Dukkha as Branch Event: Committed Deviation under Bounded Non-Closure

This paper extends the serial-transparency framework by introducing a minimal event-level definition of dukkha. Under the assumptions of bounded non-closure and \Delta-indexing, dukkha is formalized as a "branch event." The model distinguishes between "distortion" (phase-altering projection of deviation) and "commitment" (the persistence and inscription of that distortion into the trace). Dukkha is defined not as the deviation itself, but as the committed transformation of deviation into an alternative indexed path through trace transfer at a registered kṣaṇa. This formalization isolates the minimal mechanics of divergence, providing a dual to the previously defined condition of satori (same-trace serial transparency).