This paper resolves the long-standing probabilistic assumptions surrounding Buniakovsky’s Conjecture by introducing a deterministic geometric framework based on Rough Operator Algebra (ROA) and Seonggil Theory of Composite Torsion (STCT). Instead of treating the values of an irreducible polynomial f (x) of degree d as random integers, we reframe them as deterministic geometric trajectories piercing through a multi-dimensional prime lattice. We establish the Topological Pressure Tensor (PT) through a discrete path integral of the inner product between the Seonggil Dissonance Tensor ˆDand the Torsion Tensor Matrix Tₖ. By exploiting the Null Space Non-Absorption Principle, we prove that PT is monotonically increasing and inevitably ruptures the absolute phase-lock threshold CSMT ≈ 1. 686077, forcing a deterministic prime spawn. Furthermore, we reconcile this framework with the Bateman-Horn density scaling by deriving the intrinsic algebraic gravitation factor d² x^ (2d−2) and implement a variable warp stride S^ (d) ⱼump (x) inside the V87 Rough Operator Engine, converting algorithmic stepping into high performance topological teleportation.
Lee Seonggil (Thu,) studied this question.