A Stable Transport-Mechanism Descriptor for Per-Pixel Rendering Difficulty
Per-pixel rendering difficulty is conventionally measured by the sample variance $\hat\sigma^2(p)$ of a Monte Carlo estimator, yet this signal is least reliable exactly where difficulty concentrates: under heavy-tailed transport its relative error is governed by the integrand's kurtosis, and the split-half reliability of variance-derived evaluation targets reaches only 0.23-0.29 even at 40,000 samples per pixel. We propose a complementary discrete transport-mechanism descriptor: every contribution event is classified by its end-vertex BSDF lobe, the presence of a delta-specular event, and a single-/multi-bounce distinction, yielding seven mutually exclusive labels whose six named mechanisms receive all observed energy on tested scenes, with continuous side-channels retaining the mechanism mixture. Across seven scenes, the dominant label agrees 87-99.6% between 64 and 4096 samples per pixel -- where quantile-binned variance agrees as little as 21% -- and is robust to restoring the estimator's MIS half. The descriptor exposes cross-scene structure a scalar variance cannot represent, including a geometry-controlled sign reversal of the delta-mediated/glossy correlation. Using the label to correct a noisy pilot variance improves on pilot-variance sample allocation at equal budget on every test-matrix scene with heavy-tailed buckets, while reducing exactly to the incumbent where such buckets are absent, with gains surviving a random-partition placebo and persisting over a robust (median-of-means) pilot baseline. Pre-registered third-party sentinel tests confirm the account out of distribution: coverage and stability transfer, a structural finding survives a blind sign prediction, and on the ajar-door scene, where pilot-variance allocation fails 6.8 dB below uniform sampling, the label identifies from the pilot alone that the failure is not of the kind it repairs, and correctly abstains.