Redefining Antimatter as a Logical Balance Operator in Finite Systems: Stability of the H_HV Hamiltonian and Resolution of Negative-Energy States

This paper presents a fundamental ontological redefinition of antimatter, transitioning from the conventional "mirror matter" model of the C∞ continuum to a logical balance operator framework (+1 - 1 = 0) within the Theory of Finite Systems. We demonstrate that the existence of antiparticles is a structural necessity for the consistency of a discrete spacetime lattice, governed by the Hernández-Valdivia Limit (ε_HV ≈ 10⁻⁷⁰ m²). By formulating a modified Kogut-Susskind Hamiltonian (H_HV) and deriving the topological limit from Ramanujan's modular geometry, we prove that antimatter acts as the topological friction required to enforce the positivity of the energy spectrum. This effectively eliminates Ostrogradsky ghosts and resolves the Map-Territory Confound in particle physics. The annihilation process is reinterpreted as a real-time error-correction protocol that prevents information saturation and systemic collapse.