fix(training): correct non-forward penalty math and add a grounding incentive

Adversarial review of the previous stage-4 retune found two problems:
non_forward_speed used planar_speed - forward_component, which under-charges
diagonal motion relative to true lateral speed (e.g. ~29% penalty at 45
degrees off the nose instead of the correct ~71%); fixed to the Pythagorean
magnitude for forward-facing angles, full speed for backward-facing ones.

Also, ground_tilt_penalty and non_forward_penalty only ever cost reward near
the floor with nothing offsetting them above it, which could teach a policy
that's still bad at ground handling to just avoid the floor rather than get
better at it. Added grounded_upright_reward (ship_ai_controller.gd) plus a
new ShipObservations.is_floor_contact helper for genuine belly-on-floor
contact detection, so grounding well while upright is the locally profitable
choice, not just the least-punished one.

Game/scripts/ship_ai_controller.gd

@@ -79,6 +79,20 @@ extends AIController3D
 # forward_velocity_to_ball_weight's ball-conditioned bonus. Same
 # GROUND_HANDLING_HEIGHT altitude fade as ground_tilt_penalty.
 @export var non_forward_penalty := 0.0
+# Per-tick bonus for genuinely resting on the floor (ShipObservations.
+# is_floor_contact, real contact — not just being below
+# GROUND_HANDLING_HEIGHT) while upright. The positive counterpart to
+# ground_tilt_penalty/non_forward_penalty: without it, staying above
+# GROUND_HANDLING_HEIGHT is reward-neutral relative to grounding, so a
+# policy that's still bad at ground handling could "solve" those penalties
+# by just avoiding the floor rather than by getting better at handling on
+# it — worsening Stage 3's already-airborne-heavy baseline instead of
+# fixing it. Kept an order of magnitude below ball_touch_reward/goal_reward
+# and comparable to time_penalty/ball_distance_penalty so grounding well is
+# attractive without making idling upright on the spot, away from the ball,
+# competitive with actually playing (see ball_distance_penalty's run04
+# lesson on why a flat positional bonus needs a countervailing cost).
+@export var grounded_upright_reward := 0.0
 # Per-tick bonus for own speed: 0 stationary, full value (+0.24/s) at
 # max_speed. Run07 lesson: after the kickoff flurry both ships parked next to
 # a cornered ball — with every other dense term near zero there, standing
@@ -333,16 +347,36 @@ func _physics_process(delta):
 	# (sideways or reverse), independent of the ball — the mirror image of
 	# forward_velocity_to_ball_weight's ball-conditioned bonus. Fades out with
 	# altitude via the same GROUND_HANDLING_HEIGHT ramp as ground_tilt_penalty.
+	# non_forward_speed is the true lateral magnitude (Pythagorean, not the
+	# cruder planar_speed - forward_component, which under-charges diagonal
+	# motion — e.g. at 45 degrees off the nose that gave ~29% of full-speed
+	# penalty instead of the correct ~71%) for any forward-facing component;
+	# a backward-facing component (dot product below zero) is fully
+	# penalized regardless of angle, same as pure sideways motion.
 	if non_forward_penalty > 0.0 and ship.global_position.y < GROUND_HANDLING_HEIGHT:
 		var non_forward_planar_velocity := Vector3(ship.linear_velocity.x, 0.0, ship.linear_velocity.z)
 		var non_forward_planar_speed := non_forward_planar_velocity.length()
 		var non_forward_planar_forward := Vector3(-ship.global_transform.basis.z.x, 0.0, -ship.global_transform.basis.z.z)
 		if non_forward_planar_speed > 0.0001 and non_forward_planar_forward.length_squared() > 0.0001:
-			var forward_component: float = maxf(non_forward_planar_velocity.dot(non_forward_planar_forward.normalized()), 0.0)
-			var non_forward_speed: float = non_forward_planar_speed - forward_component
+			var forward_component: float = non_forward_planar_velocity.dot(non_forward_planar_forward.normalized())
+			var non_forward_speed: float
+			if forward_component >= 0.0:
+				non_forward_speed = sqrt(maxf(
+					non_forward_planar_speed * non_forward_planar_speed - forward_component * forward_component, 0.0
+				))
+			else:
+				non_forward_speed = non_forward_planar_speed
 			var non_forward_ground_factor: float = 1.0 - clampf(ship.global_position.y / GROUND_HANDLING_HEIGHT, 0.0, 1.0)
 			reward -= non_forward_penalty * (non_forward_speed / ship.max_speed) * non_forward_ground_factor
 
+	# Dense bonus: genuinely resting on the floor while upright (see
+	# grounded_upright_reward) — the positive counterpart to
+	# ground_tilt_penalty/non_forward_penalty, so grounding is worth
+	# pursuing, not just less punished than staying airborne.
+	if grounded_upright_reward > 0.0 and ShipObservations.is_floor_contact(ship):
+		var grounded_uprightness: float = ship.global_transform.basis.y.dot(Vector3.UP)
+		reward += grounded_upright_reward * maxf(grounded_uprightness, 0.0)
+
 	# Dense penalty: height above the floor (see airborne_penalty). The
 	# floor sits at world y = 0 (see training_mode.gd's FIELD_MIN_Y/
 	# _escaped bounds); normalized so the worst case is pinned at the

Game/scripts/ship_observations.gd

@@ -143,3 +143,21 @@ static func contact_normal(ship: Ship) -> Vector3:
 		if normal.y < FLOOR_NORMAL_MIN_Y:
 			return normal
 	return Vector3.ZERO
+
+
+# True belly-on-floor contact — the complement of contact_normal, which
+# deliberately excludes floor contact (see its comment). Used by
+# ShipAIController.grounded_upright_reward to reward genuinely resting on
+# the floor rather than just being below the GROUND_HANDLING_HEIGHT proxy
+# altitude, so a ship can't collect ground-handling reward by hovering just
+# under the threshold without ever touching down.
+static func is_floor_contact(ship: Ship) -> bool:
+	var state := PhysicsServer3D.body_get_direct_state(ship.get_rid())
+	if state == null:
+		return false
+	for i in state.get_contact_count():
+		if not state.get_contact_collider_object(i) is ArenaBoundary:
+			continue
+		if state.get_contact_local_normal(i).y >= FLOOR_NORMAL_MIN_Y:
+			return true
+	return false

Game/scripts/training_mode.gd

@@ -251,8 +251,8 @@ const SHIP_AI_OVERRIDES := [
 	"ball_touch_reward", "ball_touch_cooldown_ticks", "ball_touch_direction_floor",
 	"velocity_to_ball_weight", "ball_velocity_to_goal_weight", "ball_distance_penalty",
 	"forward_velocity_to_ball_weight", "wall_contact_penalty", "tilt_penalty",
-	"ground_tilt_penalty", "non_forward_penalty", "speed_reward_weight", "time_penalty",
-	"airborne_penalty",
+	"ground_tilt_penalty", "non_forward_penalty", "grounded_upright_reward",
+	"speed_reward_weight", "time_penalty", "airborne_penalty",
 ]
 
 
@@ -313,6 +313,7 @@ func _ai_default(name: String) -> Variant:
 		"tilt_penalty": return 0.0005
 		"ground_tilt_penalty": return 0.0
 		"non_forward_penalty": return 0.0
+		"grounded_upright_reward": return 0.0
 		"speed_reward_weight": return 0.004
 		"time_penalty": return 0.001
 		"airborne_penalty": return 0.0