PAPER-DCQ1-A Discrete-Continuous-Quantum Correspondence

We construct a kinematic framework that unifies discrete, continuous, and quantum
descriptions of physical states. The core of the model is a 64-element binary
configuration space H6 = {±1}6, which is isometrically embedded into the complex
Grassmannian Gr(3, 6) via a novel phase-encoding map. We prove that the
discrete Hamming-style metric on H6 coincides exactly with the geodesic distance
on Gr(3, 6) under this embedding, establishing metric compatibility. The induced
quantum state space reveals a fundamental bipartition into bosonic and fermionic
sectors with a total dimension of 24, intriguingly reminiscent of the ln 24 term in
black hole entropy. Furthermore, the determinant line bundle on Gr(3, 6) equips the
model with a Berry connection whose curvature is integrally quantized, ensuring
global consistency of geometric phases. This work provides a rigorous kinematic
foundation for a unified structural theory of physics, serving as a basis for future
dynamical and physical investigations.