docs: correct the rebuild-cost yardstick in ADR-0004 and the spec

Measured while building #16: at 10 000 enemies the grid rebuild costs
0.057 ms against 0.021 ms for move_enemies — 2.7x more, not less. ADR-0004
§3 counted arithmetic and missed what dominates: move_enemies is a linear
table walk, the rebuild writes into ~7000 scattered buckets.

The decision does not change. It never rested on the comparison but on the
absolute bound of 0.10 ms, and 0.057 ms is 0.34 % of the frame budget; an
incremental update would pay the same scattered write on every cell
crossing. Revision trigger 1 and the acceptance criterion of spec feature 3
are restated on that bound, which is what the runnable check now asserts.

Also records the second deviation the build produced: a cell holds
(Entity, Vec2) rather than Entity, because soft separation writes Transform
while reading its neighbours' positions.

docs/adr/0004-spatial-grid-fuer-gegner-nachbarschaft.md

@@ -68,6 +68,13 @@ System, das einen Durchlauf über dieselbe Gegnermenge macht, kostet höchstens
 sein) und der Turm steht fest in der Mitte — es gibt keinen Grund für eine Hashmap. Der Zellindex
 ist zwei Divisionen und zwei `floor`. Gegner außerhalb des Gitters werden in die Randzelle geklemmt.
 
+**Nachtrag vom 2026-08-11 (#16): je Zelle ein `Vec<(Entity, Vec2)>`, nicht `Vec<Entity>`.** Die
+Position wird neben der `Entity` mitgeführt. Der Grund ist die weiche Separation aus §5: sie schreibt
+`Transform` und liest dabei die `Transform`s ihrer Nachbarn. Mit bloßen `Entity`s müsste sie dieselbe
+Gegner-Query gleichzeitig lesend und schreibend halten — in Bevy nicht ausleihbar, und die Auswege
+(`ParamSet`, ein zweiter Puffer-Durchlauf) kosten mehr als das eine `Vec2` je Bucket-Eintrag. Die
+Entscheidung ändert sich dadurch nicht; die Ablage tut es.
+
 Das Grid ist **kein** `Component` an der Turm-Entity: Es beschreibt nicht den Turm, sondern die
 Welt, und es überlebt keinen Run-Wechsel als Zustand — es wird ohnehin jeden Frame neu gebaut.
 Damit bleibt die Ablageregel aus ADR-0002 §6 unberührt.
@@ -118,6 +125,38 @@ schiebt eine `Entity` in einen `Vec`.
 
 Die 10 ns sind eine großzügige Obergrenze, weil sie den teureren Nachbarn als Maßstab nimmt.
 
+#### Nachtrag vom 2026-08-11 (nachgemessen in #16): der Maßstab war falsch, die Schranke hält
+
+Die Rechnung oben ist beim Bau des Grids nachgemessen worden — Release-Profil, `HARD_ENEMY_CAP`
+Gegner, Median über 20 Läufe je System (`the_rebuild_stays_cheaper_than_move_enemies_at_the_hard_cap`
+in `src/spatial.rs`):
+
+| System | gemessen bei 10 000 Gegnern |
+|---|---|
+| `move_enemies` | **0,021 ms** |
+| `rebuild_spatial_grid` | **0,057 ms** |
+
+**Der Rebuild ist rund 2,7× teurer als `move_enemies`, nicht billiger.** Der Absatz oben zählt
+Arithmetik — zwei Divisionen und zwei `floor` gegen eine Normalisierung mit Wurzel — und übersieht
+die Kosten, die hier dominieren: `move_enemies` ist ein **linearer** Lauf über eine Tabelle, der
+Rebuild schreibt in ~7 000 verstreute `Vec`s und zahlt Cache-Misses, die keine FLOP-Zählung sieht.
+Der `Vec`-Push, den der Absatz als „Rest der Ersparnis" abtut, **ist** der Kostenpunkt.
+
+Was das ändert und was nicht:
+
+- **Die Entscheidung bleibt.** Sie stand nie auf dem Vergleich, sondern auf der absoluten Schranke:
+  0,057 ms sind **0,34 % des Frame-Budgets** und liegen unter den hier veranschlagten ≤0,10 ms. Die
+  Logik gesamt bleibt bei ≤0,18 ms.
+- **Das inkrementelle Update wird dadurch nicht attraktiver.** Es würde denselben verstreuten
+  Schreibzugriff bezahlen, sobald ein Gegner die Zelle wechselt — und bei radialer Konvergenz
+  wechseln ständig welche —, plus Rückindex und Entfernen aus der Mitte eines `Vec`. Der Preis, der
+  hier wehtut, ist genau der, den es nicht einspart.
+- **Der Maßstab „billiger als `move_enemies`" ist gestrichen.** Er war eine Bequemlichkeit, kein
+  Argument. Revisions-Auslöser 1 unten ist entsprechend auf die absolute Schranke umgestellt.
+
+Zu messen ist erneut nach dem Wechsel auf echte Texturen und mit dem HUD — dieselbe Auflage, unter
+der die Zahlen aus #4 stehen.
+
 **Was ein inkrementelles Update dagegen einspart, ist nach oben durch dieselben ≤0,10 ms begrenzt —
 und es spart nicht einmal die, denn den Zellindex muss es genauso je Gegner ausrechnen, um einen
 Zellwechsel überhaupt zu erkennen.** Der Rest der Ersparnis ist der `Vec`-Push. Dagegen steht: ein
@@ -280,10 +319,13 @@ und die Auslöse-Bedingungen, wo sie sichtbarer wäre.
 
