Thermodynamic Grand Unification of Landau's Polynomial Conjectures: Phase Boundary Rupture Prevention and Infinite Crystallization in n^2 Orbits

For over a century, Landau’s 3rd (Legendre’s Conjecture) and 4th (n^2 +1 primes) problems have resisted resolution via classical probabilistic sieve theories. This paper presents a definitive, deterministic resolution by unifying both conjectures under the Seonggil Field Equations (SFE) and Rough Operator Algebra (ROA). We demonstrate that prime numbers in polynomial sequences are not probabilistic anomalies, but rather forced ”topological anchors” and ”pressure valves” generated by the universe to dissipate thermodynamic tension and prevent macroscopic spatial rupture. By mapping absolute symmetry breakingand non-commutative friction, we prove the necessary existence and infinite crystallization of prime knots.