII). The single-particle spectrum is computed exactly; the sump gap is ∆sump ≈0.967J, giving ∼9.7 meV at the graphene DM coupling scale J ∼10 meV — well above the kBT ∼1.7 µeV thermal energy at T = 20 mK. The realisation in ABC-stacked rhombohedral graphene is the Dzyaloshinskii-Moriya Hamiltonian HDM = P Dij · (Si × Sj) with Dij = Jφijkˆek — structure constants exact, zero free parameters beyond J. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
Bharathi Jagadeesan (Tue,) studied this question.