Saxena et al. (2020) reported that electromagnetic resonance in microtubules exhibits a self-similar “triplet-of-triplet” pattern preserved across tubulin (4 nm), microtubule (25 nm), and neuron (~1 μm) scales—spanning six orders of magnitude in physical size. We show that the exceptional Lie group G₂, acting on a 7-dimensional representation space identified with the daemon architecture of the Perceptual Cognitive Intelligence framework, provides the algebraic constraint required. We construct a concrete Hamiltonian from the 14 generators of G₂, decompose its spectrum under the maximal SU (3) subalgebra, and demonstrate that the resulting spectral family is organized as 1⊕3⊕3̄ with at most two independent Cartan parameters (rank-2 constraint). The six non-singlet modes are interpreted as Goldstone modes of the spontaneous breaking G₂→SU (3), with the singlet identified as the void mode Ωᵥoid. The coherent fraction of any Boltzmann distribution on this Hamiltonian satisfies CF ≤ 6/7 < 1−e⁻², an internal consistency check confirming the structural bound does not exceed the coherence ceiling. We test the spectral topology against microtubule resonance data and find preliminary structural compatibility across five topology tests. This convergence motivates the central hypothesis: the exceptional Lie group G₂ provides a candidate algebraic constraint surface for the spectral topology of self-referential systems.
Martin Luther Graise (Thu,) studied this question.