all_length
plain-language theorem explainer
Kinship systems are the eight vectors in F₂³. Researchers in mathematical anthropology cite this result to anchor the total count before splitting into seven non-trivial classes. The proof is a one-line decide tactic applied directly to the enumerated list definition.
Claim. Let $K$ be the list of all kinship systems encoded as elements of $F_2^3$. Then $|K| = 8$.
background
Kinship systems are encoded as triples in $F_2^3$ with axes for lineage (patrilineal vs matrilineal), residence (projected to $F_2$), and marriage (cross-cousin vs parallel). The module constructs the complete set of eight such systems from the $2^D$ structure with $D=3$, yielding seven non-trivial classes plus the trivial null. This parallels the length-7 enumerations in NarrativeGeodesic.all and ModalPreferenceFromPhi.all, each omitting the trivial case per the $2^D-1=7$ count law stated in the module doc.
proof idea
The proof is a term-mode one-line wrapper that applies the decide tactic to the explicit list of eight KinshipSystem constructors, computing its length directly.
why it matters
This supplies the all_count field inside kinshipGraphCohomologyCert and is invoked by cross_cousin_half to obtain the half-count of cross-cousin systems. It realizes the eight-tick octave (T7) and $D=3$ (T8) from the forcing chain for the anthropology track, closing the enumeration step toward the master certificate.
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