A simplicial complex is a mathematical construction from algebraic topology that represents topological spaces by assembling simple geometric building blocks. These blocks include points, line segments, triangles, and their higher-dimensional analogues, known as simplices. These components are joined together along their faces in a specific manner. This structure provides a discrete and combinatorial way to study the shape and connectivity of complex data or abstract spaces. It serves as a fundamental tool in computational topology.
Context
While primarily a concept from pure mathematics, simplicial complexes are applied in advanced analyses of network structures, including those found in blockchain and distributed ledger technologies. Researchers employ them to model network connectivity, analyze consensus mechanisms, or identify structural vulnerabilities within decentralized systems. This theoretical framework aids in understanding the underlying geometry of complex data relationships, offering insights into system resilience and performance.
This framework introduces Proof-of-Consensus, leveraging topological networks and quantum mechanics to achieve scalable, secure, and decentralized blockchain systems.
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