# Validation and remaining gaps

## Executed evidence · 2026-10-14

- Python 3.12.14, Linux x86_64, actual PyTorch 2.9.1+cpu; CPU only, one thread, deterministic algorithms requested
- Isolated validation environment, with system-site-packages disabled; exact versions recorded in outputs/environment-packages.json; pip check passed
- 14 reference unit tests passed, covering split disjointness/completeness, generator repeatability, train-only scaling, constant features, shape contracts, exact backprop, loss values, eval/no-grad behavior, confusion counts, checkpoint reproducibility, sample-weighted aggregation and stage reference
- All six example programs and six lesson Python blocks executed successfully
- All three full training tasks executed; an independent review reran them twice and reproduced every candidate history, selected epoch and test value exactly in this environment
- Five staged learner functions checked separately; the incomplete starter fails intentionally. Ten deliberately broken/starter variants were rejected after strengthening the public checker
- Independent CSV audit matched all exported float32 features/targets, hashes and split IDs to generated tensors
- Independent capstone probes confirmed selection is unchanged when test tensors are replaced with NaNs, final evaluation requires matching selection, and a second final invocation refuses overwrite
- All diagnostic cases executed, including the honest case where regularization did not beat the best checkpoint of the wider model
- 161 static source/HTML/asset checks passed; independent review confirmed all local targets/fragments, heading structure, prompt/answer counts and chart points
- All nine SVG diagrams were rendered with Inkscape and visually inspected for clipping, spacing and mathematical labels. Browser rendering remains unverified.

This evidence is from actual PyTorch execution. NumPy is an installed interoperability dependency; no NumPy implementation is substituted for the framework.

## Measured outputs and tolerances

Reference full three-task internal runtime was about 4.95 seconds in the first run, excluding interpreter startup. Independent reruns took about 5.2–5.3 seconds internally and 6.8–7.0 seconds including startup. These are authoring-machine measurements, not timing promises for learner devices.

Regression selected MLP: test RMSE 0.161159, MAE 0.125866; train-mean baseline test RMSE 2.285362. Rings selected MLP: 120/120 correct. Bars selected CNN: 120/120 correct. Test labels contain 57 class-zero and 63 class-one samples. The bars linear candidate also had perfect validation accuracy; CNN selection reflects lower validation loss. Perfect toy scores support no claim of real-world perfection.

Within the exact same verified environment, reruns matched exactly. For supported but different CPU builds, use absolute tolerance 1e-5 for deterministic small numerical checks where documented, and diagnose rather than blindly fail if full-training metrics change slightly. A practical reference comparison band is ±0.02 RMSE or ±0.02 accuracy, not a statistical confidence interval or universal pass requirement. Different versions or architectures can alter optimization enough to need a new reference record. Hand backprop/finite-difference checks use float64 and tighter explicit tolerances.

## Installation footprint and scope

The official CPU torch wheel was 184,378,187 bytes. Initial dependency downloads totaled approximately 211 MB from rounded installation logs; the later ignore-installed resolution check downloaded approximately another 211 MB to validate package availability. No GPU or torchvision packages were installed. Final environment logical size was 905,253,518 bytes (about 863 MiB), excluding external interpreter targets. Exact footprint is recorded in outputs/runtime-footprint.json. Runtime binaries, wheels, virtual environments, checkpoints and caches are excluded from the learner archive.

The distributed CPU requirements were resolved with pip from the official PyTorch/PyPI indexes. The isolated environment was assembled in two installation steps, then checked against these requirements; a second newly created environment was not installed solely to repeat identical downloads. macOS requirements and Windows commands were reviewed but not executed. The chosen historical stable version is pinned for reproducibility, not claimed newest.

## Explicit unverified areas

No user Mac, VPS or live site was modified. No publication occurred. Real Windows/macOS installation, mobile-browser interaction, full browser navigation/printing, screen-reader behavior, hosted-notebook execution, integration with the existing Aabha lab, and a beginner learner pilot remain unverified. An attempted headless Chromium launch failed because the cloud sandbox disallowed its socket creation; no browser rendering pass is claimed. Static link/markup checks and local image inspection are not accessibility certification. Suggested pacing and grading thresholds have not been piloted.

Before release, verify the actual supported learner platforms, keyboard/screen-reader access, mobile reflow, download paths and lab runtime. Keep the numerical and evaluation-integrity tests when editing content or upgrading dependencies.