diff --git a/crates/pikl-core/src/query/filter.rs b/crates/pikl-core/src/query/filter.rs
new file mode 100644
index 0000000..55bf042
--- /dev/null
+++ b/crates/pikl-core/src/query/filter.rs
@@ -0,0 +1,234 @@
+//! Item filtering. Currently just fuzzy matching via nucleo,
+//! but the [`Filter`] trait is here so we can swap in regex,
+//! exact, or custom strategies later.
+
+use nucleo_matcher::pattern::{CaseMatching, Normalization, Pattern};
+use nucleo_matcher::{Config, Matcher, Utf32String};
+
+/// Trait for incremental filter strategies. Items are pushed
+/// in once, queries are updated, and results are read back
+/// by position. Implementations own their item text and
+/// match state.
+pub trait Filter: Send {
+    /// Notify the filter about a new item. Called once per
+    /// item at insertion time.
+    fn push(&mut self, index: usize, label: &str);
+
+    /// Update the query. Implementations may defer actual
+    /// matching until results are read.
+    fn set_query(&mut self, query: &str);
+
+    /// Number of items matching the current query.
+    fn matched_count(&self) -> usize;
+
+    /// Get the original item index for the nth match
+    /// (sorted by relevance, best first).
+    fn matched_index(&self, match_position: usize) -> Option<usize>;
+}
+
+/// Fuzzy matching powered by nucleo. Smart case, smart
+/// unicode normalization. Results sorted by score, best
+/// match first. Supports incremental narrowing: if the new
+/// query extends the previous one, only items that matched
+/// before are re-scored.
+pub struct FuzzyFilter {
+    matcher: Matcher,
+    items: Vec<(usize, Utf32String)>,
+    last_query: String,
+    results: Vec<(usize, u32)>,
+}
+
+impl Default for FuzzyFilter {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl FuzzyFilter {
+    /// Create a new fuzzy filter with default nucleo config.
+    pub fn new() -> Self {
+        Self {
+            matcher: Matcher::new(Config::DEFAULT),
+            items: Vec::new(),
+            last_query: String::new(),
+            results: Vec::new(),
+        }
+    }
+
+    /// Re-score a set of (index, haystack) pairs against a pattern.
+    fn score_items<'a>(
+        matcher: &mut Matcher,
+        pattern: &Pattern,
+        candidates: impl Iterator<Item = (usize, &'a Utf32String)>,
+    ) -> Vec<(usize, u32)> {
+        let mut matches: Vec<(usize, u32)> = candidates
+            .filter_map(|(idx, haystack)| {
+                pattern
+                    .score(haystack.slice(..), matcher)
+                    .map(|score| (idx, score))
+            })
+            .collect();
+        matches.sort_by(|a, b| b.1.cmp(&a.1));
+        matches
+    }
+}
+
+impl Filter for FuzzyFilter {
+    fn push(&mut self, index: usize, label: &str) {
+        debug_assert_eq!(
+            index,
+            self.items.len(),
+            "FuzzyFilter::push requires sequential indices starting from 0"
+        );
+        let haystack = Utf32String::from(label);
+        self.items.push((index, haystack));
+    }
+
+    fn set_query(&mut self, query: &str) {
+        if query.is_empty() {
+            // Empty query matches everything in insertion order.
+            self.results = self.items.iter().map(|(idx, _)| (*idx, 0)).collect();
+            self.last_query = String::new();
+            return;
+        }
+
+        let pattern = Pattern::parse(query, CaseMatching::Smart, Normalization::Smart);
+
+        // Incremental: if the new query extends the previous one,
+        // only re-score items that already matched.
+        if !self.last_query.is_empty() && query.starts_with(&self.last_query) {
+            let prev_results = std::mem::take(&mut self.results);
+            let candidates = prev_results.into_iter().filter_map(|(idx, _)| {
+                // Items are pushed sequentially (enforced by debug_assert in push),
+                // so idx == position in self.items. Direct index is O(1).
