Underlying principle for parity-dependent superposition in polygonal GPTs

Identify a higher principle underlying the parity-dependent distinction between odd and even regular polygon GPTs, in which odd polygons satisfy the full suite of superposition principles while even polygons generally fail to satisfy uniform superposition.

Background

The paper compares regular polygon GPTs with real qubit theory. Odd-sided polygons inherit complete, uniform, and mutual superposition, whereas even-sided polygons fail to satisfy uniform superposition except in the appropriate continuous-limit behavior. The authors observe this parity-dependent structural gap but do not identify a more general principle explaining it.

References

Whether there is a higher principle underlying such explanation is not known to us.

— No extension of the Quantum Tensor Product admits a Superposition principle  (2608.17572 - Fiorentino et al., 18 Aug 2026) in Section 3, paragraph following Table 1