ZIDF v4:Indeterminate Cause-Count Calculus — A Restricted Symbolic Term-Rewriting System for Strategy-Independent Indeterminate-Event Propagation

ZIDF v4 is a restricted symbolic term-rewriting system for deterministic propagation of selected indeterminate events. The framework recognizes three primitive event classes: 0/0, ∞/∞, and 0×∞ (including ∞×0). Instead of assigning numerical values to these expressions, ZIDF v4 rewrites them into non-numerical internal states K[P], where P = (z,i,m) is a canonical cause-count vector recording the multiplicity of the three supported event classes. The principal formal guarantee is rewrite-strategy independence: whenever a supported expression normalizes to K[P], every legal complete rewrite order produces the same final cause-count vector. The frozen Core is shown to terminate, is argued to be orthogonal and confluent, and therefore admits unique normal forms for finite source terms. Finite arithmetic is performed exactly over the rational numbers. Expressions outside the defined Core, such as 5/0 and ∞−∞, are not assigned invented values and remain classified as VALID_OUTSIDE_CORE. A Python reference implementation accompanies the specification. The current implementation passes 23 author-developed tests and has been checked using bounded exhaustive enumeration over 84,036 generated expression trees with up to three binary operator nodes, with no conflicting normal forms detected within that finite test universe. ZIDF v4 does not claim to solve division by zero, redefine ordinary arithmetic, provide a general theory of infinity, or constitute a physical or quantum-mechanical theory. It is a deliberately limited research calculus for studying canonical, rewrite-order-independent cause-count propagation in selected symbolic indeterminate computations.