MP: COUPLED peer motion -- authentic gait-driven position + master gait send-mirror (task #50, env-gated)

Finishes the coupled IntegrateMotion path the decomp workflow (wh1h5gnmc, 3
make-or-break claims CONFIRMED by adversarial verify) proved authentic:
 - Peer LINEAR position is SINGLE-SOURCE gait: IntegrateMotion integrates the
   body-channel cycleDistance into projectedOrigin.linear@0x260, copied verbatim
   to localOrigin -- NOT velocity dead-reckon (that is angular/heading ONLY).
   0x260 'motionDelta' and 'projectedOrigin' are literally the same field; the
   'contradiction' was our reconstruction's two misnamed shadows.
 - Master and peer run the SAME predictor; the master's SEND-mirror must run it
   too (binary FUN_004a9b5c @0x4aab9c) so a gait-driven peer stays anchored. Our
   mirror used the constant-velocity deadReckoner + overwrote bodyTargetSpeed
   live every frame -> could not model a gait peer (the tug-of-war).
 - T4 CONFIRMED: both channels pose the full skeleton (same JointedMover); keep
   the peer LEG channel (our body channel is unbound on the peer).

CHANGES (all behind BT_MASTER_GAITMIRROR / BT_ROOT_POS, DEFAULT OFF -- zero
change to shipped behavior until visually confirmed):
 - mech4.cpp: send-mirror advances projectedOrigin by the mj=0 body channel
   travel (mirrorBodyAdv) rotated by heading + last-sent angular vel, re-seeded
   to localOrigin on each send, instead of the deadReckoner; and stops the
   per-frame live bodyTargetSpeed overwrite so the mirror slews toward last-sent.
 - mech.hpp/mech.cpp: mirrorBodyAdv member.

Measured A/B (autonomous through-zero sweep circle, the speed-change regime):
   velocity two-source (current default): ratio 1.0022 BUT user-visible glitch
   coupled, NO mirror (dense):            ratio 1.86  (tug-of-war)
   coupled + gait mirror, dense OFF:      ratio 1.14, back-steps 0.1%
   coupled + gait mirror, dense ON:       ratio 1.043, back-steps 0.1%, maxStep 2.9u
The single-source coupling is proven (backward-stepping 0.1% vs the split's
churn). Residual 2.9u occasional snap = leg(peer)-vs-body(mirror) channel
mismatch, second-order. Awaiting visual confirmation before default promotion.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

game/reconstructed/mech.cpp

@@ -915,6 +915,7 @@ Mech::Mech(
 	Wword(0xe6)  = 0;
 	poseSyncLatch = 0;									// @0x77c (was absorbed Wword(0x1df))
 	heatLevelSnapshot = 0;								// @0x780 (type-7 deadband baseline)
+	mirrorBodyAdv  = 0.0f;								// master send-mirror gait travel
 	angMirrorYaw   = 0.0f;								// scalar peer-yaw mirror (port addition)
 	angMirrorRate  = 0.0f;
 	angMirrorValid = 0;

game/reconstructed/mech.hpp

@@ -625,6 +625,12 @@ public:
 	// one is recomputed by the master's own reckoner each frame from lastUpdate
 	// timing it does not control, and its false pi-drift waves FLOODED type-4
 	// resyncs (measured maxAng~=pi bursts).  Scalars, wrap-safe, self-timed.
+	// Master send-mirror gait travel (BT_MASTER_GAITMIRROR): the invisible mj=0
+	// body channel's per-frame cycleDistance, stashed in the drive block and
+	// consumed by the send gate to advance projectedOrigin the way the PEER
+	// predicts (gait), instead of the constant-velocity deadReckoner. This is the
+	// authentic FUN_004a9b5c mirror = IntegrateMotion(mj=0) on projectedOrigin.
+	Scalar		mirrorBodyAdv;				// body cycleDistance this frame (master)
 	Scalar		angMirrorYaw;				// yaw at the last type-4 send (rad)
 	Scalar		angMirrorRate;				// yaw rate sent with it (rad/s)
 	Time		angMirrorTime;				// lastPerformance at that send

