My take on this is to focus on the mechanics and preparation, which I think is an important part (though perhaps not all) of a cappuccino being properly made.
Fundamentally, a cappuccino consists of espresso and steamed milk (see distinction from a latte). The World Barista Championship specifies the proper construction in their beverage definitions (.PDF) in §2.2.2. It consists of a single-shot of espresso (25 mL / ~0.8 fl. oz.), textured (steamed) milk, and at least 1 cm of foam (other places suggest 2 cm). Total volume is 150-180 mL / 5-6 fl. oz. To the extent that you subscribe to the WBC being a benchmark, the components, volume, and amount of foam define physical properties of a properly made cappuccino. It also states that the components should be in "harmonious balance."
The WBC states that aspects of the service are also crucial, such as
- visual appearance, such as that the beverage should fill the cup;
- served with accoutrements, such as "spoon, napkin and unflavoured water";
- logistical aspects of drinking, such as temperature and holding the cup.
Beyond that, there's a lot of variability that might lean closer to personal preference. Some other topics mentioned at WBC and Wikipedia include being "wet" (referring to the foam, versus "dry"), and "traditional" (solid central circle of white foam, versus having latte art).
Other recipes for cappuccino at home vary greatly:
- Folgers suggests to use equal parts of coffee (French press or drip), steamed milk, and foam. You'll get a rather different outcome from using coffee instead of espresso.
- illy suggests quantities for a more traditional preparation, using espresso and steamed/foamed milk.