Synthetic Realization of a Collapsed-Z 4D Tesseract (S3 Analogue) Using Time-Modulated Photonic Crystals

This paper proposes a theoretical architecture for
constructing a synthetic analogue of a four-dimensional tesseract
whose collapsed spatial dimension behaves as an effective threesphere
(S3) boundary. Unlike static geometric embeddings, the
model uses a time-modulated photonic crystal to emulate fourthdimensional
orthogonality through phase-locked temporal modulation.
This approach draws on analogies from topological photonics,
Floquet engineering, graphene-like resonance structures,
and collapsed-dimension physics. The objective is not the physical
manifestation of literal higher dimensions, but the creation of a
controllable 3D system that mathematically behaves as if one
dimension is compactified or folded.