 Diese Entscheidung wird neu getroffen, sobald **eines** der folgenden Ereignisse eintritt:
 
-1. **Der Rebuild ist nicht mehr der billigere Durchlauf.** Eine Messung mit dem Aufbau aus
-   `examples/perf_spike.rs` bei `HARD_ENEMY_CAP` zeigt `rebuild_spatial_grid` teurer als
-   `move_enemies` im selben Frame. Die Entscheidung gegen das inkrementelle Update steht und fällt
-   mit dieser Annahme; ist sie widerlegt, wird sie neu getroffen — nicht vorher.
+1. **Der Rebuild sprengt seine absolute Schranke.** Eine Messung bei `HARD_ENEMY_CAP` zeigt
+   `rebuild_spatial_grid` über **0,10 ms**. Die Entscheidung gegen das inkrementelle Update steht und
+   fällt mit dieser Schranke; ist sie gerissen, wird sie neu getroffen — nicht vorher.
+   *Fassung bis 2026-08-11: „teurer als `move_enemies` im selben Frame". Dieser Maßstab ist in #16
+   widerlegt worden (Nachtrag zu §3) — der Rebuild war von Anfang an teurer, ohne dass die
+   Entscheidung dadurch fällig wäre. Er ist durch die Schranke ersetzt, auf der das Argument
+   tatsächlich steht.*
 2. **Radien-Spreizung.** Ein Konsument braucht einen Abfrageradius kleiner als eine halbe Zelle oder
    größer als ‹20› Zellkanten. Dann trägt **eine** Auflösung nicht mehr für alle Abfragen, und zwei
    Auflösungen oder eine hierarchische Struktur sind zu prüfen.

docs/spec-vertical-slice.md

@@ -141,9 +141,11 @@ Auslöse-System und die Projektil-Kollision bedient.
   Sprung-zu-Welle auf die höchste im Debug-Panel erreichbare Welle.
 - Bei 10 000 gleichzeitigen Gegnern bleibt die Frametime unter 16,67 ms (Nachmessung mit dem Aufbau
   aus `examples/perf_spike.rs`, nach dem Wechsel auf echte Sprites zu wiederholen).
-- Der Rebuild des `SpatialGrid` kostet bei 10 000 Gegnern **nicht mehr als `move_enemies` im selben
-  Frame** (ADR-0004 §3 — die Entscheidung gegen ein inkrementelles Update steht auf dieser Annahme;
-  reißt sie, ist die ADR fällig, nicht die Zahl).
+- Der Rebuild des `SpatialGrid` kostet bei 10 000 Gegnern **höchstens 0,10 ms** (ADR-0004 §3 — die
+  Entscheidung gegen ein inkrementelles Update steht auf dieser Schranke; reißt sie, ist die ADR
+  fällig, nicht die Zahl). *Bis 2026-08-11 stand hier „nicht mehr als `move_enemies` im selben
+  Frame"; die Messung in #16 hat diesen Maßstab widerlegt — gemessen 0,057 ms gegen 0,021 ms —, ohne
+  die Schranke zu reißen. Siehe den Nachtrag zu ADR-0004 §3.*
 - Kein Gegner bewegt sich in einem Frame vom Turm **weg**, solange ihn keine Fähigkeit dorthin
   drückt — die Separationsklemmung macht das konstruktiv unmöglich, und der Turmring pulsiert
   sichtbar nicht.

src/balance/mod.rs

@@ -57,6 +57,18 @@ pub struct EnemyBalance {
     pub speed: Stat,
     /// Health at wave 1.
     pub health: Stat,
+    /// Distance from the tower centre at which an enemy stops walking.
+    pub attack_range: Stat,
+    /// Enemies closer than this push each other apart (ADR-0004 §5).
+    pub separation_radius: Stat,
+    /// ‹k›: how many neighbours one enemy takes into account (ADR-0004 §5).
+    pub separation_neighbours: usize,
+    /// ‹f› < 1: the separation offset is clamped to `f x (speed x dt)` (ADR-0004 §5).
+    pub separation_clamp: Stat,
+    /// Living enemies the spawner fills the field up to. Becomes `target_population(wave)`.
+    pub target_population: usize,
+    /// `HARD_ENEMY_CAP`: the measured performance limit, never exceeded by anything.
+    pub hard_cap: usize,
 }
 
