TrafficFlowRegimesCert
plain-language theorem explainer
Traffic flow models in Recognition Science fix the state space to exactly five dynamical regimes via a certificate structure. Highway analysts cite this when anchoring simulations to free-flow, synchronized, stop-and-go, jammed, and incident-driven phases. The structure is realized as a one-field wrapper that records the Fintype cardinality of the enumerated regime type.
Claim. Let $R$ be the finite type enumerating the five traffic flow regimes. The certificate structure asserts that the cardinality of $R$ equals five.
background
Recognition Science assigns configDim equal to five for transportation, yielding the five canonical regimes listed in the module: free flow, synchronized flow, stop-and-go waves, jammed, and incident-driven. These are the principal dynamical states employed in highway-flow modeling. The local setting is supplied by the inductive enumeration of these regimes, which carries a Fintype instance used to compute cardinality.
proof idea
The definition constructs the structure by populating its single field with the cardinality value obtained from the Fintype instance on the regime enumeration. It functions as a direct wrapper around that cardinality computation.
why it matters
The certificate supplies the fixed dimensionality for traffic flow states inside the Recognition framework. It is consumed by the downstream instantiation that produces a concrete certificate value for use in transportation theorems. This choice of five regimes complements the spatial dimension D equals three obtained from the forcing chain T8 and aligns with the overall configDim convention.
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