Quantum theory keeps its books with three kinds of accounting systems, called operator algebras. In a type III algebra — the kind that describes any region of space in quantum field theory — entropy cannot be defined at all. In a type II algebra itcan, but only as differences: like altitude without a sea level, there is no zero. In a type I algebra entropy is absolute: it counts states. Witten and collaborators showed that adding an observer to a gravitating region upgrades its algebra from type III totype II — and that a finite capacity (Bekenstein) bound would upgrade it to type I, turning black-hole entropy into a genuine count. This letter builds that entire bridge — III → II → I — as one exact, finite-dimensional structure in which every step can be checked on a computer, and proves what the famous “additive constant” of gravitational entropy actually is: a chemical potential for the gravitational constraint charge. Bridging the algebras this way means the entropy of gravity is no longer defined only up to an unknown offset; the offset itself becomes a physical, computable object, with a semiclassical part and a topological part that survives every limit exactly.
Jeffrey S. Cambria (Thu,) studied this question.