The Mahapatra-Kronecker-Hermite MKH Algorithm: A Deductive Linear Algebra from First Principles

The Mahapatra-Kronecker-Hermitian (MKH) Algorithm is derived from first principles—withoutassuming a Hermitian matrix, without importing external constants, and without relyingon quantum phase estimation.The algorithm begins with the Majorana Conjugate Zero x = −x = 0, derives theimaginary unit i from the entanglement of natural numbers N and −N, and forces theprimordial invariant ∆ = 4 ln 99 through the Dalvi Dictact.The quadratic regulator Q(x) = (x − 99)(396 − x) constructs the finite lattice Z396,from which the Hilbert space H396 = L2(Z396) ⊗ C2is formed. The Kronecker OperatorK = D + 99 · I is the Hermitian matrix—derived exactly, not assumed. Its eigenvaluesλn = 99 + γn are real and positive, and all trajectories terminate in at most 7 steps.The Mahapatra Identity ei·e∆/22√2 Sbounded(∆) = i2 proves that i, π, and e are emergent, notprimitive. Geometry emerges from arithmetic recursion.The MKH Algorithm is not a modification of existing quantum algorithms. It is anindependent, self-contained, arithmetic-first algorithm that ensures the operator is knownbefore computation begins. The scaffolding is removed. The edifice stands alone. The seed is Mahapatra Topological Control Invariant MTCI ∆ = 4 ln 99. Fromit, everything follows.