trivial
plain-language theorem explainer
The trivial kinship system is the zero element obtained by setting all three Boolean axes to false in the F_2^3 encoding. Mathematical anthropologists classifying cross-cultural kinship structures cite it as the null case completing the 2^D-1=7 count. The definition is supplied by direct record construction on the three-field structure.
Claim. The trivial kinship system is the element of the structure with lineage = false, residence = false, and marriage = false.
background
Kinship systems are encoded as elements of F_2^D for D=3, with axes lineage (patrilineal vs matrilineal), residence (patrilocal vs matrilocal, projected to F_2), and marriage (cross-cousin vs parallel-cousin permitted). The KinshipSystem structure packages these three Boolean fields. The module derives the eight axis assignments collapsing into seven non-trivial systems plus this null case, matching Murdock's six basic types plus one syncretic seventh.
proof idea
Direct definition by record constructor: the structure is instantiated with false for each of the three fields.
why it matters
This definition supplies the null element required by the 2^D-1=7 count law applied to the kinship-axis Q_3 structure in Recognition Science. It completes the basis for the seven non-trivial classes in Track I1 of Plan v5. The module states the falsifier as any documented kinship system outside the seven structural classes derived from the F_2^3 basis.
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