Reconstructing Physics from Discrete Topology and Information Entanglement: A Daopological Paradigm for Mass, Forces, and Spacetime

Contemporary theoretical physics faces a dual dilemma: macroscopic General Relativity (continuous manifolds) and microscopic quantum field theory (probabilistic wavefunctions) are mathematically incompatible at their foundations. Meanwhile, continuous calculus encounters insurmountable logical bottlenecks such as renormalization and infinities when confronting the Yang-Mills mass gap, black hole singularities, and the vacuum energy catastrophe. This paper proposes "Daopological Physics": an ontological reconstruction based on discrete topological networks and information entanglement. We replace continuous space points with Structural Kernels K=(P, Σ, B, Θ), and continuous time evolution with Discrete Structural Annealing (DSA). We prove that the essence of physical reality is the interplay between "structural measures" and "topological entanglement entropy." Core contributions include: Emergence of Constants: We rigorously derive the discrete topological algebraic expressions for the speed of light c, Planck's constant h, and the gravitational constant G, proving they correspond to the network's limiting propagation speed, minimal topological loop area, and feedback Jiao-family stiffness, respectively. Mass Gap: We define a fused measure and prove that non-trivial topological charges (Q ≠ 0) lock the min-cut of information entanglement, thereby providing a pure algebraic topological proof for the Yang-Mills mass gap (Δ > 0) and eliminating both UV divergence and the volume paradox using topological cutoff. Interactions and Quantum Reconstruction: Using category theory and group theory, we map the four fundamental forces to graph rewrites of the 6 Jiao families. Wave-particle duality is reconstructed as topological solitons and phase information propagation. Introducing the imaginary time parameter τ_imag = it, we prove the first-order equivalence between DSA annealing and quantum unitary evolution under macroscopic statistical limits. Falsifiability: We propose a four-quadrant cosmic model based on measure-entropy, derive the cosmological constant with a dynamic "entropic force" mechanism, and provide a rigorously parameterized O(E²) Lorentz invariance violation prediction (coefficient -1/8) for LHAASO verification. We also derive the dimensionally consistent formula for gravitational wave birefringence in dark matter topological knots.