all
plain-language theorem explainer
The definition supplies the exhaustive list of eight kinship systems encoded as Boolean triples on the lineage, residence, and marriage axes. Researchers modeling cross-cultural structures under Recognition Science cite this enumeration when classifying systems or recovering the predicted count of seven non-trivial types. The body is an explicit listing of every combination in the F_2^3 space.
Claim. Let $K$ be the set of kinship systems. Then all $:= [(false,false,false), (true,false,false), (false,true,false), (false,false,true), (true,true,false), (true,false,true), (false,true,true), (true,true,true)]$, where each triple assigns Boolean values to the lineage, residence, and marriage axes.
background
A KinshipSystem is a structure with three Boolean fields: lineage, residence, and marriage. These correspond to the three axes in F_2^3, each taking values in {-1, +1} or equivalently false/true. The module models kinship rules as elements of F_2^D for D = 3 and applies the 2^D - 1 = 7 count law to obtain seven non-trivial systems plus the trivial null, matching Murdock's six basic types plus a syncretic seventh. This construction parallels the seven-element lists in NarrativeGeodesic.all for plot families and ModalPreferenceFromPhi.all for Greek modes.
proof idea
The definition directly enumerates the eight possible Boolean triples. It lists the trivial system followed by the seven combinations with one or more axes set true. No lemmas are applied; the body is the complete list itself.
why it matters
This supplies the concrete 8-element set whose non-trivial subset realizes the Recognition Science prediction of seven kinship classes under the Q_3 structure with D = 3. It feeds into convexity and minimization theorems in Action.FunctionalConvexity that treat the full list of admissible structures. The construction instantiates the eight-tick octave landmark and closes the anthropological track of the forcing chain.
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