Reductionism does have a caveat, and this is "a fact about maps" and not "a fact about the territory": the real world level can be below the algorithm. Example: a CD. A chromodynamic model would spend immense computing resources simulating the heat and location and momentum and bonds of a slew of atoms (including those in the surrounding atmosphere, or the plasticizer would boil off). In reality there are about four things that matter in a CD: you can pick it up, it fits into a standard box, it fits into a standard reader tray, and when you measure the pattern of pits they encode a particular blob of binary data. From a human utility perspective, the CD is fully replaceable with a chromodynamically dissimilar other CD that happens to have those same characteristics.

Computers are full of examples of this, where the least important level is not the fundamental level. In in some cases, each level is not just built upon lower levels, but ought to be fully independent of them. If your lisp doesn't implement the lambda calculus because of a silicon fault, an atomic model would correctly represent this, but it would be representing a mathematically unimportant bug. A correct lisp would be representable on any compute substrate, from a Mac to a cranks-and-gears Babbage engine. A model which took account of the substrate would be missing the point.