IndisputableMonolith.Hydrology.HydraulicGeometryFromSigma
The module defines the Leopold-Maddock at-a-station exponents (b, f, m) for single-thread stream reaches under sigma conservation. These satisfy b + f + m = 1 with each component positive. Hydrologists and RS modelers working on channel geometry cite it for the closure identity. The module is purely definitional, organizing sibling declarations around positivity and the equipartition constraints.
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 places hydraulic geometry inside the sigma-conservation law. The module introduces the at-a-station triple following Leopold and Maddock, with the closure identity b + f + m = 1. It imports the RS time quantum τ₀ = 1 tick from Constants and builds sibling definitions such as HydraulicExponents, width_pos, depth_pos, velocity_pos, equipartitionExponents, and leopoldMaddockExponents.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the core definitions for the hydrology domain in Recognition Science. It supports HydraulicGeometryCert and the sigma-derived exponents that connect to the forcing chain and phi-ladder constants. No downstream theorems are listed yet, but the closure identity is required for any RS-native treatment of river morphology.
scope and limits
- Does not derive the exponents from the J-cost or phi-ladder.
- Does not treat braided or multi-thread channels.
- Does not include temporal evolution or sediment transport.
- Does not specify numerical values for b, f, m beyond the closure.
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