+                self.items.get(idx).map(|(_, h)| (idx, h))
+            });
+            self.results = Self::score_items(&mut self.matcher, &pattern, candidates);
+        } else {
+            let candidates = self.items.iter().map(|(idx, h)| (*idx, h));
+            self.results = Self::score_items(&mut self.matcher, &pattern, candidates);
+        }
+
+        self.last_query = query.to_string();
+    }
+
+    fn matched_count(&self) -> usize {
+        self.results.len()
+    }
+
+    fn matched_index(&self, match_position: usize) -> Option<usize> {
+        self.results.get(match_position).map(|(idx, _)| *idx)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn push_text_items(f: &mut FuzzyFilter, labels: &[&str]) {
+        for (i, label) in labels.iter().enumerate() {
+            f.push(i, label);
+        }
+    }
+
+    #[test]
+    fn empty_query_returns_all() {
+        let mut f = FuzzyFilter::new();
+        push_text_items(&mut f, &["apple", "banana", "cherry"]);
+        f.set_query("");
+        assert_eq!(f.matched_count(), 3);
+        assert_eq!(f.matched_index(0), Some(0));
+        assert_eq!(f.matched_index(1), Some(1));
+        assert_eq!(f.matched_index(2), Some(2));
+    }
+
+    #[test]
+    fn fuzzy_match() {
+        let mut f = FuzzyFilter::new();
+        push_text_items(&mut f, &["apple", "banana", "apricot"]);
+        f.set_query("ap");
+        assert!(f.matched_count() >= 2);
+        let indices: Vec<usize> = (0..f.matched_count())
+            .filter_map(|i| f.matched_index(i))
+            .collect();
+        assert!(indices.contains(&0)); // apple
+        assert!(indices.contains(&2)); // apricot
+    }
+
+    #[test]
+    fn no_matches() {
+        let mut f = FuzzyFilter::new();
+        push_text_items(&mut f, &["apple", "banana"]);
+        f.set_query("xyz");
+        assert_eq!(f.matched_count(), 0);
+    }
+
+    #[test]
+    fn empty_items() {
+        let mut f = FuzzyFilter::new();
+        f.set_query("test");
+        assert_eq!(f.matched_count(), 0);
+    }
+
+    #[test]
+    fn incremental_narrowing() {
+        let mut f = FuzzyFilter::new();
+        push_text_items(&mut f, &["apple", "banana", "apricot", "avocado"]);
+
+        f.set_query("a");
+        let count_a = f.matched_count();
+        assert!(count_a >= 3); // apple, apricot, avocado at minimum
+
+        // Extending the query should narrow results
+        f.set_query("ap");
+        assert!(f.matched_count() <= count_a);
+        assert!(f.matched_count() >= 2); // apple, apricot
+    }
+
+    #[test]
+    fn incremental_narrowing_large_set() {
+        let mut f = FuzzyFilter::new();
+        // Push 1000 items, all starting with "item-"
+        for i in 0..1000 {
+            f.push(i, &format!("item-{i:04}"));
+        }
+
+        f.set_query("item");
+        let count_broad = f.matched_count();
+        assert_eq!(count_broad, 1000);
+
+        // Incremental narrowing: "item-00" should match ~10 items
+        f.set_query("item-00");
+        assert!(f.matched_count() < count_broad);
+        assert!(f.matched_count() >= 10);
+
+        // Further narrowing
+        f.set_query("item-001");
+        assert!(f.matched_count() >= 1);
+    }
+
+    #[test]
+    #[should_panic(expected = "sequential indices")]
+    fn non_sequential_push_panics_in_debug() {
+        let mut f = FuzzyFilter::new();
+        f.push(0, "first");
+        f.push(5, "non-sequential"); // should panic in debug
+    }
+
+    #[test]
+    fn non_incremental_new_query() {
+        let mut f = FuzzyFilter::new();
+        push_text_items(&mut f, &["apple", "banana", "cherry"]);
+
+        f.set_query("ap");
+        assert!(f.matched_count() >= 1);
+
+        // Completely different query, not incremental
+        f.set_query("ban");
+        assert!(f.matched_count() >= 1);
+        let indices: Vec<usize> = (0..f.matched_count())
+            .filter_map(|i| f.matched_index(i))
+            .collect();
+        assert!(indices.contains(&1)); // banana
+    }
+}
diff --git a/crates/pikl-core/src/query/mod.rs b/crates/pikl-core/src/query/mod.rs
new file mode 100644
index 0000000..68b94eb
--- /dev/null
+++ b/crates/pikl-core/src/query/mod.rs
@@ -0,0 +1,2 @@
+pub mod filter;
+pub mod navigation;
diff --git a/crates/pikl-core/src/query/navigation.rs b/crates/pikl-core/src/query/navigation.rs
new file mode 100644
index 0000000..8bbeb7f
--- /dev/null
+++ b/crates/pikl-core/src/query/navigation.rs
@@ -0,0 +1,356 @@
+//! Cursor and scroll state for a list of filtered items.
