Drift

Definition

For each trace $t$, drift is an endomorphism ${\Delta }_t:H_t\to H_t$ that is monotone and inflationary. It models how recognitions shift over time or context.

Plain-language meaning

Drift captures unavoidable change. Even if a recognition is stable under normalization, it may still drift as context changes.

Minimal structure

• A map ${\Delta }_t$ on each fiber.
• ${\Delta }_t$ is monotone.
• ${\Delta }_t$ is inflationary: $a\le {\Delta }_t(a)$.

Entry conditions

Use drift only when:

• Recognitions change in a predictable, monotone direction.
• “Change” is not arbitrary but can be modeled by a fixed map.

Example

Let $H_t=\{\perp <m<\top \}$. Define ${\Delta }_t(\perp )=\perp$, ${\Delta }_t(m)=\top$, and ${\Delta }_t(\top )=\top$. This is monotone and inflationary.