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This work aims to establish a unified semantic operator within the integer Clifford algebra Cl(3,0; Z).

April 25, 2026Open Access

Integer Clifford Algebra Cl(3, 0; Z) as a Unified Semantic Operator

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Randomized trials reformulated quaternionic operators into a unified framework, implying enhanced computational efficiency.

This work aims to establish a unified semantic operator within the integer Clifford algebra Cl(3,0; Z).
Reformulated quaternionic semantic operator as a geometric product in Cl(3,0; Z)
Established operations like Hamilton product and Hodge duality as derivations of the geometric product
Validated all lemmas through computational verification over 340,638 test cases
Defined the dialectical triad of thesis, antithesis, and synthesis within the algebra framework
Demonstrated closure under integer arithmetic without floating-point errors
Achieved zero failures in extensive computational validation

J.Arturo Ornelas Brand (2026) studied this question.

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