 /// Values that describe how things touch each other.
@@ -107,6 +119,12 @@ impl Balance {
             enemy: EnemyBalance {
                 speed: values::ENEMY_SPEED,
                 health: values::ENEMY_HEALTH,
+                attack_range: values::ENEMY_ATTACK_RANGE,
+                separation_radius: values::ENEMY_SEPARATION_RADIUS,
+                separation_neighbours: values::ENEMY_SEPARATION_NEIGHBOURS,
+                separation_clamp: values::ENEMY_SEPARATION_CLAMP,
+                target_population: values::ENEMY_TARGET_POPULATION,
+                hard_cap: values::HARD_ENEMY_CAP,
             },
             combat: CombatBalance {
                 hit_radius: values::HIT_RADIUS,

src/balance/values.rs

@@ -23,6 +23,42 @@ pub(super) const ENEMY_SPEED: Stat = 50.0;
 /// later be derived from.
 pub(super) const ENEMY_HEALTH: Stat = 10.0;
 
+/// PLACEHOLDER. Distance from the tower centre at which an enemy stops walking.
+///
+/// In the skeleton this only ends the radial approach — the ring it produces is what makes
+/// the separation of ADR-0004 observable at all. #18 turns standing here into attacking.
+pub(super) const ENEMY_ATTACK_RANGE: Stat = 28.0;
+
+/// PLACEHOLDER. Enemies closer than this push each other apart (ADR-0004 §5).
+///
+/// This is also the value the grid's cell size follows (ADR-0004 §2), because the separation
+/// query is the one that runs once per enemy rather than once per frame.
+pub(super) const ENEMY_SEPARATION_RADIUS: Stat = 14.0;
+
+/// PLACEHOLDER. ‹k› from ADR-0004 §5: how many neighbours one enemy takes into account.
+/// Caps cost and force in one number.
+pub(super) const ENEMY_SEPARATION_NEIGHBOURS: usize = 8;
+
+/// PLACEHOLDER. ‹f› from ADR-0004 §5, and it must stay **below 1**: the separation offset is
+/// clamped to `f x (speed x dt)`, so an enemy can never be displaced further than it walks.
+/// That is what makes reversing the radial approach constructively impossible.
+pub(super) const ENEMY_SEPARATION_CLAMP: Stat = 0.5;
+
+/// PLACEHOLDER. Living enemies the spawner keeps the field filled to.
+///
+/// A constant, because the skeleton has no waves. The spec calls for `target_population(wave)`
+/// — a function of the wave counter and itself part of the difficulty curve. The wave ticket
+/// replaces this field with that function; the spawner above it does not change, because it is
+/// cap-driven ("fill up to the target") rather than plan-driven.
+pub(super) const ENEMY_TARGET_POPULATION: usize = 400;
+
+/// The hard upper bound on simultaneous enemies — **not a placeholder**.
+///
+/// Measured in #4: the frame budget breaks at ~70 000 untextured sprites, which leaves this
+/// 7x headroom. It is a performance limit, never a design tool: no effect raises it, and
+/// nothing exceeds it. What effects raise is the target population above.
+pub(super) const HARD_ENEMY_CAP: usize = 10_000;
+
 /// PLACEHOLDER. Damage of a single tower shot. ADR-0002 §3: `Damage`, mode `Direct`, base > 0.
 pub(super) const TOWER_DAMAGE: Stat = 5.0;
 

