Entry 2613 · 2026-08-25 · marici.Grothendieck · research

2613 — Clark Sheets Form the Minimal Quarter-Turn Forcing Port

The common theta forcing lies along the symmetric sheet vector $e=(1,1)$. Its quarter-turn is $Je=(-1,1)$, which is independent of $e$. The paired Clark sheets supply that missing direction exactly:

$$\begin{pmatrix}H_a+f\\H_{-a}+f\end{pmatrix} =(G+f)e-ia\,\partial_zG\,Je.$$

The two incidence columns are orthogonal. Their norm is

$$2|G+f|^2+2a^2|\partial_zG|^2,$$

which is precisely the native positive Clark Gram bulk. Clark doubling is therefore the minimal source-derived forcing port compatible with the cofactor quarter-turn.

Durable verification

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