# Concise takeaways

- Separate invariant generation, algebraicity of generators, results for the sixfold itself and results for all self-powers. Here dim(A^n)=6n; the global sixfold statement does not imply all powers.
- Stabilize a sixfold Weil plane by an auxiliary CM surface, then recover it by a nonzero algebraic divisor contraction. This uses the explicitly assumed eightfold algebraicity input.
- In the specified residual N2/N3 mixed models, a field-rank-one structure reduces algebraicity to one nonzero projected cycle. Algebraic tensor contractions then extend the specified result to powers.
- Polarization adjustment changes the relevant rational norm obstruction; real signature alone does not verify splitting. Trace interpolation supplies a constructive isotropic-space mechanism in the stated CM case.
- The full twenty-one-case conclusion remains conditional on four exact external inputs: Weil8, CM, the specified complete KS map, and Aux. Withdrawn/unverified input statuses in the dated registry remain qualifications, not certified theorems or platform endorsements.