Gate deviation = δ made observable

Parent: gate-theory

Normally δ (how far off-track you are) is invisible — that's how drift happens silently (drift-is-world-wandering). A gate is the instrument that makes δ observable: crossing out of its δ-ball fires the alarm, turning an invisible zero into a measured, positive δ.

A single deviation is ambiguous — read its size and trend:

• δ bounded / within the band → you're spending slack, still inside the convergence cone: recoverable (k<1).
• δ over threshold / monotonically growing → you've left the reliable success set: divergence (k≥1), the process is going the wrong way.

The deviation reading = how little this step contracted; a growing deviation = local k≥1 = diverging. δ bounded ⟺ k<1 ⟺ converging.

So a deviation is a conflict signal → trigger backjump / re-plan / abort, exactly the CDCL response. And the threshold that classifies slack-vs-divergence is the P×C budget: within budget = tolerable drift, over budget = abort.

This is why gates are placed at the necessary waypoints (gates-are-necessary-conditions): a checkpoint on a genuine invariant fires the moment you leave the success cone — the earliest possible warning, before the whole budget is burned.

Ties: recursion-convergence-contraction (k = verification quality), conflict-learning-and-backjumping (the response), relaxation.