The window, and why it is bounded on both sides
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The floor, and what is below it
Below the density, the water activity rises and the product can support mold. It does not fail immediately; it fails on a shelf, weeks later, in somebody else’s kitchen. A thin batch that looked fine on bottling day is the classic version of this failure.
The ceiling, and what is above it
Above it, the sugar is past what the water will hold and comes back out as crystals, usually in the bottom of the bottle and often weeks after bottling. Nothing is unsafe about it and it is a defect the buyer sees, which for a retail product amounts to the same problem.
How wide the window actually is
For maple syrup carrying a USDA grade, Grade A is not less than 66.0 nor more than 68.9 percent solids by weight. That is a span of under three points, and the practical target sits in the middle of it rather than at either edge, because the reading has error in it and so does the finish.
Vermont narrows the bottom further, requiring packaged syrup at a minimum of 66.9 Brix at 60 °F. A producer there aiming at the federal floor is already under the state one before any measurement error is counted.
Why you aim at the middle
Because every source of error pushes you toward one edge or the other: a hydrometer read at the wrong temperature, a syrup still evaporating in the pan while you read it, a thermometer a degree out. Aiming at the floor means half your honest readings land below it.
Both failures are invisible on the day
Neither mold nor crystals shows up while you are bottling. That is the argument for recording the reading rather than trusting the memory of it, because when a complaint arrives weeks later the reading is the only thing that tells you which side of the window you were on.