feat(multiplayer): Phase 5 task 5.1 - match lifecycle state machine

Adds the §6.1 state machine, its broadcast, and the client side that
follows it. Physics, freezing and input are deliberately NOT gated on
state yet - 5.3 and 5.4 own freeze/unfreeze at kickoff and goal, and
doing it here would change the conditions every Phase 4 prediction gate
was measured under.

scripts/match_state.gd holds the enum and transition table as pure data
with no scene or RPC dependency, so the table is checked exhaustively
rather than by example: every state reachable, every state has an exit,
no self-transitions, abort-to-LOBBY from anywhere per §6.4, illegal
shortcuts rejected, unknown values refused rather than coerced. The enum
values are the wire format - match_state has been a u8 in the snapshot
header since §2.4 - so a test pins them; only append, never renumber.

The server validates every transition and push_errors an illegal one
rather than following it. Clients deliberately do NOT enforce the table:
authoritative state must be accepted, and a late joiner legitimately
jumps straight to PLAYING.

Two channels carry the state. state_change (reliable, channel 0) is
prompt and carries an absolute at_tick, never a duration. The snapshot's
match_state byte is the catch-up path for a client not yet sent a
transition - a late joiner, or the window between scene load and the
first RPC.

The byte needs a tick guard, and this was found the hard way. Snapshots
are unreliable_ordered on channel 2 and ordering holds only within a
channel, so a state_change for tick N routinely arrives before an
in-flight snapshot from tick N-2. Without the guard the client applies
the new state then gets dragged back by the older byte, oscillating on
every transition - observed directly as LOADING -> WARMUP -> LOBBY ->
PLAYING -> LOBBY while running a deliberately-broken-byte control. Only
a byte at least as new as match_state_since_tick is accepted.

WARMUP_TICKS/GOAL_PAUSE_TICKS are honest placeholders so 5.1 drives real
transitions to verify against; 5.3 and 5.4 replace them. The server also
leaves LOADING immediately rather than waiting for scene_ready, which
does not exist yet.

New smoke flag --exercise-match-state, passed to both roles: the host
forces a goal to drive a GOAL_PAUSE cycle, the client records the
sequence and asserts every consecutive pair is legal, that ticks are
monotonic, and that the wire byte agrees with its own state. Observed
LOADING -> WARMUP -> PLAYING -> GOAL_PAUSE -> WARMUP with tick deltas
matching the configured durations exactly.

Verified against a control: hardcoding the snapshot byte back to 0 fails
both the byte assertion and the transition-legality assertion. The byte
is asserted separately from the RPC precisely because everything else in
the check is RPC-driven and would pass with a dead byte - the same gap
that hid the Phase 4 label bug (gotcha 47).

Regression: 81 unit tests; 60s free-flight LAN (p99 0.148m, 0 hard
snaps, marker 0/3364); transition gate 0.00%; ball contact; two-bot CI.

Game/scripts/networked_match.gd

@@ -20,6 +20,10 @@ extends GameMode
 # but-dead signal shows a permanently frozen timer rather than correctly
 # hiding it the way free_play.gd's total absence of the signal does.
 signal score_changed(score: Dictionary)
+# §6.1 task 5.1. Emitted on BOTH peers — server-side when it drives a
+# transition, client-side when it follows one — so HUD/camera work can bind to
+# one signal regardless of which process it runs in.
+signal match_state_changed(state: int, at_tick: int)
 
 const NetCodec = preload("res://scripts/net_codec.gd")
 const NetBodyState = preload("res://scripts/net_body_state.gd")
@@ -213,6 +217,27 @@ var _reset_gen := 0                       # server only: bumped on every kickoff
 var _pending_reset_gen_bump := false
 var _pending_reset_gen_bump_tick := -1
 
+# §6.1 task 5.1. Authoritative on the server; on a client this mirrors what
+# the server last told us, via state_change (prompt, carries at_tick) or the
+# snapshot's match_state byte (the catch-up path — see _apply_match_state).
+var match_state := MatchState.State.LOADING
+var match_state_since_tick := 0
+# Client only: the match_state byte of the most recently decoded snapshot.
+# Distinct from `match_state` on purpose — it is what the WIRE said, so a test
+# can prove the byte is genuinely populated rather than passing on the
+# reliable state_change RPC alone.
+var _last_snapshot_match_state := -1
+# Server only: the tick the current state's own timer expires on, or -1 when
+# the state has no timer (PLAYING ends on a goal or the clock, not a deadline).
+var _state_deadline_tick := -1
+# Placeholder durations. Task 5.3 replaces the WARMUP one with the real
+# broadcast kickoff (reset transforms + a countdown derived from server_tick),
+# and 5.4 replaces the GOAL_PAUSE one with _goal_pause_seconds() and the
+# client-cinematic split. They exist here only so 5.1 drives REAL transitions
+# to verify against, rather than a state machine nothing ever moves.
+const WARMUP_TICKS := 90          # 1.5s
+const GOAL_PAUSE_TICKS := 120     # 2s
+
 
