Information-Zero Periodic Random-Elimination Chains: Schedule Order, Residue-Class Limits, and Guarded Scaling

Abstract

Braverman, Etesami, and Mossel (2008, Conjecture 1) predicted an R^(d/r) balance scale when d of every r rounds are daytime actions. For the declared periodic random-elimination executor with weak-majority stopping—not for the unrestricted partial-information game—we settle this exponent for every fixed mixed period. Explicit finite certificates give p <= 4r eta, p^r <= (4r)^d eta^r, and eta/(eta+6r) <= p under the corresponding scale inequalities, and their sequence closures give the off-critical zero/one laws. On the critical scale, the exponent depends only on (r,d), while order survives in the first denominator correction and exact stopped rankings. Every population residue admits a nontrivial subsequential limit. Alternating orders have distinct parity-indexed Gaussian profiles; the non-cyclic period DDNN has four quarter-Gamma profiles and differs from DNDN. Endpoint schedules are exact. For rational guard rate g, protection changes the exponent to 1/(2-g), with matching zero/one regimes for 0 <= g < 1 and the exact profile min(1,2 eta) at g=1. These conclusions concern the declared information-zero count chain. The finite scaling certificates and listed model transports are machine checked. The four-profile theorem has a conventional analytic proof; Lean checks its discrete and domination kernels but not the final four-residue composition.