The Primordial Split: Why the Universe Cannot Remain at Unity

We prove that the initial condition of the universe, the mechanism of structure genesis, and the amplitude of the first perturbation are all uniquely forced by the Recognition Composition Law (RCL) with zero free parameters. The argument has four parts. (1) The Past Theorem: the unique zero-cost configuration of the discrete ledger is the unity state (all entries xᵢ = 1, total defect J(xᵢ) = 0). (2) CoEternal exclusion: the unity state carries no Z-patterns (conserved topological invariants), so Z-patterns cannot be co-eternal with the ledger. (3) Split-from-vacuum is forced: the only remaining genesis mechanism is symmetric pair creation (z, −z) conserving total Z = 0. (4) The first split is necessary: the unity state is recognition-dead (no active bonds, no recognition events), but Recognition Forcing (T4) requires that recognition occur, so departure from unity is forced, not contingent. The split amplitude is set by the coherence quantum E_coh = φ⁻⁵, where φ = (1 + √5)/2. This extends the forcing chain to T12. All theorems are machine-verified in Lean 4 with zero sorry.