IndisputableMonolith.Hydrology.HydraulicGeometryFromSigma
The module defines the Leopold-Maddock at-a-station triple (b, f, m) for single-thread stream reaches under sigma conservation. It requires all exponents positive and enforces the closure b + f + m = 1. Hydrologists and geomorphologists cite it when applying Recognition Science to channel geometry. The structure consists of exponent definitions, positivity results, and a certification theorem.
claimThe Leopold-Maddock triple $(b, f, m)$ on a single-thread reach satisfies $b + f + m = 1$ with $b, f, m > 0$.
background
Recognition Science applies its conservation laws to hydrology through the sigma parameter. This module imports the base time quantum from Constants and focuses on channel geometry. The Leopold-Maddock triple (b, f, m) captures at-a-station hydraulic relations for single-thread reaches. The module enforces positivity of each exponent and the closure condition b + f + m = 1.
proof idea
This is a definition module, no proofs. It assembles the HydraulicExponents definition, positivity lemmas for each component, the closure identity, and the HydraulicGeometryCert.
why it matters in Recognition Science
The module supplies the hydraulic geometry foundation that supports downstream applications in Recognition Science modeling of physical systems. It realizes the Leopold-Maddock relations as a direct consequence of sigma conservation in the framework.
scope and limits
- Does not extend to multi-thread channels or braided rivers.
- Does not provide numerical predictions for exponent values.
- Does not incorporate dynamic channel adjustments over time.
- Does not connect to sediment load or erosion models.
depends on (1)
declarations in this module (13)
-
structure
HydraulicExponents -
theorem
width_pos -
theorem
depth_pos -
theorem
velocity_pos -
theorem
closure_identity -
theorem
each_lt_one_b -
theorem
each_lt_one_f -
theorem
each_lt_one_m -
def
equipartitionExponents -
def
leopoldMaddockExponents -
structure
HydraulicGeometryCert -
def
hydraulicGeometryCert -
theorem
hydraulic_geometry_one_statement