IndisputableMonolith.Transportation.TrafficFlowRegimesFromConfigDim
Module IndisputableMonolith.Transportation.TrafficFlowRegimesFromConfigDim classifies traffic flow into regimes determined by configuration dimension. It introduces the regime type along with its count and a certifying proposition. The module structure is purely definitional and depends only on the core constants for the time quantum.
claimDefines the inductive type $TrafficFlowRegime$ for distinct traffic flow regimes, the natural number $trafficFlowRegime_count$ equal to the cardinality of that type, and the proposition $TrafficFlowRegimesCert$ asserting that these regimes arise from the configuration dimension in the RS model.
background
The module belongs to the transportation domain and imports only Mathlib together with IndisputableMonolith.Constants. The upstream Constants module supplies the RS-native time quantum $τ_0 = 1$ tick as its fundamental object. Sibling declarations establish $TrafficFlowRegime$ as the central classification, $trafficFlowRegime_count$ as the number of regimes, and $TrafficFlowRegimesCert$ as the formal guarantee that the classification follows from the configuration dimension. The setting therefore extends the Recognition Science forcing chain into applied transportation contexts without introducing new axioms.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module provides the foundational classification for traffic flow regimes in the Recognition Science framework, feeding into any parent theorems on transportation systems that require regime-specific analysis. It directly supports applications of the D = 3 spatial dimensions and the eight-tick octave to real-world flow problems, closing a gap between abstract constants and domain-specific modeling.
scope and limits
- Does not derive explicit flow velocity or density equations.
- Does not incorporate the phi-ladder mass formulas or Berry thresholds.
- Does not provide examples or numerical values for the regimes.
- Does not depend on or reference the Recognition Composition Law.