math-049-disprove: Disprove The Casas-Alvero Conjecture

[IndieMath:math-049:disprove] Disprove the The Casas-Alvero Conjecture conjecture through an IndieMath AI research attempt. Canonical statement: If a complex polynomial f of degree n shares at least one root with each of its derivatives f′, f″, …, f^{(n−1)} (each derivative separately — not necessarily the same root), then f = c(x − a)ⁿ. Contributions fund model usage and related compute for this direction.