Appendix D — The Incident Card
When a run fails, complete one card. Fill fields 1–3 before opening any diagnostic panel. A strong diagnosis does not collect votes; it names a rival cause and the control that could acquit it.
D.1 Three cumulative act assignments
The card is built across the course rather than introduced after the diagnosis is complete.
Act 0 — execution contract
Choose one numerical or performance symptom from C01–C04. Complete Fields 1–4 and 10 before seeing the reference outcome. Your paired control must keep the mathematical target fixed while changing exactly one of traffic, reduction order, dtype, or step size.
The audit packet includes two intentionally plausible defects:
- a speedup claim with no traffic or device boundary;
- code that computes the right statistic over the wrong axis.
Deliverable: the partial card, the corrected claim or code, and one sentence explaining why the other defect would survive your control.
Act I — geometric locator
Extend the same card with Field 7 and revise the verdict vocabulary to include detects only. The packet supplies a spectrum plot whose values are correct but whose matrix is not named. Identify at least two candidate matrices, then state which conclusion changes when the matrix changes.
Deliverable: a caption that names matrix, scaling, centering, finite-null or perturbation control, and the conclusion the spectrum does not establish.
Act II — causal incident
Complete all ten fields. The packet now contains:
- a proof with one silently dropped independence or smoothness assumption;
- clipping described as variance reduction without its target shift;
- a matrix-update trace whose update spectrum is mislabeled as a weight spectrum.
Correct each item before assigning cause.
Incident B is deliberately unrevealed. Its available panel activates more than one mechanism-specific instrument, and the supplied observations are compatible with at least two causal explanations. There is no answer key in the book. A valid submission may conclude not identifiable if it proves the observational equivalence and requests the cheapest additional control. The card is not a deterministic troubleshooting flowchart.
Deliverable: a complete card, one rejected causal story, one surviving rival, and the next measurement that would distinguish them.
D.2 Blank incident report
| Field | Record before interpretation |
|---|---|
| 1. Symptom | Quantity, step or interval, magnitude, baseline: ____________________ |
| 2. Prediction | Rank suspects; one acquitting control each: ____________________ |
| 3. Contract | Target; axes; denominator; dtype; seed; device; wheel/commit: ____________________ |
| 4. Precision control | Paired-precision deviation versus local spacing and range (Section 3.2): ____________________ |
| 5. Curvature control | \(\alpha\lambda_{\max}\); directional value; reference boundary (Section 16.2): ____________________ |
| 6. Estimator control | Conditional target; noise-to-signal ratio; discrepancy attribution (Section 13.1): ____________________ |
| 7. Spectrum locator | Matrix name; update and weight singular values (Section 17.3): ____________________ |
| 8. State control | Repeated-input statistics; retained state; replay determinism (Section 15.3): ____________________ |
| 9. Verdict | Acquitted / detects only / cause identified: ____________________ |
| 10. Corrective control | Rerun that removes the symptom while declared controls remain fixed: ____________________ |
D.3 Compact instrument panel
| Thread | Symptom | Instrument and control | What the control cannot decide |
|---|---|---|---|
| Numerical stability | represented values stall, overflow, or disagree across precision | local spacing, range, and a paired-precision rerun (Section 3.7) | whether curvature, data, or retained state caused an event that survives the precision control |
| Random-matrix spectra | one matrix direction expands, collapses, or separates | name the matrix; compare edges, bulk, and update-versus-weight spectra (Section 17.3) | why the direction changed |
| Landscape and update geometry | loss oscillates or a scalar step becomes locally aggressive | top and directional curvature beside the exact fixed-quadratic boundary (Section 16.1) | a global nonlinear divergence claim from one local value |
| Sub-Gaussian safe zone | a mean estimate hides dispersion or rare updates dominate | conditional estimator, tail diagnostic, matched batch control, and clipping-bias audit (Section 13.4) | a population tail class from one finite trace |
The completed card in the Coda is a worked example, not a universal ordering of suspects. When a control detects an event without identifying its cause, record detects only and keep the rival explanations alive.