 func _ready() -> void:
 	add_to_group("game")
@@ -238,6 +263,7 @@ func _ready() -> void:
 		MatchSim.match_config_received.connect(_on_match_config_received)
 		MatchSim.snapshot_received.connect(_on_snapshot_received)
 		MatchSim.score_update_received.connect(_on_score_update_received)
+		MatchSim.state_change_received.connect(_on_state_change_received)
 		_request_match_config_until_received()
 
 
@@ -301,6 +327,14 @@ func _start_server() -> void:
 	MatchSim.send_match_config(arena_path, peer_ids, teams, spawn_indices)
 	MatchSim.input_received.connect(_on_input_received)
 
+	# §6.1: the arena, ball and every slot's ship now exist and match_config is
+	# out, so LOADING is genuinely over. Task 5.3 gates this on the clients'
+	# own scene_ready (with a 10s timeout) instead of leaving immediately —
+	# there is no scene_ready message yet, and inventing half of one here
+	# would be worse than the honest placeholder.
+	_apply_match_state(MatchState.State.LOADING, Engine.get_physics_frames())
+	_set_match_state(MatchState.State.WARMUP)
+
 
 func _on_input_received(peer_id: int, decoded: Dictionary) -> void:
 	for slot in _slots:
@@ -386,6 +420,72 @@ func _on_input_received(peer_id: int, decoded: Dictionary) -> void:
 	_unknown_sender_input_count += 1
 
 
+# --- §6.1 match state machine (task 5.1) -----------------------------------
+#
+# Deliberately does NOT gate physics, freezing or input this task. Tasks 5.3
+# and 5.4 own freeze/unfreeze at kickoff and goal, and doing it here would
+# both duplicate that work and silently change the conditions every Phase 4
+# prediction gate was measured under. 5.1's job is the machine, the broadcast
+# and the client following it.
+func _set_match_state(new_state: int) -> void:
+	if not multiplayer.is_server():
+		push_error("NetworkedMatch: only the server may drive match state")
+		return
+	if new_state == match_state:
+		return
+	if not MatchState.can_transition(match_state, new_state):
+		# Loud, not silent: this is a server logic error, and the symptom it
+		# produces otherwise (clients faithfully following into a state the
+		# server's own code never meant to reach) is near-impossible to
+		# diagnose from a field report.
+		push_error("NetworkedMatch: illegal match state transition %s -> %s" % [
+			MatchState.to_name(match_state), MatchState.to_name(new_state)
+		])
+		return
+	var at_tick := Engine.get_physics_frames()
+	_apply_match_state(new_state, at_tick)
+	MatchSim.send_state_change(new_state, at_tick)
+
+
+# The one place either peer's state actually changes, so the signal and the
+# bookkeeping cannot drift apart between the server and client paths.
+func _apply_match_state(new_state: int, at_tick: int) -> void:
+	if new_state == match_state:
+		return
+	match_state = new_state
+	match_state_since_tick = at_tick
+	_state_deadline_tick = -1
+	if multiplayer.is_server():
+		match new_state:
+			MatchState.State.WARMUP, MatchState.State.OVERTIME_WARMUP:
+				_state_deadline_tick = at_tick + WARMUP_TICKS
+			MatchState.State.GOAL_PAUSE:
+				_state_deadline_tick = at_tick + GOAL_PAUSE_TICKS
+	match_state_changed.emit(new_state, at_tick)
+
+
+# Server only, once per physics tick. Advances the states that end on their
+# own timer; goal- and clock-driven exits are pushed in from their own events.
+func _update_match_state() -> void:
+	if _state_deadline_tick < 0 or Engine.get_physics_frames() < _state_deadline_tick:
+		return
+	match match_state:
+		MatchState.State.WARMUP:
+			_set_match_state(MatchState.State.PLAYING)
+		MatchState.State.OVERTIME_WARMUP:
+			_set_match_state(MatchState.State.OVERTIME)
+		MatchState.State.GOAL_PAUSE:
+			# Task 5.5 decides RESULTS-vs-another-kickoff here once full time
+			# and overtime exist; until then a goal always leads to a kickoff.
+			_set_match_state(MatchState.State.WARMUP)
+
+
+func _on_state_change_received(state: int, at_tick: int) -> void:
+	# Client path. MatchSim already rejected an unknown state value, and the
+	# server is the only peer allowed to send this (rpc "authority").
+	_apply_match_state(state, at_tick)
+
+
 func _on_goal_registered(conceding_team: int) -> void:
 	_record_goal(1 - conceding_team)
 	MatchSim.send_score_update(score.duplicate())
@@ -396,6 +496,11 @@ func _on_goal_scored(_conceding_team: int) -> void:
 	reset_ships()
 	_pending_reset_gen_bump = true
 	_pending_reset_gen_bump_tick = Engine.get_physics_frames()
+	# Only from a live state: GameMode debounces the sensor, but a second goal
+	# landing while already in GOAL_PAUSE would otherwise be an illegal
+	# transition and get push_error'd for something that is not a bug.
+	if multiplayer.is_server() and MatchState.is_live(match_state):
+		_set_match_state(MatchState.State.GOAL_PAUSE)
 
