# Preface - The set of information elements can be canonically defined via dichotomy systems under which the kindred intertype relation is invariant when mapped to a vector space induced by the system. Although all 16 "Varlawend" dichotomy systems preserve the orbital 2-cocycle, orbital preservation alone is insufficient to guarantee kindred invariance. Among these systems, only two ($\mathcal{D}_{2}$ and $\mathcal{D}_{14}$) fix the kindred relation. In each of these systems, a heptad of dichotomies suffices to distinguish the information metabolism elements (IMEs) uniquely. For more information on which relationships are invariant when mapped to the vector space, check out Section 7 of [[A Representation-Theoretic Framework for Intertype Relations in Socionics]]. - **Side Note:** HEF = High Energy Function. These correspond to the Energetic functions of Model-G, which is a Gulenko-Newman trait. Alternatively, 'HEF' can be understood as a syntactic placeholder term for the subset that constitutes the identity, benefactor, supervisee and dual relations of the group that comprises all classical intertype relationships. For more information on the Gulenko-Newman dichotomies, check out [Encyclopaedia of Model G and Model A Dichotomy Systems (contains proofs of new mathematical discoveries)](https://varlawend.blogspot.com/2023/06/encyclopedia-of-model-g-and-model.html). And for information on how various function dichotomies translate to tetrachotomies for sociotype under the interpretation of injection, check out [[Injections - Function Dichotomies to TIM Tetrachotomies]]. # Semidual Mirage HEF System ($\mathcal{D}_2$) 1. Extroversion / Introversion 2. Irrational / Rational 3. Static / Dynamic 4. LIE+EII HEF / ESE+LSI HEF 5. SEI+IEE HEF / SLE+ILI HEF 6. LII+ESE HEF / ESI+LSE HEF 7. ILE+SLI HEF / IEI+SEE HEF # Tencer-Minaev System ($\mathcal{D}_{14}$) 1. Extroversion / Introversion 2. Irrational / Rational 3. Static / Dynamic 4. 1stAbstract / 1stInvolved 5. 1stInternal / 1stExternal 6. 1stAlpha / 1stGamma 7. 1stDelta / 1stBeta