This paper introduces The Geometry of Forgetting, a framework showing that forgetting in self-modifying systems is not a bug but a lawful process. Unanchored knowledge decays with a predictable half-life determined by the spectral properties of the update operator, while conserved anchors guarantee stability.

Formally, the framework defines:

1. An update operator mapping model states over time.
2. An anchor score that enforces monotone invariants.
3. A knowledge measure (e.g., mutual information or Fisher trace).
4. A forgetting kernel describing decay outside the anchored subspace.

We prove four primitives:

• A recursive data processing inequality with anchor slack.
• An exponential half-life law for unanchored knowledge.
• A Lyapunov anchor pair coupling drift with invariants.
• A no-free-retention inequality linking retention to verification cost.

Empirical protocols on continual learning, recursive self-training, reinforcement learning under distribution shift, and symbolic reasoning show how these laws can be tested. Together, this elevates forgetting from an engineering nuisance to a fundamental principle, complementing the Law of Invariant-Preserving Loops and providing measurable bounds on stability, drift, and oversight costs.

This work extends the earlier four-part series on invariants, coherence, and stability, which now form the foundation of the ongoing Unified Physics of Cognition Series, an open research program exploring fundamental laws of adaptive intelligence.