 
 func _broadcast_snapshot() -> void:
@@ -412,7 +517,7 @@ func _broadcast_snapshot() -> void:
 		bodies.append(_ship_to_net_body_state(slot.ship, slot.jitter_buffer.stalled) if is_instance_valid(slot.ship) else NetBodyState.new())
 	if is_instance_valid(ball):
 		bodies.append(_ball_to_net_body_state(ball))
-	var segment := NetCodec.pack_snapshot_body_segment(server_tick, 0, _reset_gen, bodies)
+	var segment := NetCodec.pack_snapshot_body_segment(server_tick, match_state, _reset_gen, bodies)
 	# Building the shared body segment once and reusing it per peer (rather
 	# than re-encoding per client) is the whole reason §2.4 splits the wire
 	# format into a per-client header + a shared body segment in the first
@@ -647,6 +752,27 @@ func _on_snapshot_received(decoded: Dictionary) -> void:
 	_expected_next_snapshot_tick = server_tick + 1
 	_last_received_snapshot_tick = server_tick
 	_last_snapshot_wall_ms = Time.get_ticks_msec()
+	# match_state catch-up (§6.1). state_change is reliable, so this is not a
+	# loss-recovery path — it covers the cases reliability cannot: a client
+	# that joined mid-match and has not been sent a transition yet, and the
+	# window between scene load and the first state_change arriving. Snapshots
+	# carry no at_tick for the transition, so attribute it to this snapshot's
+	# own server_tick, which is the tightest bound available and is never
+	# later than the true transition tick.
+	var snapshot_state: int = decoded["match_state"]
+	_last_snapshot_match_state = snapshot_state
+	# The tick guard is load-bearing, not defensive padding. state_change is
+	# reliable on channel 0 while snapshots are unreliable_ordered on channel
+	# 2, and ordering is only guaranteed WITHIN a channel — so a state_change
+	# for tick N routinely arrives before a snapshot that was sent at tick
+	# N-2 and is still in flight. Without this the client would apply the new
+	# state, then be dragged straight back by the older snapshot's byte, and
+	# oscillate on every single transition. Observed exactly that while
+	# testing a deliberately-broken byte: LOADING -> WARMUP -> LOBBY ->
+	# PLAYING -> LOBBY -> ... Only accept a byte at least as new as whatever
+	# told us the current state.
+	if snapshot_state != match_state and MatchState.is_valid(snapshot_state) and server_tick >= match_state_since_tick:
+		_apply_match_state(snapshot_state, server_tick)
 	# Per-client header (§2.4): unlike the shared body segment, this is
 	# genuinely this recipient's own — input_buffer_depth is THIS client's
 	# own slot's server-side InputJitterBuffer.depth() at send time, which
@@ -931,6 +1057,8 @@ func get_net_debug_stats() -> Dictionary:
 	if _last_local_prediction_comparison.get("authoritative_state", null) != null:
 		server_stalled = (_last_local_prediction_comparison["authoritative_state"] as NetBodyState).stalled
 	return {
+		"match_state": match_state,
+		"snapshot_match_state": _last_snapshot_match_state,
 		"input_buffer_depth": _last_known_input_buffer_depth,
 		"input_lead": _input_lead_controller.lead,
 		"input_target_depth": _current_input_target_depth(),
@@ -1001,6 +1129,9 @@ func _physics_process(_delta: float) -> void:
 	if _owns_world_simulation():
 		_respawn_escaped_bodies()
 	if multiplayer.is_server():
+		# Before the broadcast, so a transition taken this tick ships in this
+		# tick's own match_state byte rather than trailing it by one.
+		_update_match_state()
 		# _physics_process runs after this frame's _integrate_forces. Snapshot
 		# FIRST: the body state therefore still describes the sequence consumed
 		# on the prior callback. Sending after consume mislabeled that old state