game/reconstructed/mech4.cpp

@@ -3167,7 +3167,21 @@ void
 					// while the animation transitioned gradually (the "physics don't
 					// line up with the animation" desync).  Signed, the SM decelerates
 					// through stop -> reverse-entry exactly like the leg channel.
-					if (s_realControls && MappingMapper() != 0)
+					// BT_MASTER_GAITMIRROR: the invisible mj=0 body channel becomes the
+					// PEER's predictor, so it must slew toward the LAST-SENT commanded
+					// speed (which the record writers stamp into bodyTargetSpeed@0x6b4 on
+					// each send, mech.cpp), NOT the live mapper demand.  Leaving
+					// bodyTargetSpeed at last-sent re-activates the authentic type-2
+					// deadband and makes the mirror model exactly what the peer computes.
+					// The master's VISIBLE motion uses the LEG channel reading live demand
+					// independently, so this does not change what the local player sees.
+					// (Default OFF: live overwrite preserved.)
+					static const int s_gaitMirror = getenv("BT_MASTER_GAITMIRROR") ? 1 : 0;
+					if (s_gaitMirror)
+					{
+						/* leave bodyTargetSpeed at the last-sent value */
+					}
+					else if (s_realControls && MappingMapper() != 0)
 						bodyTargetSpeed = MappingMapper()->speedDemand;
 					else
 						bodyTargetSpeed = ((throttle < 0.0f) ? -1.0f : 1.0f)
@@ -3234,6 +3248,7 @@ void
 						// BT_BODY_MJ=1 restores the old double-writer for A/B.
 						static const int s_bodyMj = BTEnvOn("BT_BODY_MJ", 0);
 						adv    = AdvanceBodyAnimation(dt, s_bodyMj);	// channel B: replication projection (mj=0)
+						mirrorBodyAdv = adv;					// stash for the send-mirror gait advance
 						legAdv = AdvanceLegAnimation(dt);		// channel A: local sim -- pose + travel
 					}
 					else
@@ -3716,7 +3731,43 @@ void
 			// the PEER's event queue busy, so its CreatingMission->LoadingMission
 			// quiet-timeout never fired -- the pods deadlocked pre-launch.  The real
 			// system never moves before launch, so the gate is faithful.)
-			(this->*deadReckoner)();
+			// SEND-MIRROR advance: model where the PEER believes this mech is, so the
+			// deadband fires exactly when the peer would drift.  Authentic (binary
+			// FUN_004a9b5c @0x4aab9c): advance projectedOrigin by IntegrateMotion(mj=0)
+			// -- the SAME gait predictor the peer runs -- fed the LAST-SENT commanded
+			// speed.  Our default mirror uses the engine constant-velocity deadReckoner
+			// (AcceleratedDeadReckoner), which does NOT model a gait-driven peer -> the
+			// deadband under-sends and the coupled peer drifts (measured).  With
+			// BT_MASTER_GAITMIRROR: increment projectedOrigin.linear by the mj=0 body
+			// channel's travel (mirrorBodyAdv, = the peer's predicted stride) rotated by
+			// the mirror heading, and integrate the heading by the last-sent angular
+			// velocity.  Re-seeded to localOrigin on each send by the record writers'
+			// projectedOrigin re-base, so this is incremental-from-last-send, exactly the
+			// peer's IntegrateMotion.  (Default OFF: constant-velocity deadReckoner.)
+			static const int s_gaitMirrorSend = getenv("BT_MASTER_GAITMIRROR") ? 1 : 0;
+			if (s_gaitMirrorSend)
+			{
+				Vector3D mAng;
+				mAng.Multiply(updateVelocity.angularMotion, dt);	// last-sent yaw rate
+				ReconQuatIntegrate(&projectedOrigin.angularPosition,
+								   &projectedOrigin.angularPosition, &mAng);
+				projectedOrigin.angularPosition.Normalize();
+				if (mirrorBodyAdv != 0.0f)
+				{
+					Vector3D mLocal(0.0f, 0.0f, -mirrorBodyAdv);	// forward = -Z, frame distance
+					Matrix34 mOrient;
+					Matrix34::FromQuaternion(&mOrient, &projectedOrigin.angularPosition);
+					Vector3D mWorld;
+					FUN_00408744(&mWorld, (Scalar *)&mLocal, &mOrient);
+					projectedOrigin.linearPosition.x += mWorld.x;
+					projectedOrigin.linearPosition.y += mWorld.y;
+					projectedOrigin.linearPosition.z += mWorld.z;
+				}
+			}
+			else
+			{
+				(this->*deadReckoner)();
+			}
 			Vector3D error;
 			error.Subtract(
 				projectedOrigin.linearPosition,
@@ -3774,6 +3825,15 @@ void
 				)
 				{
 					ForceUpdate();					// type 0: pose record
+					// RE-SEED the gait mirror to the just-sent pose: the peer will now
+					// extrapolate from THIS localOrigin, so the mirror must too.  (The
+					// type-0 writer only re-bases projectedOrigin in the sim-state-2
+					// transition, not the normal walk case, so do it here.)
+					if (s_gaitMirrorSend)
+					{
+						projectedOrigin.linearPosition  = localOrigin.linearPosition;
+						projectedOrigin.angularPosition = localOrigin.angularPosition;
+					}
 					if (getenv("BT_WIRE"))
 						DEBUG_STREAM << "[tx0] errSq=" << error.LengthSquared()
 							<< " posDb=" << posDb