How the Line governs the Residue.
The Kav (Line) is Eyn Sof's perfect action entering the contracted space — looking down into the Residue, executing perfect action that we receive only within limits.
The Tzimtzum has opened the chalal; the Reshimu fills it. Now what acts? Op. 27 introduces the Kav — the line of light that Eyn Sof draws into the chalal — and specifies its operational role. The Kav governs the Residue. Eyn Sof, through the Kav, acts perfectly within the contracted space, but the action as we receive it is bounded.
The imagery is precise. After the Tzimtzum, with the chalal opened and the Reshimu present, Eyn Sof draws a line of light from above into the chalal — penetrating the contracted space without filling it (which would undo the Tzimtzum). The Kav is therefore partial: a measured presence within the contracted space, not the full encompassing limitlessness.
What does the Kav do? Eyn Sof, through it, governs the Residue. The verbs Op. 27 uses are striking: looking down into the Residue, executing perfect action. He has not become distant from the cosmos; He is active governor through the Kav. The action is perfect — it has all the precision of His Will. But what we receive of the action is within limits — bounded by the Tzimtzum's contraction.
This is the cosmogonic seed of every later operational claim. When the book later says that Eyn Sof's mercy descends through the Beard's thirteen Tikkunim (Op. 93–108), or that the cycle of governance runs through Zeir Anpin (Z"A)'s CHaDaR (Op. 116), or that the Coupling order has eight stages (Op. 138) — every one of these is Kav-action received within limits. The structural framework is set in Op. 27.
Op. 28 will say the Kav divides into Inner and Encompassing Light within the Sefirot. Op. 29 will say the Kav shines through a garb (the cosmogonic seed of hitlabshut, the clothing-doctrine of the second half of the book). And Op. 64's MaH (gematria 45) = Line, BaN (gematria 52) = Residue* identification settles the Kav's identity as the active partner of the cosmogonic-operational pair that runs through the rest of the book.