diff --git a/src/movegen.rs b/src/movegen.rs
index 2dce6da..7794b22 100644
--- a/src/movegen.rs
+++ b/src/movegen.rs
@@ -626,24 +626,41 @@ fn gen_classic_cross_set<'a, N: kwg::Node, L: kwg::Node>(
         let mut p = 1;
         let mut score = 0i32;
         let mut last_empty = len;
+        // Within each tile group (contiguous nonempty tiles), the seek chain
+        // starts from p=1. If tiles from the right edge of the group haven't
+        // changed AND the group boundary is in the same place, the cached
+        // seek results are valid.
+        let mut chain_valid = true; // right edge is always a valid group start
         for j in (0..len).rev() {
             let b = board_strip[j as usize];
             if b != 0 {
                 let b_letter = b & 0x7f;
-                p = kwg.seek(p, b_letter);
-                score += alphabet.score(b) as i32;
-                cross_set_buffer[j as usize] = CrossSetComputation {
-                    score,
-                    b_letter,
-                    end_range: last_empty,
-                    p,
-                };
+                if chain_valid && cross_set_buffer[j as usize].b_letter == b_letter {
+                    // Same tile, chain unbroken — use cached seek result.
+                    p = cross_set_buffer[j as usize].p;
+                    score = cross_set_buffer[j as usize].score;
+                } else {
+                    chain_valid = false;
+                    p = kwg.seek(p, b_letter);
+                    score += alphabet.score(b) as i32;
+                    cross_set_buffer[j as usize] = CrossSetComputation {
+                        score,
+                        b_letter,
+                        end_range: last_empty,
+                        p,
+                    };
+                }
+                // Always update end_range (depends on current scan state, not cached).
+                cross_set_buffer[j as usize].end_range = last_empty;
                 last_nonempty = j;
             } else {
                 // empty square, reset
                 p = 1; // cumulative gaddag traversal results
                 score = 0; // cumulative face-value score
                 last_empty = j; // last seen empty square
+                // Chain is valid at this group boundary only if the cached
+                // state was also empty here (group boundary hasn't moved).
+                chain_valid = cross_set_buffer[j as usize].b_letter == 0;
                 cross_set_buffer[j as usize].b_letter = 0;
                 cross_set_buffer[j as usize].end_range = last_nonempty;
             }
@@ -982,11 +999,11 @@ fn gen_cross_set<'a, N: kwg::Node, L: kwg::Node>(
 // Non-adjacent empty squares get !0u64 (all bits, no constraint).
 fn gen_extension_sets<N: kwg::Node>(
     kwg: &kwg::Kwg<N>,
-    board_strip: &[u8],
+    cross_set_buffer: &[CrossSetComputation],
     left_extension_sets: &mut [u64],
     right_extension_sets: &mut [u64],
 ) {
-    let len = board_strip.len();
+    let len = cross_set_buffer.len();
 
     // Collect extension set bits from a GADDAG node's children.
     // Excludes separator (bit 0), then adds blank bit if non-empty.
@@ -1010,33 +1027,31 @@ fn gen_extension_sets<N: kwg::Node>(
         bits | (bits != 0) as u64
     };
 
-    // Single right-to-left pass. For each tile group, one GADDAG traversal
-    // yields both left extension (children of p) and right extension
-    // (children of seek(p, separator)).
-    let mut p: i32 = 1;
+    // Read GADDAG state (p) from cross_set_buffer instead of recomputing.
+    // The cross set reverse scan already traversed the same tiles in the
+    // same order, so cross_set_buffer[j].p is the GADDAG state at each
+    // nonempty position.
     let mut group_right_empty: usize = len;
     for j in (0..len).rev() {
-        if board_strip[j] != 0 {
-            if j + 1 == len || board_strip[j + 1] == 0 {
+        if cross_set_buffer[j].b_letter != 0 {
+            if j + 1 == len || cross_set_buffer[j + 1].b_letter == 0 {
                 group_right_empty = j + 1;
-                p = 1;
             }
-            p = kwg.seek(p, board_strip[j] & 0x7f);
         } else {
-            if j + 1 < len && board_strip[j + 1] != 0 {
+            if j + 1 < len && cross_set_buffer[j + 1].b_letter != 0 {
                 // Empty square immediately left of a tile group.
-                // p = GADDAG state after traversing entire group right-to-left.
+                let p = cross_set_buffer[j + 1].p;
                 left_extension_sets[j] = collect_bits(kwg, p);
                 if group_right_empty < len {
                     right_extension_sets[group_right_empty] =
                         collect_bits(kwg, if p > 0 { kwg.seek(p, 0) } else { -1 });
                 }
             }
-            p = 1;
         }
     }
     // Handle group starting at position 0.
-    if !board_strip.is_empty() && board_strip[0] != 0 && group_right_empty < len {
+    if len > 0 && cross_set_buffer[0].b_letter != 0 && group_right_empty < len {
+        let p = cross_set_buffer[0].p;
         right_extension_sets[group_right_empty] =
             collect_bits(kwg, if p > 0 { kwg.seek(p, 0) } else { -1 });
     }
@@ -3136,7 +3151,8 @@ fn kurnia_gen_place_moves_iter<
                     .fill(!0u64);
                 gen_extension_sets(
                     board_snapshot.kwg,
-                    &board_snapshot.board_tiles[strip_range_start..strip_range_end],
+                    &working_buffer.cross_set_buffer_for_down_plays
+                        [strip_range_start..strip_range_end],
                     &mut working_buffer.left_extension_set_for_across_plays
                         [strip_range_start..strip_range_end],
                     &mut working_buffer.right_extension_set_for_across_plays
@@ -3162,7 +3178,8 @@ fn kurnia_gen_place_moves_iter<
                     .fill(!0u64);
                 gen_extension_sets(
                     board_snapshot.kwg,
-                    &working_buffer.transposed_board_tiles[strip_range_start..strip_range_end],
+                    &working_buffer.cross_set_buffer_for_across_plays
+                        [strip_range_start..strip_range_end],
                     &mut working_buffer.left_extension_set_for_down_plays
                         [strip_range_start..strip_range_end],
                     &mut working_buffer.right_extension_set_for_down_plays