Quantum Gravity from Ledger Accounting: A Machine-Checked Theory with No Fitted Constants and Its Three Dark-Sector Numbers

A theory of gravity is built from double-entry bookkeeping: a ledger of integer postings whose recognition cost is J(x) = (1/2)(x + x^-1) - 1. Impossibility theorems first fix what such a substrate cannot supply, and each names the premise it forces; on exactly those premises the theory is assembled, and the classical face is recovered at stated scope, the weak-field Einstein-Hilbert action and the Dirac constraint algebra among the recoveries, with no fitted dimensionless constant anywhere. The same machinery yields three parameter-free dark-sector numbers: the two measured Hubble constants must stand in the exact ratio 13/12 (73.02 from 67.4, measured 73.04 +/- 1.04); the dark-energy equation of state today is w_0 = -1 + phi^-4 J(phi) ~= -0.9828 on the thawing line w_0 + w_a = -1, registered ahead of the data that will decide it; and the cold dark-matter fraction is sin(pi/12) + phi^-4/24 = 0.2648981, 0.09 sigma from the Planck value. Two of the three are retrodictions and are scored as such. Every mathematical claim is machine-checked in an open library; every physical identification is one of twenty explicit premises, each carried with its falsifier.