Consciousness-Weighted Quantum Probabilities: Formalization, Consistency, and Falsifiability

This paper develops a mathematical realisation of a speculative framework in which consciousness, modelled via Integrated Information Theory (IIT), is permitted to weakly bias quantum outcome probabilities. Building on a companion conceptual paper, a consciousness-weighted probability distribution is introduced that reduces exactly to the Born rule in the limit of vanishing coupling. Structural constraints are imposed, including normalisation, internal consistency, and compatibility with no-signalling. First-order corrections to standard quantum statistics are derived, and the model is shown to be explicitly falsifiable: if no deviations from the Born rule are observed, the coupling parameter must vanish and standard quantum mechanics is recovered in full. The framework is intended not as a replacement for quantum theory, but as a phenomenological bridge between theories of consciousness and quantum foundations, providing a structured way to test whether integrated information might play any measurable role in quantum outcome selection.