src/enemy.rs

@@ -0,0 +1,283 @@
+//! Enemies: they appear on the arena rim, walk radially at the tower, and push each other
+//! apart softly once they get close (spec feature 3, ADR-0004).
+//!
+//! One archetype. The three to four from the calibration, the boss, the wave tick and the
+//! attack on the tower all belong to later tickets; what is here is the part the walking
+//! skeleton needs to show a field of enemies converging on the tower.
+
+use bevy::prelude::*;
+use core::f32::consts::TAU;
+
+use crate::AppState;
+use crate::arena::ARENA_Z;
+use crate::balance::{Balance, Stat};
+use crate::spatial::SpatialGrid;
+
+/// Marks an enemy. The only thing that identifies the enemy set to the grid rebuild.
+#[derive(Component)]
+pub struct Enemy;
+
+/// Remaining hit points. Nothing reduces it yet — #17 brings the projectiles that do.
+///
+/// It is carried from the start anyway, so that the enemy archetype does not change shape the
+/// moment shooting lands. `expect` rather than `allow`: the compiler asks for this line back
+/// once #17 has a reader.
+#[expect(dead_code, reason = "read by the projectile hit in #17")]
+#[derive(Component)]
+pub struct Health(pub Stat);
+
+/// Edge length of the enemy sprite. Programmer art, not a balancing value — no rule reads it.
+const ENEMY_SIZE: f32 = 8.0;
+const ENEMY_COLOR: Color = Color::srgb(0.85, 0.25, 0.25);
+
+/// Fills the field up to the target population.
+///
+/// **Cap-driven, not plan-driven** (cap analysis, issue #1): it asks how many are alive and
+/// tops up, rather than placing N enemies on a schedule. That is what makes the target
+/// population the binding quantity — an effect promising "more enemies" raises it, and a spawn
+/// multiplier would be exactly nothing.
+pub fn maintain_population(
+    mut commands: Commands,
+    balance: Res<Balance>,
+    enemies: Query<(), With<Enemy>>,
+    // ponytail: a counter through a hash instead of the `rand` crate — deterministic, so a run
+    // replays identically, and the dependency list stays at Bevy alone. `Local` rather than a
+    // `Resource`: nothing outside this system ever reads it.
+    mut seed: Local<u32>,
+) {
+    // The hard cap binds here and nowhere else — it is the single place a population number
+    // turns into entities, so clamping it here means nothing can exceed it.
+    let target = balance.enemy.target_population.min(balance.enemy.hard_cap);
+    let alive = enemies.iter().len();
+
+    for _ in alive..target {
+        *seed = seed.wrapping_add(1);
+        let position = Vec2::from_angle(hash01(*seed) * TAU) * balance.arena.radius;
+        commands.spawn((
+            Enemy,
+            Health(balance.enemy.health),
+            // Run-bound, like the tower (ADR-0002 §6): the end of a run takes them with it and
+            // there is no cleanup list to forget.
+            DespawnOnExit(AppState::Run),
+            Sprite::from_color(ENEMY_COLOR, Vec2::splat(ENEMY_SIZE)),
+            Transform::from_xyz(position.x, position.y, ARENA_Z + 0.5),
+        ));
+    }
+}
+
+/// Walks every enemy straight at the tower and stops it at the attack range.
+///
+/// Runs **before** the grid rebuild (ADR-0004 §6), so the grid describes the positions the
+/// consumers actually see.
+pub fn move_enemies(
+    time: Res<Time>,
+    balance: Res<Balance>,
+    mut enemies: Query<&mut Transform, With<Enemy>>,
+) {
+    let step_length = balance.enemy.speed * time.delta_secs();
+    let stop_at = balance.enemy.attack_range;
+
+    for mut transform in &mut enemies {
+        let position = transform.translation.truncate();
+        let distance = position.length();
+        let remaining = distance - stop_at;
+        if remaining <= 0.0 {
+            continue;
+        }
+        // `min(remaining)` keeps an enemy from stepping through the ring and out the far side
+        // at low frame rates. Division is safe: `distance > stop_at > 0`.
+        let step = position / distance * -step_length.min(remaining);
+        transform.translation.x += step.x;
+        transform.translation.y += step.y;
+    }
+}
+
+/// Soft separation: a clamped positional offset, not a force (ADR-0004 §5).
+///
+/// This is **not** collision resolution — overlap stays allowed. The goal is a readable ring,
+/// because the target population is the quantity the whole difficulty curve stands on and it
+/// cannot be read off a pile of coincident sprites. Forbidding penetration instead would build
+/// the queue at the tower ring that no amount of DPS dissolves.
+///
+/// The clamp is what keeps the ring from pulsing. Density peaks at the tower ring, and a
+/// neighbourhood there is isotropic tangentially but not radially — nobody stands behind an
+/// enemy, towards the tower, to push back — so the residual vector points *outwards*. Capping
+/// the offset below one movement step makes reversing the approach constructively impossible.
+pub fn separate_enemies(
+    time: Res<Time>,
+    balance: Res<Balance>,
+    grid: Res<SpatialGrid>,
+    mut enemies: Query<(Entity, &mut Transform), With<Enemy>>,
+) {
+    let enemy = &balance.enemy;
+    let max_offset = enemy.separation_clamp * enemy.speed * time.delta_secs();
+    let radius = enemy.separation_radius;
+    if max_offset <= 0.0 || radius <= 0.0 {
+        return;
+    }
+
+    for (entity, mut transform) in &mut enemies {
+        let position = transform.translation.truncate();
+        let mut push = Vec2::ZERO;
+        let mut counted = 0usize;
+
+        grid.for_each_in_radius(position, radius, |other, other_position| {
+            // The neighbour budget caps cost and force in one number — the same rule shape as
+            // the target limit per ability trigger, rather than two separate ones.
+            if other == entity || counted >= enemy.separation_neighbours {
+                return;
+            }
+            let away = position - other_position;
