Algebraic Universality of the Symbiotic Hamiltonian: A Shared Ising Operator Across Atomic Condensates and a Spaceflight Transcriptomic Module

The Symbiotic Hamiltonian, H = H_local + λ·V_symbiotic, has been applied across heterogeneous domains — combinatorial optimization (QUBO), genomic risk prediction, brain–computer interfaces, colorimetry, financial time series, and spacecraft telemetry. A recurring concern is whether this cross-domain reuse reflects a genuine shared mathematical structure or merely a naming convention. Here we test the strongest version of the universality claim against real data. We show that two physically unrelated systems — an ultracold potassium Bose–Einstein condensate (the quantum-field simulator of Viermann et al., Nature 2022, realizing curved-spacetime dynamics and cosmological particle-pair production) and a 26-gene mitochondrial oxidative-phosphorylation (OXPHOS) co-expression module discovered de novo in mouse-liver spaceflight transcriptome (NASA OSDR OSD-245, N=59) — reduce, under the standard QUBO/Ising mapping, to the identical canonical operator: a z–z Ising coupling with site-local fields. The coupling coefficient is form-invariant under λ in both systems (J_ij = λ/4). Critically, the two interaction graphs are not isomorphic (Laplacian spectral distance 6.92 between backbone-matched topologies), establishing that the universality resides in the operator algebra, not in problem topology. The OXPHOS interaction matrix is reconstructed directly from public NASA data with measured internal coupling 0.984, reproducing the previously validated module exactly. This provides an external, experimentally instantiated physical realization of the formalism and a precise, falsifiable statement of what "universality" means for the Symbiotic Hamiltonian.