One core for correlation or calibration is insufficient. I usually require at least 3 cores for each correlation or calibration.
Density testing is usually done on large pavement projects at a frequency of at least one test per 500 square yards of pavement. If you have a small project, you might want to test more frequently, since small projects often have more density problems than large projects, because of the difficulty of working in smaller, more confined areas. Further, the contractors doing the work are usually not as aware of asphalt technology as those who do larger pavement projects.
I would do a correlation/calibration of the density gage, using cores, for each day's production, assuming you have a multiple day paving job. This helps to pick up mix issues and pavement laydown procedure problems. For instance, the asphalt plant may have variations in the mix on a daily basis (due to variations in the plant settings, mix constituents, the stockpiles, and the consumption of asphalt cement).
The reason I use a 3-core minimum is that a single core might be anomalous, with either a high density or low density...you won't know which unless you take multiple cores to average them.
BigH...thanks for your more clear paraphrasing!