Quotient Tree Arithmetic: Deferred-Division Computation with Bounded Symbolic Depth and Cross-Subtree Cancellation

We introduce Quotient Tree Arithmetic (QTA), a computational substrate in which values are represented as deferred quotient pairs (N, D) whose ratio is evaluated lazily at a designated materialization boundary. The framework applies to any domain: IEEE 754 doubles used as exact integer containers give exact rational arithmetic within the 2^53 exactness window; arbitrary IEEE doubles extend cove…