Two Root Two, Priced: Every Principle That Claims the Tsirelson Bound

There is a number that nature respects and no principle has yet earned. Two parties, each choosing between two measurements with two outcomes, can correlate their results up to a strength the Clauser-Horne-Shimony-Holt ledger records as S. Classical physics — any local, realistic bookkeeping — caps the ledger at S = 2. Quantum mechanics permits S up to 2√2 ≈ 2.828, Tsirelson's bound, and not a hair more. Pure logic permits 4: the Popescu-Rohrlich box, a hypothetical device that violates no rule of relativity — it cannot signal — and still correlates at the algebraic maximum. So the world sits at 2.828, between the 2 it could have kept and the 4 it could have spent, and the question "Why there?" is one of the deepest open accounts in the foundations of physics. This paper runs my ledger's standard instrument over that account: a census. Every principal principle that has been offered as the reason for the bound is entered in the table, its claim stated at full strength, and its price read off — what it actually proves, and what it merely assumes. The findings: no-signaling alone fails by the full width of the gap; nontrivial communication complexity prices a bound at 3.27, not 2.83; information causality recovers 2√2 exactly, but only in the limit of its own protocol, only on the CHSH face, and only by assuming itself and its information calculus; macroscopic locality recovers 2√2 exactly at the CHSH face, while provably overshooting the quantum set everywhere else; local orthogonality, the census's most instructive failure, provably stops above the quantum set even with infinitely many copies; and quantum mechanics itself, the one entry that prints the number as a theorem, prints it from a formalism — tensor products and the Born rule — that assumes the structure whose strength was the question. The number is fenced on three sides and owned by none. Grade: THE BOUND IS SURROUNDED, NOT DERIVED. This paper stands outside my corpus's vacuum ledger; it neither spends that ledger nor repairs it.