+//! Pure logic, no rendering, no channels. The menu owns a
+//! [`Viewport`] and calls its methods in response to
+//! movement actions.
+
+/// Tracks cursor position and scroll offset within a
+/// filtered item list. Height comes from the frontend
+/// (terminal rows minus chrome). Filtered count comes
+/// from the filter engine. Everything else is derived.
+pub struct Viewport {
+    cursor: usize,
+    scroll_offset: usize,
+    height: usize,
+    filtered_count: usize,
+}
+
+impl Default for Viewport {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl Viewport {
+    /// Create a viewport with everything zeroed out. Call
+    /// [`set_height`](Self::set_height) and
+    /// [`set_filtered_count`](Self::set_filtered_count) to
+    /// initialize.
+    pub fn new() -> Self {
+        Self {
+            cursor: 0,
+            scroll_offset: 0,
+            height: 0,
+            filtered_count: 0,
+        }
+    }
+
+    /// Current cursor position in the filtered item list.
+    pub fn cursor(&self) -> usize {
+        self.cursor
+    }
+
+    /// Index of the first visible item in the viewport.
+    pub fn scroll_offset(&self) -> usize {
+        self.scroll_offset
+    }
+
+    /// Set the viewport height (visible rows). Clamps cursor
+    /// and scroll offset if they fall outside the new bounds.
+    pub fn set_height(&mut self, height: usize) {
+        self.height = height;
+        self.clamp();
+    }
+
+    /// Update the total number of filtered items. Resets
+    /// cursor and scroll to the top.
+    pub fn set_filtered_count(&mut self, count: usize) {
+        self.filtered_count = count;
+        self.cursor = 0;
+        self.scroll_offset = 0;
+    }
+
+    /// Move cursor up by `n` items. Clamps to the top.
+    /// Scrolls the viewport if the cursor leaves the visible
+    /// range.
+    pub fn move_up(&mut self, n: usize) {
+        if self.cursor > 0 {
+            self.cursor = self.cursor.saturating_sub(n);
+            if self.cursor < self.scroll_offset {
+                self.scroll_offset = self.cursor;
+            }
+        }
+    }
+
+    /// Move cursor down by `n` items. Clamps to the last
+    /// item. Scrolls the viewport if needed.
+    pub fn move_down(&mut self, n: usize) {
+        if self.filtered_count > 0 {
+            self.cursor = (self.cursor + n).min(self.filtered_count - 1);
+            if self.height > 0 && self.cursor >= self.scroll_offset + self.height {
+                self.scroll_offset = self.cursor - self.height + 1;
+            }
+        }
+    }
+
+    /// Jump cursor to the first item and reset scroll.
+    pub fn move_to_top(&mut self) {
+        self.cursor = 0;
+        self.scroll_offset = 0;
+    }
+
+    /// Jump cursor to the last item and scroll to show it.
