DuPair and Tetrapolar Spacetime: A Duality-First Framework. I. Quantum Gravity, Gauge Group Selection, and Dark Energy

This work introduces the DuPair axiomatic framework, a novel discrete mathematical foundation built upon duality-pairing primitive structures. It demonstrates how continuous Lorentzian spacetime geometry emerges via coarse-graining and Gromov–Prokhorov convergence from discrete infotron graphs. The framework derives a parameter-free relation for the cosmological constant from topological entropy, and obtains necessary topological filtering conditions selecting the \(su(3)(2)(1)\) gauge algebra as admissible candidate symmetry structure. The paper clearly distinguishes rigorous theorems, physically motivated working assumptions, and results deferred to a companion paper. This construction advances mathematical physics by realising gauge symmetries as automorphisms of an underlying duality structure, rather than treating symmetries as fundamental postulates.