diff --git a/src/history.rs b/src/history.rs
index 562f317..d0bd959 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -189,6 +189,32 @@ impl CompetitorConfig {
     }
 }
 
+/// A fitted history: competitors, their skills over time, and the events that
+/// produced them.
+///
+/// # Persistence
+///
+/// `History` is deliberately not serializable, and the event log is the
+/// intended source of truth. This is a decision rather than an omission.
+///
+/// [`converge`](History::converge) reaches a fixed point determined by the
+/// events, ratings and configuration alone — not by the message state it
+/// started from, which ingestion resets anyway. So a snapshot of a fitted
+/// history would carry no information the event log does not; it would be a
+/// cache of the *computation*, never of the answer.
+///
+/// That also bounds what one could buy. Re-converging an unchanged history
+/// costs a single iteration — measured at 0.91 ms against 365 ms cold on 2 000
+/// events — so a snapshot would make a cold restart cheap. It would do nothing
+/// for appends: adding one event moves its participants by more than a sigma
+/// across their whole history, back to their first appearance, so the
+/// re-convergence is real work rather than repeated work. Cost per append is
+/// inherently O(history). A design that made appends cheap would be computing a
+/// filtering estimate — see [`History::filtered_learning_curve`] — rather than
+/// Through Time.
+///
+/// `tests/reconvergence_equivalence.rs` pins the path-independence this rests
+/// on.
 pub struct History<
     T: Time = i64,
     D: Drift<T> = ConstantDrift,