governanceFailureCert
plain-language theorem explainer
The definition constructs a certificate asserting exactly five governance failure modes by direct assignment from the enumerated count. Researchers modeling institutional stability under configDim constraints would cite this when enforcing the five-mode limit. The construction is a one-line wrapper that populates the failure modes certificate structure using the pre-proven cardinality result.
Claim. Let $F$ be the finite type of governance failure modes. The certificate asserts that $|F|=5$ by instantiating the structure with the cardinality field set to the established count.
background
The module sets configDim to 5 and identifies five canonical governance failure modes: capture, fragmentation, authoritarian drift, corruption, and legitimacy collapse. These correspond to failures of five canonical institutions. The upstream theorem establishes by exhaustive decision that the cardinality of the failure modes type equals 5, while the referenced structure packages this assertion as a field five_failures requiring Fintype.card of the type to equal 5.
proof idea
The definition is a one-line wrapper that directly assigns the value of the upstream cardinality theorem to the cardinality field of the certificate structure.
why it matters
This supplies the certified count of five failure modes for the configDim=5 case in the E7 depth governance analysis. It anchors the failure mode enumeration within the Recognition framework's institutional modeling, consistent with the five-institution correspondence. No parent theorems appear in the used-by list, indicating it serves as a terminal definition in this module.
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