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You can buy proprietary brands of sugar syrup, or if you'd prefer to make your own, I recommend making a 'rich' two parts sugar to one part water (2:1)...
Regarding point 5 above, high temperatures do indeed cause rapid hydrolysis of sucrose into glucose and fructose *in the presence of mineral acids or invertase* (enzyme):
It may be just “exponential kinetics”, but the maths and science in the links are unfathomable. Are you saying that in the process of making a rich sugar syrup, even with prolonged boiling, there will be NO conversion to glucose and fructose? Or just minimal conversion?
I nearly always add a shot of vodka to a bottle (500ml) of syrup as a preservative. The resulting mixture would be less than 1%ABV. Is this a good or a bad idea?
I keep my simple syrup in a glass bottle. I make it by pouring the sugar in (2-1), adding hot water from the tap and shaking; it seems to come out fine. Is there any reason that shouldn't work?
If sugar is fine, the water is hot enough and you are patient and vigorous in your shaking, then I can see this method working for rich syrup. It is how most make 1:1 simple syrup.
https://qsstudy.com/first-order-reaction-hydrolysis-sucrose-glucose-fructose/
but only incredibly slowly in a simple water-sucrose syrup:
https://chemistry.stackexchange.com/questions/116764/how-long-would-it-take-for-sucrose-to-undergo-hydrolysis-in-boiling-water