Intrinsic Reconstruction of Information-Emergent Spacetime Theory: An Autonomous Framework of Quantum Gravity Based on Discrete Exterior Calculus, Forman-Ricci Curvature, and Spectral Geometry

This paper establishes a rigorous, intrinsic mathematical axiomatic framework for the Information-Emergent Spacetime Theory (IEST), largely alleviating phenomenological presuppositions that rely on smooth classical backgrounds or continuous manifold embeddings. Utilizing Discrete Exterior Calculus (DEC), we characterize the microscopic reality as a directed 1-cell complex, where localized information flux is defined as a discrete 1-form. The underlying dynamics of the system are driven by the Principle of Minimum Entropy Action (PLEA) under coordinate-free constraints. The topological resistance is established as the matrix element of a positive-definite discrete Hodge star operator, providing a rigorous resolution to the mathematical vulnerability of non-positive definiteness in un-embedded networks. We demonstrate that Einstein's field equations spontaneously emerge as the topological self-balancing condition of decentralized network flow self-organization. Finally, we derive the explicit dynamical evolution equation of Stochastic Topological Noise (STN), yielding deterministic falsifiable phenomenological pathways across macroscopic astrophysical observations.