29.4 E7: one actually trained prior
A 16-48-48-1 MLP with 3,217 parameters predicts visibility from receiver XY, light XY, and twelve renderer-owned sphere coordinates/radii. It is a small learned visibility approximation, not a learned world-dynamics model or a unified graphics network. Training uses 73,728 exact ray labels from 48 procedural scenes. Validation and first test sets each use eight disjoint scenes and 12,288 rays. Weights are selected by validation loss only. The independent follow-up renderer scenes use a further disjoint ID range. No external model or image dataset is required.
Test Brier loss is 0.183449, compared with 0.231951 for a constant equal to training-set mean visibility. The model was trained for 40 epochs; epoch 3 was selected. Later epochs overfit. NumPy inference differs from PyTorch by at most 1.19e-07 on the checked test set. Training took 1.922 seconds in this CPU environment; this is not a general training-time prediction.
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29.5 E8: a physical ray benchmark
The scene consists of Lambertian point receivers on a floor, three opaque sphere occluders and 36 finite point emitters. A physical shadow ray is a segment/sphere intersection test. Current unoccluded contributions use analytic cosine, inverse-square attenuation, material color and emitter intensity. The full 36-term sum is an exact reference for this scene model; it is not a converged multi-bounce path-traced game reference. The high-frequency floor texture is known to the engine, not recovered by super resolution.
There are 2,048 canonical receiver cells, a moving 16 by 20 receiver viewport, eight held-out scenes, three sampling replicates, and two fresh shadow rays per receiver per frame. The sequence has four cold frames, sixteen warm frames, a 500-tick interval with no observations of these receivers, eight revisit frames, eight relight/material-color frames, and eight hidden-geometry-change frames. The clock gap is not 500 fully rendered frames. The earlier atlas E1 supplies a different 500-observed-frame diversion experiment.
Every method receives the same allowed engine geometry and physical ray budget. Ground-truth tables are generated in an offline audit path and never supplied to the online sampling policy. Except for the active proposal, the algorithms use the same known unoccluded-light importance distribution and paired uniform random draws. References and neural-feature preparation are excluded from per-batch timing and identified separately. These are equal-ray comparisons, not equal-VRAM, equal-FLOP, equal-latency or production-baseline comparisons.
All entries below are conditional expected linear-RGB MSE, averaged over receivers, channels, frames, replicates and scenes. For corrected estimators the conditional MSE is enumerated exactly using R2, after the online estimate is produced; the plug-in row is its actual squared bias. Independent observed sample MSE is also recorded in CSV.
| Method | Cold | Warm | Revisit | Relight | Hidden change |
|---|---|---|---|---|---|
| Raw importance | 0.004162 | 0.004162 | 0.004162 | 0.009814 | 0.009575 |
| Neural CV | 0.003797 | 0.003797 | 0.003797 | 0.006035 | 0.002487 |
| Constant world CV | 0.003878 | 0.002617 | 0.001497 | 0.001634 | 0.007572 |
| Screen CV | 0.003604 | 0.002534 | 0.003371 | 0.003893 | 0.005485 |
| World CV | 0.003604 | 0.002413 | 0.001370 | 0.001474 | 0.007301 |
| Active world CV | 0.003201 | 0.000916 | 0.000074 | 0.000061 | 0.013077 |
| World plug-in | 0.002478 | 0.000957 | 0.000283 | 0.000223 | 0.004943 |
The first protocol was fixed before its first benchmark run. The original adverse result is retained. Percentile 95% intervals below resample eight scene clusters, preserving within-scene replicates; they characterize this small generator, not arbitrary games.
| Comparison | Expected MSE reduction | 95% scene interval |
|---|---|---|
| World CV vs Screen CV, revisit | 59.36% | [52.74%, 63.06%] |
| World CV vs Raw importance, revisit | 67.08% | [59.17%, 72.62%] |
| Active world CV vs World CV, hidden_change | -79.11% | [-86.20%, -70.75%] |
| World CV vs Screen CV, hidden_change | -33.12% | [-39.91%, -24.66%] |
| World CV vs Constant world CV, revisit | 8.46% | [-10.12%, 27.65%] |
A negative reduction means a regression. The 8.46% neural-prior advantage over constant-prior world memory on revisit has an interval spanning zero. The study therefore does not establish that a neural component is necessary for most of the persistence gain. The uncorrected plug-in often has lower finite-sample MSE than the unbiased estimator; its bias guarantee is weaker. Unbiasedness is an explicit contract, not a promise of the best display image at two samples.
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29.6 E9: an independent correction experiment
The initial result exposed severe overconfidence: active sampling largely ignores previously learned terms, so changed occluders can move residuals into directions with little sampling probability. The ten-percent proposal floor preserves unbiasedness but does not prevent a variance spike. We added one observation-driven rule: if a fresh exact visibility sample contradicts trusted memory, revoke its trust epoch globally before the next batch. Stored values remain fallible controls. The first surprise frame is necessarily unchanged.
This follow-up uses new scenes 300-307 and new sampling seeds, with no weight retraining, no geometry-change notification and no access to the reference in the policy. Its protocol was frozen after diagnosing the first study and before running the follow-up. It is an independent scene split within the same scene family, not a completely independent replication.
| Hidden-change comparison | Expected MSE reduction | 95% scene interval |
|---|---|---|
| Guarded active vs Active world CV | 46.61% | [43.98%, 50.89%] |
| Guarded active vs World CV | 7.12% | [2.67%, 12.28%] |
| Guarded active vs Raw importance | 59.39% | [40.55%, 77.24%] |
| Guarded active vs Screen CV | -8.53% | [-23.24%, 6.53%] |
The guard reduces the unguarded active failure by 46.61% in this follow-up. It still has 8.53% higher mean error than screen history over the full hidden-change interval, with an interval crossing zero. There is no uniform dominance claim. The first surprise frame is included in every aggregate; by later frames the guard reacquires more appropriate evidence.
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The two physical studies produced 12,672 frame-method records and 8,110,080 online shadow-ray calls in total. Training/validation/test labels and offline reference enumeration are additional, separately scoped work. Runtime memory per persistent method is 589,824 bytes (0.5625 MiB) for this tiny 2,048-receiver scene. Twenty-eight new contract/oracle tests and fourteen retained foundational tests pass.
What has advanced: an actual trained prior, a physical oracle, causal world memory, a residual-correction API, an active controller, observed contradiction handling, and independently split diagnostic evidence now exist. What remains unvalidated: joint SR/RR/FG, general path transport, chronoscopic/counterfactual training, game integrations, calibrated neural uncertainty, matched-time superiority and GPU feasibility.