Three Axioms for Reality: Cost, Death, Memory

We show that three pre-geometric axioms (additive cost, obligatory dissipation, barycentric inheritance) generate a theorem chain yielding 3+1 Lorentzian geometry and an emergent wave equation, with no assumed spatial, temporal, or metric structure. The exponent in the beyond-GR viability cost is uniquely determined by transfer-naturality of the canonical inheritance coordinate. Key numerical signatures: fixed-point uniqueness r = 1.0000 under exact equalization; backbone fraction f_bb = 0.94 ± 0.002 (d = 3); volume doubling C_D ≈ 6.5; bridge-free topological threshold at f_bb ≥ 0.70; lattice geometric constant J₁/λ₀ = 0.080; UV gap frequency ω* = 1.15 (CV = 0.9%); inter-mode coupling ratio 0.88; death-hazard exponent α_Φ = 1.08 ± 0.06 (|r| > 0.90, 3/3 seeds); dual irreversibility arrows 26/29 directional consistency with cross-correlation r = +0.13.