Recognition Science Quantum Gravity

We present the complete Recognition Science program for quantum gravity as a physics program: a discrete, parameter-free framework in which an information-bearing substrate carries a uniquely forced comparison cost, the gravitational action generalizes the Regge action by evaluating the forced cost gradient on deficit angles, quantum amplitudes arise from an eight-tick register that forces complexification, and the cosmological sector produces a single falsifiable dark-energy point with no tunable coefficient. Every major result is derived at physics level in this paper. A separate evidence layer, a Lean 4 formalization with a machine-checked flag ledger, is reported alongside each result as a status tier: THEOREM where a kernel-checked proof exists (with module and theorem name), MEASURED where the evidence is numerical with convergence tables, DERIVED-UNFORMALIZED where the derivation is in this paper and the formalization is pending, MODEL where a named constitutive premise enters, and OPEN where a gap remains, in several cases with a machine-checked blocker theorem that names the exact missing premise. The classical chapter is anchored by a new continuum-limit theorem: the finite Regge transverse-traceless Bloch symbol per momentum squared converges to the raw TT moment (canonicalFiniteH_div_momentumNormSq_tendsto), with the isotropy value −1/4 established numerically on fourteen preregistered directions and open analytically. The cosmology chapter states the discriminating prediction (w₀, w_a) = (−1 + φ⁻⁴J(φ), −φ⁻⁴J(φ)) under a frozen preregistered observational gate. The closing chapter reports what no other quantum gravity program offers: a kernel-checked map of exactly what remains unproved, in which each of seven benchmark flags is either open or blocked by a certified theorem naming its missing premise, and the master self-audit full_theory_not_yet_closed remains provable until every flag flips.