Abstract. The correlated grade form of twisted blades (twisted simple multivectors) faithfully renders in symbols their native geometric structure. The discovery of this paper's nonassociative Clifford-like algebra was driven by trying to calculate exterior products of straight and twisted multivectors directly in a basis of this form. The key was found to be the orientation congruent (OC) algebra. This paper is being published electronically in about ten sections, each offered as soon as written. In this first section we axiomatize the orientation congruent algebra by generators and relations. The next section derives the sign factor function and proves that the Clifford product times it is the multiplication of an explicitly Clifford-like algebra isomorphic to the orientation congruent algebra. Later sections are planned to show how to calculate the OC product in Mathematica and Clical; to define the orientation congruent contraction operators, deduce their properties, derive other expressions for them, and use them to compute the OC product within the exterior algebra using a modified Cartan decomposition formula; to develop the algebra's edge colored product sequence graph; to derive a predictor of a null associator as a function of the grades of the three elements in it; to prove the associomediative property of the algebra's counit; to develop matrix representations (under a nonassociative matrix product) of the orientation congruent product; and to discuss the motivating application per se and as inspiration for the first set of axioms.
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