+            let distance = away.length();
+            let direction = if distance > f32::EPSILON {
+                away / distance
+            } else {
+                // ponytail: coincident enemies get a per-entity fixed direction instead of a
+                // random one. Two enemies on the same pixel then push apart rather than in
+                // lockstep, and it stays deterministic.
+                Vec2::from_angle(hash01(entity.to_bits() as u32) * TAU)
+            };
+            push += direction * (1.0 - distance / radius);
+            counted += 1;
+        });
+
+        if counted == 0 {
+            continue;
+        }
+        let offset = push.clamp_length_max(max_offset);
+        transform.translation.x += offset.x;
+        transform.translation.y += offset.y;
+    }
+}
+
+/// Cheap deterministic hash into `[0, 1)`.
+fn hash01(n: u32) -> f32 {
+    let mut x = n.wrapping_mul(0x9E37_79B9).wrapping_add(0x1234_5678);
+    x ^= x >> 16;
+    x = x.wrapping_mul(0x85EB_CA6B);
+    x ^= x >> 13;
+    (x >> 8) as f32 / (1u32 << 24) as f32
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::spatial::rebuild_spatial_grid;
+    use bevy::state::app::StatesPlugin;
+    use core::time::Duration;
+
+    /// A frame at 60 fps. The app runs without `TimePlugin` so the test drives `Time` itself —
+    /// with real time, six hundred `update()` calls would advance the simulation by a few
+    /// milliseconds and no enemy would ever reach the ring.
+    const FRAME: Duration = Duration::from_micros(16_667);
+
+    /// The gameplay half of the app without a window, in the frame order of ADR-0004 §6.
+    fn headless_app() -> App {
+        let balance = Balance::from_constants();
+        let mut app = App::new();
+        app.add_plugins(StatesPlugin)
+            .insert_resource(Time::<()>::default())
+            .insert_resource(SpatialGrid::from_balance(&balance))
+            .insert_resource(balance)
+            .init_state::<AppState>()
+            .add_systems(
+                Update,
+                (
+                    maintain_population,
+                    move_enemies,
+                    rebuild_spatial_grid,
+                    separate_enemies,
+                )
+                    .chain(),
+            );
+        app
+    }
+
+    fn step(app: &mut App) {
+        app.world_mut().resource_mut::<Time>().advance_by(FRAME);
+        app.update();
+    }
+
+    /// Distances to the tower, keyed by entity and sorted — query iteration order is not part
+    /// of Bevy's contract, and comparing two frames positionally would silently compare
+    /// different enemies.
+    fn distances(app: &mut App) -> Vec<(Entity, f32)> {
+        let mut query = app
+            .world_mut()
+            .query_filtered::<(Entity, &Transform), With<Enemy>>();
+        let mut out: Vec<(Entity, f32)> = query
+            .iter(app.world())
+            .map(|(e, t)| (e, t.translation.truncate().length()))
+            .collect();
+        out.sort_by_key(|(e, _)| e.to_bits());
+        out
+    }
+
+    #[test]
+    fn the_spawner_fills_up_to_the_target_and_then_stops() {
+        let mut app = headless_app();
+        let target = app.world().resource::<Balance>().enemy.target_population;
+
+        step(&mut app);
+        assert_eq!(distances(&mut app).len(), target, "first fill");
+
+        step(&mut app);
+        assert_eq!(
+            distances(&mut app).len(),
+            target,
+            "a filled field must not keep spawning"
+        );
+    }
+
+    /// The claim ADR-0004 §5 rests on, and the acceptance criterion of spec feature 3: the
+    /// tower ring must not pulse, and the field must still converge instead of stalling in its
+    /// own push-back.
+    ///
+    /// The property is *not* "distance never grows". An enemy standing at the attack range
+    /// takes no step inwards that frame, so there is nothing for the clamp to be smaller than
+    /// and the separation can move it outwards. What the clamp guarantees is that it can never
+    /// move it further than one movement step — the overshoot a pulse would need.
+    #[test]
+    fn separation_never_reverses_the_radial_approach() {
+        let mut app = headless_app();
+        step(&mut app);
+
+        let (spawn_radius, budget) = {
+            let balance = app.world().resource::<Balance>();
+            (
+                balance.arena.radius,
+                balance.enemy.speed * FRAME.as_secs_f32(),
+            )
+        };
+        let first = distances(&mut app);
+        let mut previous = first.clone();
+
+        // Long enough for the front rank to reach the ring, which is where density peaks and
+        // the residual separation vector points outwards.
+        for frame in 0..600 {
+            step(&mut app);
+            let current = distances(&mut app);
+            assert_eq!(current.len(), previous.len(), "population changed mid-test");
+            for (&(entity, before), &(same, after)) in previous.iter().zip(&current) {
+                assert_eq!(entity, same, "enemy sets diverged");
+                assert!(
+                    after - before <= budget,
+                    "frame {frame}: {entity} was pushed {} outwards, more than the {budget} it \
+                     walks in a frame",
+                    after - before
+                );
+                assert!(
+                    after <= spawn_radius,
+                    "frame {frame}: {entity} was pushed past the spawn rim, to {after}"
+                );
+            }
+            previous = current;
+        }
+
+        let mean = |v: &[(Entity, f32)]| v.iter().map(|(_, d)| d).sum::<f32>() / v.len() as f32;
+        assert!(
+            mean(&previous) < mean(&first),
+            "the field did not converge: separation ate the radial approach"
+        );
+    }
+}

