A Rolle word records the derivative orders of the roots of a real-rooted polynomial and all its
nonconstant derivatives, listed from left to right
(Shapiro and Shapiro 2012, Novikov 2026). For a polynomial 
of polynomial
degree 
, require 
distinct real roots and no common
root of different nonconstant derivatives,
including 
itself. Replace each root of 
by the label 
. The word has length 
,
with label 
appearing 
times.
Rolle's theorem imposes interlacing between consecutive derivative orders. A formal interlacing word need not be realizable by a polynomial. In degree 6 there are 33592 formal words, and Novikov (2026) reports exactly 2706 realizable words, with a word and its reversal counted separately. The classification uses integer realization certificates and a chain of 53 exclusion stages. The author states that the complete mathematical proof chain has not received an independent human audit. Most of the mathematics, checking code, and certificates were generated with ChatGPT under the author's direction (Novikov 2026).
