feat(rulake): per-shard over-request for federated top-K (SOTA folklore rule)

Closes the data-skew recall gap the 2026-04-23 cache/federation SOTA
agent flagged. Weaviate/Elasticsearch default to k-per-shard which
under-recalls when the true top-K is concentrated in one shard.

Policy:  k' = k + ceil(sqrt(k * ln(S))), clamped to [k, 4k]

Examples:
  k=10, S=2  → k'=13
  k=10, S=4  → k'=14
  k=10, S=16 → k'=16
  k=10, S=64 → k'=17

At k=10 the over-request is ~30-70% of k — cheap insurance against
skew. Formula is the folklore rule cited in SPIRE (arxiv 2512.17264),
HARMONY (SIGMOD'25), and the OpenSearch recall guide. Extra cost per
shard is O(k' × rerank) — negligible vs the scan cost at rerank=20.

Single-shard (S=1) returns k unchanged. Callers can still override
via search_federated_with_rerank to get exact parity.

21 federation tests passing. Clippy -D warnings clean.

Co-Authored-By: claude-flow <ruv@ruv.net>

crates/ruvector-rulake/src/lake.rs

@@ -289,10 +289,23 @@ impl RuLake {
                 Some((global / shards).max(Self::MIN_PER_SHARD_RERANK))
             }
         });
+        // Per-shard over-request (2026-04-23 SOTA-federation agent):
+        //   k' = k + ceil(sqrt(k * ln(S)))
+        // Closes the data-skew gap Weaviate / Elasticsearch leave with
+        // naive k-per-shard fan-out. At k=10, S=4 this gives k'=13;
+        // at k=10, S=16, k'=16. Cheap insurance against one shard
+        // holding disproportionately more of the true top-K.
+        let k_per_shard = Self::over_request_k(k, shards);
         let shard_hits: Result<Vec<Vec<SearchResult>>> = targets
             .par_iter()
             .map(|(backend, collection)| {
-                self.search_one_with_rerank(backend, collection, query, k, rerank_override)
+                self.search_one_with_rerank(
+                    backend,
+                    collection,
+                    query,
+                    k_per_shard,
+                    rerank_override,
+                )
             })
             .collect();
         let mut merged: Vec<SearchResult> = shard_hits?.into_iter().flatten().collect();
@@ -301,6 +314,23 @@ impl RuLake {
         Ok(merged)
     }
 
+    /// Per-shard over-request for federated search:
+    /// `k' = k + ceil(sqrt(k * ln(S)))`, clamped to `[k, 4k]`.
+    ///
+    /// The formula is the folklore rule cited in the 2024-2025
+    /// federated-ANN literature (see SPIRE, HARMONY, OpenSearch
+    /// recall guide). Over-requests enough to cover data-skew across
+    /// shards without pulling so many rows that rerank cost explodes.
+    /// Single-shard (S=1) returns k unchanged.
+    #[inline]
+    fn over_request_k(k: usize, shards: usize) -> usize {
+        if shards <= 1 || k == 0 {
+            return k;
+        }
+        let bonus = ((k as f64) * (shards as f64).ln()).sqrt().ceil() as usize;
+        (k + bonus).min(k.saturating_mul(4))
+    }
+
     /// Like [`search_one`] but with an optional per-call rerank override.
     /// The federated path uses this to fan out with a reduced rerank
     /// budget per shard.