+    pub fn move_to_bottom(&mut self) {
+        if self.filtered_count > 0 {
+            self.cursor = self.filtered_count - 1;
+            if self.height > 0 && self.cursor >= self.height {
+                self.scroll_offset = self.cursor - self.height + 1;
+            } else {
+                self.scroll_offset = 0;
+            }
+        }
+    }
+
+    /// Move cursor up by `n` pages (viewport height each).
+    /// Clamps to the top of the list.
+    pub fn page_up(&mut self, n: usize) {
+        if self.height == 0 {
+            return;
+        }
+        let distance = self.height.saturating_mul(n);
+        self.cursor = self.cursor.saturating_sub(distance);
+        if self.cursor < self.scroll_offset {
+            self.scroll_offset = self.cursor;
+        }
+    }
+
+    /// Move cursor down by `n` pages (viewport height each).
+    /// Clamps to the last item.
+    pub fn page_down(&mut self, n: usize) {
+        if self.height == 0 || self.filtered_count == 0 {
+            return;
+        }
+        let distance = self.height.saturating_mul(n);
+        self.cursor = (self.cursor + distance).min(self.filtered_count - 1);
+        if self.cursor >= self.scroll_offset + self.height {
+            self.scroll_offset = self.cursor - self.height + 1;
+        }
+    }
+
+    /// Range of indices into the filtered list that are
+    /// currently visible. Returns `0..0` if height or count
+    /// is zero.
+    pub fn visible_range(&self) -> std::ops::Range<usize> {
+        if self.height == 0 || self.filtered_count == 0 {
+            return 0..0;
+        }
+        let end = (self.scroll_offset + self.height).min(self.filtered_count);
+        self.scroll_offset..end
+    }
+
+    /// Clamp cursor and scroll offset to valid positions after
+    /// a height or count change.
+    fn clamp(&mut self) {
+        if self.filtered_count == 0 {
+            self.cursor = 0;
+            self.scroll_offset = 0;
+            return;
+        }
+        if self.cursor >= self.filtered_count {
+            self.cursor = self.filtered_count - 1;
+        }
+        if self.height > 0 && self.cursor >= self.scroll_offset + self.height {
+            self.scroll_offset = self.cursor - self.height + 1;
+        }
+        if self.cursor < self.scroll_offset {
+            self.scroll_offset = self.cursor;
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn viewport(height: usize, count: usize) -> Viewport {
+        let mut v = Viewport::new();
+        v.set_height(height);
+        v.set_filtered_count(count);
+        v
+    }
+
+    #[test]
+    fn initial_state() {
+        let v = viewport(10, 20);
+        assert_eq!(v.cursor(), 0);
+        assert_eq!(v.scroll_offset(), 0);
+        assert_eq!(v.visible_range(), 0..10);
+    }
+
+    #[test]
+    fn move_down_basic() {
+        let mut v = viewport(5, 10);
+        v.move_down(1);
+        assert_eq!(v.cursor(), 1);
+        assert_eq!(v.scroll_offset(), 0);
+    }
+
+    #[test]
+    fn move_down_scrolls() {
+        let mut v = viewport(3, 10);
+        for _ in 0..4 {
+            v.move_down(1);
+        }
+        assert_eq!(v.cursor(), 4);
+        assert_eq!(v.scroll_offset(), 2);
+        assert_eq!(v.visible_range(), 2..5);
+    }
+
+    #[test]
+    fn move_down_at_bottom() {
+        let mut v = viewport(5, 3);
+        v.move_down(1);
+        v.move_down(1);
+        v.move_down(1); // should be no-op
+        assert_eq!(v.cursor(), 2);
+    }
+
+    #[test]
+    fn move_up_basic() {
+        let mut v = viewport(5, 10);
