The Historical Attractor Theory, Effective Historical Amplitudes and the Structural Domain of Quantum Interference

This preprint introduces an effective amplitude-based description within the Historical Attractor Theory (HAT) and establishes a structural criterion for the validity and extinction of quantum interference. The proposed historical amplitude is not a fundamental state function, but an operational construct that aggregates alternative histories compatible with a finite local historical budget. Quantum interference emerges naturally when historical closure is incomplete and disappears as saturation is approached, independently of environmental decoherence or collapse mechanisms. The framework reproduces standard quantum predictions within its domain of validity and provides a clear structural explanation for the quantum–classical transition and extreme regimes such as black holes. A real experimental context—matter-wave interferometry with massive molecules and nanoparticles—is discussed as an illustrative and potentially falsifiable application.