stage three (C) — real-environment evaluation by occlusion

150 episodes x 200 steps, seeds 5000..5149, identical starts for every row. Band (0.13, 0.63), paddle width 0.16.

oracle has perfect vision and perfect memory; wait_and_see has perfect vision and NO memory (it tracks the true ball only while ball_visible > 0.5 and STAYs otherwise). Every trained row should be read as a position between those two, and the single most important fact about any row is which side of wait_and_see it falls on: above it is memory, below it is not. Any row whose name contains poshead is a PRIVILEGED CEILING — its dynamics model was trained with a supervised head on the simulator’s true ball position — and is not a world-model result.

The two numbers everything is graded against, measured here on these 150 episodes: oracle 0.99, memoryless (wait-and-see) bound **0.51, stand still 0.38.**

Each controller is driven by the (V, M) it was trained with; the policy reads h, so M is part of the policy:

The headline: every row against the memoryless bound

wait_and_see = 0.51 is the best a policy with perfect vision and no memory can do in this world. A row above it is using memory; a row below it is not, whatever else it is doing well.

The CI is a 4000-sample bootstrap over EPISODES, the unit of independence; “above the bound” is read off the point estimate, so a row whose interval straddles the bound is not a claim.

Interceptions per floor visit, by required move

The required move is the distance between the paddle’s x at the moment the ball became fully hidden on its way down and the ball’s landing x. Flat across the bins = object permanence; collapsing on long = memoryless.

The bins are policy-dependent and that is not a bug to hide. The required move is measured from this policy’s own paddle position, so a policy that already tends to stand near the ball generates few long visits and a policy that parks in a corner generates many. The counts are therefore reported per row, and a row with a handful of long visits should be read as noise. The episodes and seeds are identical throughout; only the paddle differs.

The reach curve (interceptions per visit at 0.1 resolution)

A required move is covered once the paddle’s centre is within half a paddle-width (0.08) of the landing x, plus whatever the visible frames between the band’s bottom edge and contact height buy. On v3’s geometry that came to ~0.43 and wait_and_see was at the ceiling out to 0.6; v3.1 halves both terms, which is the whole point of the re-design. This table says where wait_and_see actually falls off, and therefore which bins above carry any information about object permanence.

Paddle motion during occlusion

Over the descending hidden runs: the fraction of hidden frames whose ACTION moved the paddle toward the eventual landing x (chance 1/3 — three actions, STAY counts as not-toward), and the displacement the paddle actually achieved toward the landing point while blind, as a fraction of the required move.

oracle is not the ceiling for these two columns and should not be read as one: it chases the ball’s CURRENT x rather than its landing x, and it is usually already inside its dead zone when the ball vanishes, so it STAYs. The references that mean something here are chance (1/3) and wait_and_see (0.000 by construction).

Overall

VAE reconstruction on each band

The frozen encoder+decoder on frames from datasets collected at each band height, so an other-band drop can be attributed to V or to C.

Dream-vs-real transfer

Pearson r between the smoothed best-of-generation dream fitness and the periodic real interception count, per training run (dream_vs_real_all.png, and dream_vs_real.png in each run directory).