Three Novel Integer Matrix Constructions Connecting Ancient Eastern Combinatorics to Noether's Theorem and Gauge Theory: Binary-Ternary Phase Lattices, T(n)+7 Prime Verification, and a Discrete Framework toward Unified Field Theory

We investigate primes p=T(n)+7=n(n+1)/2+7 and prove eight structural results. Three novel matrix constructions are introduced for the first time (Kwon 2026): (D1) Xugua Complex State-Transition Matrix M_64; (D2) 100-Cell Integrated Matrix M_100; (D3) 361-Cell Unified Matrix M_19 (361=100+180+81). The central hypothesis: M=S+iA is the discrete realization of Noether's theorem for the binary(e)-ternary(pi) symmetry pair. Key observations: alpha~1/(144-7)=1/137 (0.026%); SU(3)+SU(2)+U(1)=8+3+1=12=2*omega. V9 algorithm: 97.6% detection, 100% accuracy.