Problem 7.1: worked solution
Example audit, using the synthetic shock tube:
| Evidence channel | Result | Interpretation |
|---|---|---|
| Discretization | L1 difference falls from 0.03066 at 32 zones to 0.00521 at 256 zones | Resolution sensitivity relative to a non-exact 512-zone reference |
| Conservation | finest-grid relative mass error 0 | Internal update check, not physical-model validation |
| Sampling | Not applicable to deterministic shock solver | No random sampling in this experiment |
| Parameter/measurement | Initial state is dimensionless and instructor-defined | No measured-parameter interval is claimed |
| Model discrepancy | 1-D ideal-gas Euler, first-order Rusanov | Omitted multi-D, radiation, magnetic, and gravity physics remain unquantified |
Alternative: audit the seeded radial-velocity result, retaining its 3.090 m/s residual RMS as a model/noise diagnostic and distinguishing fit covariance from model inadequacy. Mark each uncertainty category inapplicable only with a reason.
Problem 7.2: worked solution
The current environment records NumPy 2.5.3, SciPy 1.18.1, Astropy 8.0.1, and REBOUND 5.2.0 under CPython 3.14.6. From a clean venv, install `materials/ASTR474/requirements.txt`, run `python materials/ASTR474/src/generate_astr474_package.py --stage all`, then run `python materials/ASTR474/src/validate_astr474_package.py --verify-checksums`. The validator compares generated files with `data/generated/SHA256SUMS`; a changed file must fail until the build regenerates the manifest from declared sources. Version pins do not guarantee bitwise identity across operating systems, compiler/BLAS builds, CPUs, or future random-generator implementations. An acceptable checksum alternative is `Get-FileHash -Algorithm SHA256` if the same file list and comparison procedure are supplied.
Problem 7.3: worked solution
Sample bounded abstract: We tested a constant-source slab with I0=0.2 and S=0.7 using an analytic formal solution and an independent DOP853 integration. At tau=0.1 the exact intensity is 0.247581; the first-order thin-limit approximation remains within 1% relative intensity error only up to tau approximately 0.1013 for these parameters. This is a synthetic numerical benchmark, not an observed atmosphere. The result is validated against the closed-form solution, while frequency dependence, scattering, and non-LTE source functions remain outside the model. A student's abstract may instead summarize another course result if it reports the actual check, provenance level, and limitations without stronger precision claims. Attach the input, code/environment record, checksum manifest, and a second-method or analytic cross-check.
Scoring guide
Each problem is scored for model/setup (25%), correct computation or derivation (30%), validation and uncertainty (25%), and physical interpretation/communication (20%). Accept alternative correct methods when they meet the same evidence standard. See assessment instructions for error classification and resubmission guidance.