A Quasicrystalline Spacetime Ansatz with Triadic Temporal Structure: Mathematical Consistency, Recovery Limits, and Effective-Field Constraints

We formulate a conservative mathematical framework for a discrete, quasicrystalline spacetime substrate equipped with an internal triadic temporal structure. Spatial discreteness is modeled by a six-dimensional cut-and-project construction whose physical projection defines an aperiodic Delone–Meyer set with long-range order. Temporal structure is represented by the triplet Ψ(t) = (t,ϕ(t),χ(t)), with a real kinetic prefactor A(t) = 1+ϵ(t), |ϵ(t)| ≪ 1. Wedefine the corresponding discrete gradient and Laplacian, derive the continuum limit, and formulate scalar, spinor, and gauge-field kinetic terms on the resulting effective background. Under boundedness and positivity assumptions on A(t), the deformed kinetic sector is shown to be stable in the Hamiltonian formulation and to recover standard relativistic quantum field theory in the limits a → 0, ϵ → 0, and ˙ ϕ, ˙χ → 0. The framework is not presented as a completed theory of quantum gravity or as a derivation of the Standard Model. Rather, it provides a falsifiable mathematical scaffold for controlled geometric deformations of continuum field theory. Possible low-energy consequences are discussed in terms of modified dispersion relations and phenomenological oblique effective-field directions, with explicit limitations on what is and is not derived. Keywords: quasicrystalline spacetime; cut-and-project geometry; discrete spacetime; triadic time; effective field theory; recovery limits; modified dispersion; SMEFT phenomenology.