Welcome to my Beltmatic speedrun of reaching level 10. As with most of my speedruns this is not an official record but just for fun since I used a saved map on which I practiced a lot and because I even switched segments in the middle! However, I was so impressed by the current records that I wanted to use the opportunity to show some different designs to maybe improve them even further in the future! :-)
The general approach is the same as in the current world record hold by Lyra Belacqua. You use 1s for the first few numbers, 2s for the calculation of 10 and then sequentially increase it by the differences to the following numbers. For the final number you use the waiting time to go for a completely separate calculation using multiplication to speed up production.
For a good setup I started new games over and over until I found good level numbers and a convenient map layout. A combination of 14 and 20 seemed to be the most perfect to me for the levels 6 and 7 because both only need one duplication of 2 and 3 each. An 11 or 12 might be quicker for level 6, but that leaves a difference of 8 and higher for the next level which in total should be slower. As for the last two levels, the numbers 31 and 42 are really outrageously good since you can merge both of their additional streams to temporarely boost the first production and then automatically switch to normal production once both belts are full! 42 is also a simple product of 6 and 7, so the multiplication is easy to set up!
In total the whole run went very well! I optimized the timings to be just in time to use the unlocked 2s, 3s, 4s, bridges and operators for the next calculations. The map is really close to perfect for the early numbers! However, the distribution of 3s and 4s needed for the last 2 levels are not so ideal because they are rare and very far away from the hub... It slowed down start of production for level 8 by a lot and it even limited me to only 4 extra production belts in the end since there were no more 3s and 4s to use in the whole area! So if I were ever trying to improve my time to below 7 minutes, I would scan the map layout for those two numbers, too!
One thing I noticed after rewatching the run: the belt upgrade is available pretty early and I kept ignoring it because I was focusing on getting the production of 3s as fast as possible. Investing that extra second would speed up the production of 2s and help with getting the extractor upgrade a little bit sooner, but in the end I am forced to wait for the 5s to unlock the bridge which is mostly independent from that, so I dont think I lost too much time there. Still, I can only recommend avoiding that in the future. ;-)
Also, the existing multiplier layout for the last number should in theory be faster, but at least for me, it turned out that copy pasting the inefficient standard designs and connecting the needed numbers to them without delay is better. The time it takes for me to build a new layout is greater than the time it saves by a quicker ramp up time... It may be different for the more dextereous players!
Now I hope to have inspired someone to hunt this run, either by better strategies or better execution, or preferably both! :-D