Gravitation from the Ledger: Full-Coefficient Derivations from Newton to Hulse–Taylor and the Cosmological Constant, Without a Time Dimension, in Doubly-Folded Cubic Geometry

Time, in its experimental content, is not a dimension but measurement information — the counting of events. Working on the ground of doubly-folded cubic geometry and using only discrete derivative–integral operators (Δ/Δn, ∂/∂r, ∫dr), this paper shows that the counter–stepledger formulation derives gravitation and the cosmological constant with full coefficients and without a time dimension. (i) Velocity dilation follows from the per-tick step budget; the quadratic-sum rule is no postulate — identical planckons and the von Ignatowski theorem fix the unique conserved norm; the closed form f = √(1−2W/c²) is the same budget applied to the escape flow, valid to all orders. (ii) The two-column reading (counter + step) yields the full coefficients of light deflection, the Shapiro delay and GPS; the counter-only reading gives half coefficients and contradicts observation (Theorem 1). (iii) The counting-action principle — a free step sequence extremizes the internal count — closes the static strong field: perihelion precession 42.98″/century, photon sphere 3Rs/2, ISCO 3Rs. (iv) The radiative regime is derived from the ledger: monopole and dipole channels are closed by record and momentum conservation; the two polarizations count the two transverse folding axes; the angular average 2/5 gives the quadrupole flux with coefficient G/5c⁵; the 1/4 in the 32πG norm is the same period-2² count as the 1/4 of the area law; for the Hulse–Taylor decay, observed/predicted = 0.9983 ± 0.0016 is found. (v) Saturation (flatness) is derived from period-2 counting; the cosmological constant is locked by a single observational input (H₀): Λ𝓁P² = 3ΩDE/nH² = 2.85×10⁻¹²², ΩDE = (2/3)²·(nH/n*)14/9 = 0.6860 (+0.18σ), t₀ = 13.82 Gyr; if the local-ladder H₀ value is confirmed, the prediction fails at 10.9σ. The volume-scaled mode sum of field theory errs by roughly 10¹²² because it skips the recording ceiling. The limitation is recorded honestly: the single remaining open channel is the cell-base interior and horizon micro-structure.