Hilbert 16 degree 8, 2026-09-12

Number of nonempty degree-eight T-curve schemes ≥ 2,394.

Nine schemes outside the 2,385 baseline (paper 2,367 + seventeen parent additions + q8's ⟨3 ⊔ 1⟨3⟩ ⊔ 1⟨12⟩⟩):

⟨3 ⊔ 1⟨5⟩ ⊔ 1⟨10⟩⟩, ⟨5 ⊔ 1⟨2⟩ ⊔ 1⟨3⟩ ⊔ 1⟨7⟩⟩, ⟨5 ⊔ 1⟨1⟩ ⊔ 1⟨2⟩ ⊔ 1⟨9⟩⟩, ⟨4 ⊔ 1⟨1⟩ ⊔ 1⟨2⟩ ⊔ 1⟨9⟩⟩, ⟨3 ⊔ 1⟨1⟩ ⊔ 1⟨2⟩ ⊔ 1⟨9⟩⟩, ⟨2 ⊔ 1⟨1⟩ ⊔ 1⟨2⟩ ⊔ 1⟨9⟩⟩, ⟨4 ⊔ 1⟨1⟩ ⊔ 1⟨3⟩ ⊔ 1⟨9⟩⟩, ⟨3 ⊔ 1⟨1⟩ ⊔ 1⟨3⟩ ⊔ 1⟨9⟩⟩, ⟨2 ⊔ 1⟨1⟩ ⊔ 1⟨3⟩ ⊔ 1⟨9⟩⟩.

The leftover 1,108 balls of the q8 one-flip radius-three plan all finished (16,870,408 evaluations) and produced five of the nine. One-flip balls of those five certificates produced the other four (115 balls). Twenty-one extra flips of the q8 certificate finished with nothing further. Neither open (19,3) deep nest is decided.

Replay: sh problems/hilbert16-degree-8/compute/q9/run_all.sh. Claim: problems/hilbert16-degree-8/compute/q9/CLAIM.md.