+        v.move_down(1);
+        v.move_down(1);
+        v.move_up(1);
+        assert_eq!(v.cursor(), 1);
+    }
+
+    #[test]
+    fn move_up_at_top() {
+        let mut v = viewport(5, 10);
+        v.move_up(1); // no-op
+        assert_eq!(v.cursor(), 0);
+    }
+
+    #[test]
+    fn move_up_scrolls() {
+        let mut v = viewport(3, 10);
+        // Go down to trigger scroll
+        for _ in 0..5 {
+            v.move_down(1);
+        }
+        assert_eq!(v.scroll_offset(), 3);
+        // Now go back up past scroll offset
+        for _ in 0..3 {
+            v.move_up(1);
+        }
+        assert_eq!(v.cursor(), 2);
+        assert_eq!(v.scroll_offset(), 2);
+    }
+
+    #[test]
+    fn move_to_top() {
+        let mut v = viewport(5, 20);
+        for _ in 0..10 {
+            v.move_down(1);
+        }
+        v.move_to_top();
+        assert_eq!(v.cursor(), 0);
+        assert_eq!(v.scroll_offset(), 0);
+    }
+
+    #[test]
+    fn move_to_bottom() {
+        let mut v = viewport(5, 20);
+        v.move_to_bottom();
+        assert_eq!(v.cursor(), 19);
+        assert_eq!(v.scroll_offset(), 15);
+    }
+
+    #[test]
+    fn move_to_bottom_small_list() {
+        let mut v = viewport(10, 3);
+        v.move_to_bottom();
+        assert_eq!(v.cursor(), 2);
+        assert_eq!(v.scroll_offset(), 0);
+    }
+
+    #[test]
+    fn page_down() {
+        let mut v = viewport(5, 20);
+        v.page_down(1);
+        assert_eq!(v.cursor(), 5);
+        assert_eq!(v.scroll_offset(), 1);
+    }
+
+    #[test]
+    fn page_down_near_end() {
+        let mut v = viewport(5, 8);
+        v.page_down(1);
+        assert_eq!(v.cursor(), 5);
+        v.page_down(1);
+        assert_eq!(v.cursor(), 7); // clamped to last item
+    }
+
+    #[test]
+    fn page_up() {
+        let mut v = viewport(5, 20);
+        // Go to middle
+        for _ in 0..3 {
+            v.page_down(1);
+        }
+        let cursor_before = v.cursor();
+        v.page_up(1);
+        assert_eq!(v.cursor(), cursor_before - 5);
+    }
+
+    #[test]
+    fn page_up_near_top() {
+        let mut v = viewport(5, 20);
+        v.page_down(1);
+        v.page_up(1);
+        assert_eq!(v.cursor(), 0);
+    }
+
+    #[test]
+    fn empty_list() {
+        let v = viewport(10, 0);
+        assert_eq!(v.cursor(), 0);
+        assert_eq!(v.visible_range(), 0..0);
+    }
+
+    #[test]
+    fn empty_list_movement() {
+        let mut v = viewport(10, 0);
+        v.move_down(1);
+        v.move_up(1);
+        v.page_down(1);
+        v.page_up(1);
+        v.move_to_top();
+        v.move_to_bottom();
+        assert_eq!(v.cursor(), 0);
+    }
+
+    #[test]
+    fn zero_height() {
+        let v = viewport(0, 10);
+        assert_eq!(v.visible_range(), 0..0);
+    }
+
+    #[test]
+    fn height_larger_than_count() {
+        let v = viewport(20, 5);
+        assert_eq!(v.visible_range(), 0..5);
+    }
+
+    #[test]
+    fn set_filtered_count_resets_cursor() {
+        let mut v = viewport(5, 20);
+        for _ in 0..10 {
+            v.move_down(1);
+        }
+        assert_eq!(v.cursor(), 10);
+        v.set_filtered_count(5);
+        assert_eq!(v.cursor(), 0);
+        assert_eq!(v.scroll_offset(), 0);
+    }
+
+    #[test]
+    fn set_height_clamps() {
+        let mut v = viewport(10, 20);
+        for _ in 0..8 {
+            v.move_down(1);
+        }
+        // Shrink viewport, cursor should remain visible
+        v.set_height(3);
+        assert!(v.cursor() < v.scroll_offset() + 3);
+    }
+}