# Verification report for version 2

The four-page English preprint Cube Ranks of Monomials proves the complete actual cube-rank classification for monomials over C and R. It strengthens version 1 under the same Zenodo concept DOI; the full source Problem C, which asks for all k >= 3, is not closed.

The complete proof and detailed originating-researcher self-audit are included in reproducibility/. The critical new step restricts a hypothetical three-cube expression to an exponent-one coordinate hyperplane and differentiates normally. The Fermat plane curve forces a common polynomial factor of degree d, whose square cannot divide the complementary monomial when o > d. The argument allows arbitrary homogeneous summands, their base loci, zero components, common factors and extra ambient variables.

The standard-library checker verifies the exact three- and four-cube identities, the symbolic coefficient-of-first-order derivative formula, and exponent arithmetic on all 11,663 positive partitions in degrees 3d for 1 <= d <= 10. It constructs UV^2 and ABC witnesses where required and independently enumerates square-divisor degrees in the smallest cases. A nontrivial three-cube identity with a cube target is retained as a control against an overbroad dependence claim.

Normal and optimized Python each pass 83,258 conditions with identical reports. Deliberately replacing the polarization coefficient 24 by 25 or moving the strict boundary o > d to o >= d is rejected. The portable package and extracted ZIP are replayed before publication. These finite calculations do not prove the geometric lemma or replace the written universal argument.

The saved source compiled with the desktop LaTeX compiler and Tectonic. All four exported PDF pages were visually inspected, including equations, author footnote and bibliography. No layout defects or unresolved references were found.

Classical upper bounds and rank-two exclusion are attributed to Carlini-Oneto; the grouping capacity method is also credited to Lundqvist-Oneto-Reznick-Shapiro. The genus-one and Riemann-Hurwitz inputs are standard. The recorded search did not locate the complete parity classification, but is not an absolute-priority certification. The inaccessible full text of a related 2026 four-form identity paper is explicitly distinguished from its inspected official abstract.

This is AI-assisted, self-audited, unrefereed work. No independent human review or proof-assistant verification is claimed. The original v1 source, PDF, deposit and hash-bound acceptance are preserved.