Prime-Multiplicative Wilson Ensembles: Congruence Reduction and Thermal Fixed Points

Prime-Multiplicative Wilson Ensembles: Congruence Reduction and Thermal Fixed Points Phan Thành Trung Independent Researcher, Vietnam pttrung@operatorology.com ORCID: 0009-0000-7520-6781 This English website edition reproduces the scientific manuscript submitted to Physical Review Letters . The scientific content follows the submitted English manuscript; the layout is adapted for clear long-form reading on the web. Abstract We construct a quantum ensemble in which the same two distinct primes determine both an additive excitation energy and the torus-knot Wilson value of T ( p , q ) in S U ( 2 ) k Chern-Simons theory. Its two-excitation partition function is where P is the prime zeta function. Our central result is an exact congruence reduction: at fixed level k , every Wilson value factors through p , q modulo The infinite prime sum consequently reduces to a finite quadratic form in par