Sandhi: An Irreversible Intermediate State Between 0 and 1

This paper introduces Sandhi, a formally defined intermediate state in causal logic that exists between inaction (0) and action (1). Conventional binary logic, probabilistic models, and fuzzy logic assume instantaneous transitions or graded uncertainty, but many irreversible processes in decision systems, control systems, and physical phase transitions exhibit a distinct pre-action state. In this state, decision thresholds have been crossed and commitment without realization has occurred, yet no observable outcome is present. Sandhi captures this missing layer as a time-neutral and non-probabilistic causal state defined by non-zero reversal cost in the absence of external confirmation. An axiomatic framework is developed to formalize Sandhi within the foundations of logic, including precise entry and exit conditions, interaction rules, and multi-agent behavior. The formulation demonstrates that such intermediate causal states cannot be reduced to uncertainty, temporal evolution, or aggregation effects, revealing a structural blind spot in existing models of irreversible commitment and decision dynamics. By explicitly representing the causal interval where intervention remains decisive after commitment but before realization, this work provides a minimal, domain-agnostic extension to causal and logical modeling relevant to systems exhibiting irreversible thresholds, pre-collapse dynamics, and activation phenomena.