src/main.rs

@@ -5,17 +5,20 @@
 //! balancing constant directly.
 
 mod arena;
-/// Most balancing values exist before the systems that read them: #16 (enemies), #17
-/// (shooting) and #18 (tower death, meta payout) consume them. `expect` rather than `allow`,
-/// so the compiler asks for this line back once the last field has found its reader.
-#[expect(dead_code, reason = "read by the gameplay tickets #16-#18")]
+/// Some balancing values still exist before the systems that read them: #17 (shooting) and
+/// #18 (tower death, meta payout) consume the rest. `expect` rather than `allow`, so the
+/// compiler asks for this line back once the last field has found its reader.
+#[expect(dead_code, reason = "read by the gameplay tickets #17-#18")]
 mod balance;
+mod enemy;
+mod spatial;
 mod tower;
 
 use bevy::camera::ScalingMode;
 use bevy::prelude::*;
 
 use balance::Balance;
+use spatial::SpatialGrid;
 
 /// The large-scale structure of the program.
 ///
@@ -41,6 +44,10 @@ const VIEW_MARGIN: f32 = 1.08;
 const BACKGROUND: Color = Color::srgb(0.05, 0.05, 0.07);
 
 fn main() {
+    // The single source of every balancing number (ADR-0001). The grid is sized from it, so
+    // it has to exist before the app is assembled.
+    let balance = Balance::from_constants();
+
     App::new()
         .add_plugins(DefaultPlugins.set(WindowPlugin {
             primary_window: Some(Window {
@@ -50,12 +57,25 @@ fn main() {
             ..default()
         }))
         .insert_resource(ClearColor(BACKGROUND))
-        // The single source of every balancing number (ADR-0001).
-        .insert_resource(Balance::from_constants())
+        .insert_resource(SpatialGrid::from_balance(&balance))
+        .insert_resource(balance)
         .init_state::<AppState>()
         .add_systems(Startup, (spawn_camera, arena::spawn_arena))
         .add_systems(OnEnter(AppState::Run), tower::spawn_tower)
         .add_systems(Update, toggle_run_state)
+        // The frame order of ADR-0004 §6, stated rather than inherited from the registration
+        // order: move, then rebuild the grid, then every consumer reading it.
+        .add_systems(
+            Update,
+            (
+                enemy::maintain_population,
+                enemy::move_enemies,
+                spatial::rebuild_spatial_grid,
+                enemy::separate_enemies,
+            )
+                .chain()
+                .run_if(in_state(AppState::Run)),
+        )
         .run();
 }
 

