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Monograph Abstract

Quantum Braid Dynamics (QBD)

A Computational Framework for Emergent Spacetime and Topological Matter

Summary of the Computational Framework and Key Mathematical Results​

Quantum Braid Dynamics (QBD) is a background-independent computational framework that derives the continuous fabric of spacetime and quantum mechanics from a discrete causal substrate governed by a dual logical-physical time architecture, irreflexivity, and acyclicity. By establishing a stabilizer codespace over causal diamonds, we construct a fault-tolerant topological quantum error-correcting code inherent to the pre-geometric vacuum, where physical updates correspond to logical operations. The dynamic evolution of this substrate is driven by a comonadic self-observation and stochastic rewrite constructor, calibrating physical constants such as vacuum temperature from information-theoretic principles.

Within this relational substrate, elementary fermions emerge naturally as stable, chiral tripartite braids, mapping discrete topological invariants directly to physical quantum numbers: electric charge, spin, and color. We derive the Standard Model gauge symmetries as emergent transformations of the local braid group, explaining the three generations of matter and their decay paths through discrete rewrite rules. Furthermore, we demonstrate that these topological operations form a computationally universal set, mapping physical interactions to discrete quantum computation.

Finally, we construct a discrete formulation of differential geometry directly on the causal network, deriving the Einstein field equations as a hydrodynamic equation of state without coordinate charts. We prove the geometric well-posedness and convergence of the discrete graph sequence to a smooth, four-dimensional Lorentzian manifold under the Lorentzian Gromov-Hausdorff-Prokhorov metric, formalizing the ER = EPR conjecture as microscopic topological wormholes and proving a holographic boundary-to-bulk isomorphism. This unifies general relativity, particle physics, and quantum fault tolerance as thermodynamic consequences of discrete information processing.

Core Theoretical Pillars​

  1. The Rules (Foundational Principles): Spacetime is a dynamic, relational Directed Acyclic Graph (DAG). There is no static spatial background; geometry and time are entirely emergent from the network of causal relations. The vacuum acts as a macroscopic Quantum Error-Correcting Code (QECC) protecting topological coherence.
  2. The Players (Topological Matter): Particles are not point-like field excitations. They are stable, irreducible, tripartite braids embedded in the graph itself, with gauge symmetries arising as emergent transformations of local braid groups.
  3. The Stage (Emergent Reality): Macroscopic gravitation emerges as the thermodynamic limit of network updates. Causal curvature maps to general relativity via discrete differential geometry, proving the convergence to smooth Lorentzian spacetimes under the Gromov-Hausdorff-Prokhorov metric.