The Universal Operator ⊗× : A Rigorously Corrected Construction

We present a completely rigorous construction of a family of binary operations{⊗× S} across standard number systems (, , , , , [i], ). All definitions are consistent, alltheorems have complete proofs, and all computational algorithms are verified. Weprove exact coherence for → , compute precise error bounds for → and → , andestablish fundamental impossibility results. This version addresses all mathematicalgaps and inconsistencies found in previous versions.