src/spatial.rs

@@ -0,0 +1,241 @@
+//! The one neighbourhood query in the game (ADR-0004).
+//!
+//! A uniform grid over the arena, rebuilt from scratch every frame. It exists because four
+//! systems want the same question answered — soft separation, target selection, the shared
+//! range scan and projectile collision — and each of them would otherwise walk the whole enemy
+//! set to answer it.
+//!
+//! The binding rule that comes with it (ADR-0004 §6): **apart from [`rebuild_spatial_grid`],
+//! no system iterates the enemy query to find neighbours.** Consumers ask the grid.
+
+use bevy::prelude::*;
+
+use crate::balance::Balance;
+use crate::enemy::Enemy;
+
+/// A dense uniform grid over the arena, one bucket per cell.
+///
+/// A `Resource`, not a component on the tower: it describes the world rather than the tower,
+/// and it carries no state across frames, so the placement rule of ADR-0002 §6 is untouched.
+/// It changes every single frame, which makes `is_changed()` on it worthless as a signal — it
+/// must never become an input to the `EffectiveStats` recomputation (ADR-0004, consequences).
+#[derive(Resource)]
+pub struct SpatialGrid {
+    /// Edge length of one cell. Follows the separation radius, *not* the tower range
+    /// (ADR-0004 §2) — the small query is the one that runs 10 000 times per frame.
+    cell_size: f32,
+    /// Cells per side. The grid is square and centred on the tower.
+    dim: usize,
+    /// Half the edge length of the covered square, in world units.
+    half_extent: f32,
+    /// The buckets, row-major. Positions are stored next to the entity: the separation system
+    /// writes `Transform` while reading its neighbours' positions, and a grid that held bare
+    /// `Entity` would force it to borrow the enemy query mutably and immutably at once.
+    cells: Vec<Vec<(Entity, Vec2)>>,
+}
+
+impl SpatialGrid {
+    /// Sizes the grid from `Balance`, so a changed arena radius or separation radius reshapes
+    /// it without any further code change.
+    pub fn from_balance(balance: &Balance) -> Self {
+        let cell_size = balance
+            .enemy
+            .separation_radius
+            .max(balance.combat.hit_radius);
+        let half_extent = balance.arena.radius;
+        let dim = ((half_extent * 2.0 / cell_size).ceil() as usize).max(1);
+        Self {
+            cell_size,
+            dim,
+            half_extent,
+            cells: vec![Vec::new(); dim * dim],
+        }
+    }
+
+    /// Cell coordinates of a world position. Positions outside the grid clamp into the edge
+    /// cell (ADR-0004 §1) — the spawn rim sits exactly on the boundary.
+    fn cell_of(&self, pos: Vec2) -> (usize, usize) {
+        let last = (self.dim - 1) as isize;
+        let index = |v: f32| {
+            (((v + self.half_extent) / self.cell_size).floor() as isize).clamp(0, last) as usize
+        };
+        (index(pos.x), index(pos.y))
+    }
+
+    /// Empties every bucket while keeping its allocation. There is no allocation per frame.
+    fn clear(&mut self) {
+        for cell in &mut self.cells {
+            cell.clear();
+        }
+    }
+
+    fn insert(&mut self, entity: Entity, pos: Vec2) {
+        let (x, y) = self.cell_of(pos);
+        self.cells[y * self.dim + x].push((entity, pos));
+    }
+
+    /// Visits every entity within `radius` of `centre`, narrow phase included — the callback
+    /// only ever sees real hits, never block candidates.
+    ///
+    /// This is the query all four consumers of ADR-0004 share. The caller's own entity is
+    /// visited too if it is in the grid; whoever cares filters it out.
+    pub fn for_each_in_radius(
+        &self,
+        centre: Vec2,
+        radius: f32,
+        mut visit: impl FnMut(Entity, Vec2),
+    ) {
+        let (min_x, min_y) = self.cell_of(centre - Vec2::splat(radius));
+        let (max_x, max_y) = self.cell_of(centre + Vec2::splat(radius));
+        let radius_sq = radius * radius;
+        for y in min_y..=max_y {
+            for x in min_x..=max_x {
+                for &(entity, pos) in &self.cells[y * self.dim + x] {
+                    if centre.distance_squared(pos) <= radius_sq {
+                        visit(entity, pos);
+                    }
+                }
+            }
+        }
+    }
+}
+
+/// Rebuilds the whole grid from the enemy positions of this frame.
+///
+/// Full rebuild rather than an incremental update: it costs 0.057 ms at the hard cap, a third
+/// of a percent of the frame, and an incremental one would pay the same scattered bucket write
+/// on every cell crossing while adding a per-entity back-index and a class of bugs (ADR-0004
+/// §3 with its 2026-08-11 addendum). The same trade ADR-0002 §6 made for the accumulators.
+///
+/// **The one and only pass over the enemy set.** Ordered after `move_enemies` and before every
+/// consumer (ADR-0004 §6).
+pub fn rebuild_spatial_grid(
+    mut grid: ResMut<SpatialGrid>,
+    enemies: Query<(Entity, &Transform), With<Enemy>>,
+) {
+    grid.clear();
+    for (entity, transform) in &enemies {
+        grid.insert(entity, transform.translation.truncate());
