Relational Geometric Hardness: A Non-Abelian Chiral Constraint Primitive Modeled on Extra-Dimensional Gauge Holonomies

Traditional public-key cryptographic primitives (e.g., RSA, ECC) rely on function-based hardness assumptions, such as the difficulty of prime factorization or discrete logarithms. These primitives are vulnerable to structural linearization and polynomial-time collapse under quantum computational models (e.g., Shor's Algorithm). This paper introduces BitKnot, a novel cryptographic primitive based on Relational Geometric Hardness. Instead of mapping secrets to static scalar bitstrings, information is encoded as a constrained relational configuration of localized connection fields ($\alpha$) over a bipartite graph governed by node chirality ($\chi$). By elevating the connection operators to the non-Abelian Lie group SU(2) and enforcing interlocking, braided commutator boundary conditions, we intentionally engineer non-convex optimization landscapes filled with deep, false attractor basins. We present empirical stress-test results demonstrating asymptotic hardness scaling, wherein standard numerical gradient descent, population-based differential evolution, and thermal dual annealing attacks are consistently trapped at precise, rigid energy thresholds. The BitKnot code itself we refer to as BK-NarCop, derived from 'BitKnot - Non-Abelian Relational Constraint Protocol. BK-NarCop is available to all for free under a copyleft license utilizing GNU 3.0 on GitHub at the following URL: \url{https://github.com/davidbsmith-bitknot/BK-NarCop}