Liberation mathematics I: the behavioral and consciousness definition of perpetual self-transcendence

Traditional definitions of liberation (such as moksha, nirvana, and kaivalya) across Hindu, Buddhist, and Jain philosophical traditions have remained empirically underspecified and conceptually divergent for over 2,500 years. This study proposes an operational definition of liberation asperpetual self-transcendence through infinite domain expansion, characterized by the inability to fix one's identity in any achieved position. The framework employs mathematical formalization of behavioral observables, comparative analysis across six traditions, and empirically testable criteria, including the Liberation Coefficient (LC) and Self-Transcendence Rate (STR). The model resolves five traditional controversies by demonstrating liberation as: (1) process rather than state, (2) ego fluidity rather than dissolution, (3) mandatory world engagement, (4) simultaneous requirement of all paths, and (5) both sudden recognition and continuous application. This framework may provide a foundation for systematic empirical investigation of consciousness liberation, establishing Liberation Science (Liberology) as a measurable behavioral and consciousness phenomenon.