Three-Index Extremal Auxiliary Functions, Exact Zero Saturation, and the Cubic One-More-Zero Barrier

Constructs an explicit T³-term three-index exponential auxiliary with exactly T³ − 1 consecutive algebraic zeros whose next value is 1 and whose later values are positive complete homogeneous symmetric polynomials; any further real zero or multiplicity would contradict, so dimension matching alone yields no contradiction — the missing bridge is the 'Cubic One-More-Zero Problem'.