governanceCert
plain-language theorem explainer
The declaration constructs a concrete GovernanceCert record asserting five institutions map bijectively onto five failure modes under the J-cost threshold. Institutional analysts would cite it to confirm the democratic maintenance condition in the recognition-ratio model. It is a direct record construction that assembles three upstream decidable facts on cardinalities and bijectivity.
Claim. Let $I$ be the set of five canonical institutions and $F$ the set of five failure modes. The certificate $C$ satisfies $|I|=5$, $|F|=5$, and there exists a bijection $I$ to $F$ given by the explicit map sending each institution to its unique failure mode.
background
In the Recognition Science treatment of governance, five canonical institutions (executive, legislative, judicial, military, free press) are assigned recognition ratios $r_i$ measuring actual versus mandated competence. The J-cost $J(r)=(r+1/r)/2-1$ quantifies deviation from health, with each failure mode exactly the transition $J(r_i)>J(φ)$. The GovernanceCert structure, defined in the same module, packages three requirements: cardinality of institutions equals five, cardinality of failure modes equals five, and a bijection exists between the two sets via the map institutionFailureMode.
proof idea
The definition is a one-line record constructor that supplies the three fields directly from the sibling theorems institutionCount, failureModeCount, and institution_failure_bijection.
why it matters
This definition supplies the concrete certificate required by the E7 governance analysis, confirming that the five institutions and five failure modes stand in bijective correspondence under the shared J(φ) threshold that governs phase transitions throughout the framework. It closes the local development in InstitutionalFailureFromJCost and connects to the broader forcing chain (T5 J-uniqueness through T8 D=3) via the common recognition-composition law. No downstream uses are recorded.
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