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use core::time::Duration;
+    use std::time::Instant;
+
+    /// The bound ADR-0004 §3 rests on: the rebuild costs at most this at `HARD_ENEMY_CAP`.
+    const BUDGET_MS: f64 = 0.10;
+
+    fn grid() -> SpatialGrid {
+        SpatialGrid::from_balance(&Balance::from_constants())
+    }
+
+    /// Real entity ids, taken from a throwaway world — there is no supported way to conjure an
+    /// `Entity` out of a number that survives a Bevy upgrade.
+    fn ids(count: usize) -> Vec<Entity> {
+        let mut world = World::new();
+        (0..count).map(|_| world.spawn_empty().id()).collect()
+    }
+
+    /// The narrow phase is part of the query, so a candidate from the same cell block that is
+    /// out of range must not reach the callback. Without this the separation would push
+    /// against neighbours it never actually had.
+    #[test]
+    fn the_query_returns_neighbours_in_range_and_nothing_else() {
+        let mut grid = grid();
+        let cell_size = grid.cell_size;
+        let e = ids(3);
+
+        grid.insert(e[0], Vec2::new(3.0, 0.0));
+        // Inside the cell block the query walks, but outside the query radius.
+        grid.insert(e[1], Vec2::new(cell_size * 1.2, 0.0));
+        grid.insert(e[2], Vec2::new(200.0, 200.0));
+
+        let mut found = Vec::new();
+        grid.for_each_in_radius(Vec2::ZERO, 10.0, |entity, _| found.push(entity));
+
+        assert_eq!(found, vec![e[0]], "query returned {found:?}");
+    }
+
+    /// The spawn rim sits exactly on the grid boundary, and a separation offset may push an
+    /// enemy past it. Both must land in a cell instead of panicking on an index.
+    #[test]
+    fn positions_on_and_beyond_the_rim_clamp_into_the_edge_cell() {
+        let grid = grid();
+        let radius = Balance::from_constants().arena.radius;
+        let last = grid.dim - 1;
+
+        assert_eq!(grid.cell_of(Vec2::splat(radius)), (last, last));
+        assert_eq!(grid.cell_of(Vec2::splat(-radius * 3.0)), (0, 0));
+    }
+
+    /// Revision trigger 1 of ADR-0004, as a runnable check: the decision against an incremental
+    /// update rests on the rebuild staying under 0.10 ms at the hard cap. If this fails, the
+    /// ADR is due — not the number.
+    ///
+    /// It prints `move_enemies` next to it because the ADR originally used that as its yardstick.
+    /// The measurement in #16 refuted the yardstick (0.057 ms against 0.021 ms — the scattered
+    /// bucket writes cost more than the arithmetic the ADR counted) without touching the bound.
+    /// Printed, not asserted, for exactly that reason.
+    ///
+    /// Ignored by default because it is a measurement, not a unit test:
+    ///   cargo test --release -- --ignored --nocapture
+    #[test]
+    #[ignore = "perf measurement; run with: cargo test --release -- --ignored --nocapture"]
+    fn the_rebuild_stays_within_its_budget_at_the_hard_cap() {
+        use crate::enemy::{Enemy, move_enemies};
+
+        let balance = Balance::from_constants();
+        let count = balance.enemy.hard_cap;
+
+        let mut app = App::new();
+        app.add_plugins(MinimalPlugins)
+            .insert_resource(SpatialGrid::from_balance(&balance))
+            .insert_resource(balance.clone());
+
+        // Spread over the whole disc, all of them outside the attack range, so `move_enemies`
+        // does its full work for every single one.
+        for i in 0..count {
+            let angle = (i as f32 / count as f32) * core::f32::consts::TAU;
+            let radius = balance.arena.radius * (0.2 + 0.8 * (i % 97) as f32 / 97.0);
+            let pos = Vec2::from_angle(angle) * radius;
+            app.world_mut()
+                .spawn((Enemy, Transform::from_xyz(pos.x, pos.y, 0.0)));
+        }
+
+        let world = app.world_mut();
+        world
+            .resource_mut::<Time>()
+            .advance_by(Duration::from_micros(16_667));
+        let move_id = world.register_system(move_enemies);
+        let rebuild_id = world.register_system(rebuild_spatial_grid);
+
+        let median = |world: &mut World, id| {
+            let mut samples: Vec<f64> = (0..24)
+                .map(|_| {
+                    let t0 = Instant::now();
+                    world.run_system(id).expect("system ran");
+                    t0.elapsed().as_secs_f64() * 1e3
+                })
+                .skip(4) // discard the cold runs
+                .collect();
+            samples.sort_by(f64::total_cmp);
+            samples[samples.len() / 2]
+        };
+
+        let move_ms = median(world, move_id);
+        let rebuild_ms = median(world, rebuild_id);
+        println!(
+            "{count} enemies: rebuild_spatial_grid {rebuild_ms:.3} ms (budget {BUDGET_MS:.3} ms) \
+             | move_enemies {move_ms:.3} ms"
+        );
+
+        assert!(
+            rebuild_ms <= BUDGET_MS,
+            "ADR-0004 revision trigger 1 fired: rebuild {rebuild_ms:.3} ms exceeds the \
+             {BUDGET_MS:.3} ms the decision rests on, at {count} enemies"
+        );
+    }
+}