Across this campaign every method — PPO, our value-aware abstraction-in-loop, raw residual, retry, two curricula, mid-size and bigger nets, deploy best-of-k — converges to ~0.79–0.83 real success on PandaPickCube. Part 30 settles why, with the two cleanest tests and a per-config diagnosis. The answer is not “we need a better learner.” It’s the orientation.

Two decisive tests

Is 0.81 a budget ceiling? — No. Stock end-to-end PPO, unmodified reward, run to 180–205M env-steps (2 seeds):

  uniform success far-reach success
PPO @180–205M (seed 1 / 2) 0.828 / 0.828 0.145 / 0.148

That is exactly “PPO-100”’s 0.832 — which PPO already reached back at 30–110M. 6× more budget buys nothing. The ceiling is not budget.

Is it a learning-paradigm ceiling? — No, and learning the grasp from scratch doesn’t help. End-to-end PPO (stock 6-DOF-capable action, no fixed controller/residual) with a far-reach curriculum (reset distribution oversamples box+target at x∈[0.8,0.9], P_far=0.6), 120M steps, 2 seeds:

  uniform far-reach
learned-grasp + far curriculum 0.828 / 0.828 0.180 / 0.180

It ties PPO and does not lift the far tail — the curriculum made the policy master far-reach reaching (reached_rate ~0.99) but not far-reach success.

Why — the success metric is orientation-weighted (verified from source)

The success metric is not “cube at target position.” From pick.py:

pos_err = ‖target_pos − box_pos‖
rot_err = ‖R_target[:6] − R_box[:6]‖          # cube tilt vs the (upright) target
box_target = 1 − tanh(5·(0.9·pos_err + 0.1·rot_err))   # success ≡ box_target ≥ 0.9

target_quat is the identity quaternion, so success requires the cube at the target position and upright. Solving box_target ≥ 0.9 gives 0.9·pos_err + 0.1·rot_err ≤ 0.0201. Plug in the measured far-reach medians (pos_err 0.006, rot_err 0.40):

case 0.9·pos + 0.1·rot box_target pass?
far median (pos 0.006, rot 0.40) 0.0454 0.777 ✗
perfect position (pos 0, rot 0.40) 0.0400 0.803 ✗
required (pos 0.006, rot ≤ 0.147) 0.0201 0.900 ✓

So even with perfect position, the far-reach tilt (rot_err 0.40) caps box_target at 0.80 — orientation alone disqualifies the tail, and passing needs rot_err ≤ 0.147 (≈ within 8° of upright). Per the best learned-grasp checkpoint, only 12% of far episodes clear that bar; position is solved (pos_err median 0.006, 72% within 3 cm) but orientation is not.

The proof: it’s physical, not a learning gap

Is rot_err ≤ 0.147 at far reach merely unlearned, or kinematically impossible? We tested it directly. For a rigid top-grasp the cube tracks the hand, so rot_err ≤ 0.147 means the hand must stay within 8.4° (x/y), 5.95° (z) of the canonical upright-holding pose. We sampled every hand orientation inside that tolerance and asked whether any admits a valid in-joint-limit IK solution at the far target — i.e. can the Panda physically hold a grasped cube upright there at all (hl_tail/upright_ik_test.json):

split n upright-graspable INFEASIBLE
hard far-tail (reach ~0.865 m) 801 0.12% 99.88%
uniform far (reach ~0.868 m) 500 0.20% 99.80%

And it is sharply reach-gated: upright-feasible 17.5% at reach 0.80–0.82 m → ~0% beyond 0.84 m. This sits exactly alongside Part 28’s finding that 100% of targets are position-reachable (with any orientation): you can put the gripper at the far target, but at full extension the wrist cannot keep a grasped cube within 8° of upright. Position-reachable ≠ upright-graspable.

So the last ~17% is not a reaching, exploration, capacity, or budget problem, and it is not learnable for the standard top-grasp — it is a kinematic fact: the success metric demands the cube upright, and the Panda physically can’t deliver that past ~0.84 m reach.

The campaign-wide picture

family real success
jumpy / vanilla TD-MPC2 0.00
value-aware abstraction-in-loop (Parts 24–27) 0.79
PPO; long-PPO 200M; learned-grasp; curriculum ~0.81–0.83
(theoretical, env allows) ~1.0

Everything that learns the task at all converges to ~0.83. That convergence — across model-free RL, model-based abstraction, and end-to-end learned grasping — is the signature of a task/metric ceiling, not a method ceiling. Part 28 already showed the env allows ~1.0 (0% of targets unreachable); Part 30 shows what stops every method short of it: the orientation requirement on far-reach grasps.

Verdict — the quest, closed honestly

You cannot break ~0.83 on PandaPickCube by training harder or smarter — and now we know it’s not even a learning problem. Budget (Part 30), capacity (Part 28), retry (Part 28), curriculum (Parts 28, 30), abstraction (Parts 24–27), and learned end-to-end grasping (Part 30) all hit it, because the binding constraint is far-reach grasp orientation, and 99.9% of the far tail is kinematically incapable of an upright cube under the box_target metric (proof above). No optimizer crosses a wall the robot physically cannot reach. To get past ~0.83 you must change the problem, not the policy:

  1. A fundamentally different grasp + reorient — the IK proof rules out the top-grasp family at far reach; a non-top grasp (e.g. side-grasp) plus an in-hand/regrasp reorientation maps the upright constraint to a different hand pose and is the only remaining mechanical escape. It is a hard manipulation problem, not a tuning lever, and is unverified here (the IK test covered the canonical top-grasp).
  2. Relax / change the success metric — drop or down-weight the orientation term, or sample the target orientation (the PandaPickCubeOrientation variant), so “upright at far reach” stops being required. This changes the task and is not comparable to the numbers here.
  3. Accept that ~0.83 is this task’s honest, kinematically-imposed ceiling under the current metric.

So the headline of the whole arc stands and is now fully explained: a value-aware abstraction in the loop matches PPO (~0.8) and beats it on sample-efficiency, and the remaining ~17% is a fundamental orientation-gated property of PandaPickCube that no method in the standard toolbox crosses.

Caveats

2 seeds per arm (the 0.828 is identical across seeds and matches the independent PPO-100 number — robust); multi-seed long-PPO confirmation (seeds 21–23) running. The upright-IK proof assumes a rigid canonical top-grasp (cube tracks the hand); a fundamentally different grasp family (side-grasp + reorient) is not ruled out and is exactly escape (1) above. The metric/algebra is verified from pick.py source; the rot_err medians are from the best learned-grasp checkpoint, and a rollout-level rot_err-vs-reach corroboration (does any far episode ever reach rot_err ≤ 0.147?) is running. Data: exp/tdmpc_glass/{hl_learngrasp/{RESULTS.json,*_far.json,diag_far.py}, hl_tail/upright_ik_test.json}. Prior: Parts 27 (tie), 28 (reachability), 29 (orientation lever).