Assumptions will be specifically declared when there are indications for influencing the outcome of an experiment.
To allow other scientists to repeat the experiment, they declare for a specific value or state. When such an experiment reproduces with the given set of assumptions, and it delivers the same result, then this is an indication that there is sufficient control over the test conditions. When a different result is measured, then this can trigger a further refinement of assumptions.
When an equation is derived from the experiments that give a mathematical description of an expected outcome, then also this equation is only valid under the stated assumptions