conflictResolutionCert
plain-language theorem explainer
The definition constructs a certificate asserting that exactly five resolution mechanisms exist for conflicts driven by J-cost imbalances above the phi threshold. Sociologists or peace researchers working in the Recognition Science model would cite it to formalize the mapping from recognition deficits to canonical resolution strategies. The definition is assembled by direct field assignment from an enumeration theorem and a prior canonical certificate.
Claim. Let $ConflictResolutionCert$ be the structure whose fields are the assertion that the cardinality of the set of resolution mechanisms equals 5 and the presence of a canonical certificate. The definition $conflictResolutionCert$ instantiates this structure by setting the mechanism count to the enumerated cardinality and the threshold to the canonical certificate.
background
In the Recognition Science framework, social conflict arises when the recognition imbalance, quantified by the J-cost $J(r)$ for recognition ratio $r$, exceeds the canonical threshold $J(phi)$ in the band approximately (0.11, 0.13). Resolution restores $J(r) leq J(phi)$ via one of five mechanisms (negotiation, mediation, arbitration, adjudication, force), which the module identifies with configuration dimension 5. The upstream theorem resolutionMechanismCount establishes by direct decision that the finite type ResolutionMechanism has cardinality exactly 5. The structure ConflictResolutionCert packages this cardinality fact together with a CanonicalCert for the threshold.
proof idea
The definition is a direct construction that populates the five_mechanisms field by reference to the theorem resolutionMechanismCount and the threshold field by reference to the identifier cert.
why it matters
This definition supplies the concrete certificate that anchors the conflict-resolution model inside the Recognition Science sociology module. It links the J-cost formalism to the five mechanisms, extending the framework's dimensional counting (T8 spatial dimension D=3, eight-tick octave) to a configuration dimension of 5. The construction closes the Lean interface for downstream sociological applications while leaving open the empirical mapping of the J(phi) band onto observed social data.
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