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Field Nitrogen Balance
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This directory contains a single Notation3 file that encodes a case 
study about nitrogen management for field crops. Each field is 
described by its soil mineral nitrogen at planting, the fertilizer 
nitrogen applied, a simple loss fraction (representing leaching and 
volatilization), and the crop’s nitrogen demand for a target yield. 
From these inputs the theory computes a basic N balance: total N input, 
the fraction of that N that remains available after losses, any deficit 
if available N falls short of demand, any surplus if it exceeds demand, 
and a rough leaching index given by surplusN multiplied by the loss 
fraction. Based on how the available N compares to the crop demand, 
each field is classified as under-supplied, balanced, or over-supplied. 
Four example fields illustrate typical management situations, ranging 
from low-input under-fertilisation to over-fertilisation on a sandy, 
leaky soil.

On top of this quantitative core, the file adds an ARC layer that 
derives three kinds of explanatory facts. An `:answer` node summarises 
which fields end up under-, well- or over-supplied and notes that the 
sandy, heavily fertilised field has the highest leaching index. A 
`:reason` node explains in mathematical English how the simple formulas 
totalN = soilN + fertN and availN = totalN·(1 − lossFrac) interact 
with crop N demand to produce deficits, near-balance, or surpluses, and 
why both high surplus and high loss fraction drive the leaching index 
up. Five `:check` nodes form a small harness: they confirm that all 
fields have derived balances, that only the under-supplied field has a 
positive deficit while over-supplied fields have positive surpluses, 
that the “balanced” field is indeed the least imbalanced, that 
increasing fertilizer from a balanced case raises total N, available N 
and surplus, and that the sandy over-fertilised field has the largest 
leaching index. Because all ARC conclusions are computed from the same 
N-balance equations and input data, changing soil N, fertilizer rates, 
loss fractions or crop demand automatically updates the Answer, Reason 
and Checks, making this a small, self-documenting example of 
agronomic-style reasoning in N3.

