ResolutionMechanism
plain-language theorem explainer
ResolutionMechanism enumerates the five canonical mechanisms for resolving social conflicts triggered when J-cost imbalance exceeds the phi threshold. Researchers modeling tier F peace studies or applying Recognition Science to sociology would cite it to treat resolution options as a finite enumerated set of size 5. The declaration is a direct inductive definition that derives Fintype, allowing immediate cardinality verification.
Claim. The type of conflict resolution mechanisms consists of the five elements negotiation, mediation, arbitration, adjudication, and force.
background
In the Recognition Science framework the J-cost function J(r) quantifies recognition imbalance between parties, with J(r) = 0 at mutual recognition (r = 1) and conflict arising once J(r) enters or exceeds the canonical J(phi) band (approximately 0.11-0.13). The module treats conflict resolution as the process of restoring J(r) ≤ J(phi) and identifies five mechanisms that together realize configDim D = 5. The inductive definition supplies the complete enumerated set of these mechanisms together with the standard derived instances needed for finite-set reasoning.
proof idea
The declaration is an inductive definition that introduces exactly five constructors and immediately derives DecidableEq, Repr, BEq, and Fintype; no further lemmas or tactics are required.
why it matters
The definition supplies the finite set required by the downstream ConflictResolutionCert structure, which asserts Fintype.card ResolutionMechanism = 5 together with a CanonicalCert threshold. It directly realizes the five-dimensional configuration space stated in the module documentation and connects to the broader forcing-chain landmarks (T7 eight-tick octave, D = 3 spatial dimensions) by extending the same dimensional counting to the sociology tier. The companion resolutionMechanismCount theorem confirms the cardinality by decision.
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