kinshipGraphCohomologyCert
plain-language theorem explainer
The declaration assembles a master certificate bundling the length, distinctness, and cross-cousin properties of all kinship systems over three Boolean axes. Mathematical anthropologists would cite it to record the exact match between the 2^3-1 enumeration and Murdock's six types plus one syncretic class. It is realized as a direct structure constructor referencing the pre-established length and filter lemmas.
Claim. The kinship graph cohomology certificate asserts that the set of all kinship systems (Boolean triples on lineage, residence, marriage) has cardinality 8, the non-trivial subset has cardinality 7 and equals $2^3-1$, is pairwise distinct, exactly four admit cross-cousin marriage, and the trivial system is excluded from the non-trivial list.
background
KinshipSystem encodes each system as a triple of Booleans for the three axes: lineage (patrilineal vs matrilineal), residence (patrilocal vs matrilocal), and marriage (cross-cousin vs parallel). The module models these as elements of F_2^3, yielding 8 total assignments that collapse to 7 non-trivial systems. Upstream results include all_length theorems establishing |all| = 8 and |nontrivial| = 7, together with cross_cousin_count fixing the filter length at 4.
proof idea
This definition is a one-line wrapper that applies the structure constructor to the pre-proved lemmas KinshipSystem.all_length, KinshipSystem.nontrivial_length, murdock_count, nontrivial_pairwise_distinct, cross_cousin_count, cross_cousin_half, and KinshipSystem.trivial_not_nontrivial.
why it matters
This certificate closes the derivation of the kinship classification from the three-axis Q3 structure, directly implementing the 2^3-1=7 count from the D=3 forcing step. It supplies the concrete data structure that would be referenced by any downstream theorem on anthropological invariants. The open question it touches is whether every documented natural kinship system falls inside these seven classes, as stated in the module falsifier.
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