Competencies, Evidence, and Remediation
Completion requires level 2 or better in every competency, passing the core lab contracts, a reviewed capstone and a delayed unseen transfer attempt. Do not average away an unsafe reconstruction or invalid state. Level 3 reflects stronger evidence within this module; it is not a professional-percentile claim.
| Competency | Evidence | Critical failure | Repair |
|---|---|---|---|
| C1: state/decomposition | A1, P1–P3, state cards | Histories with different futures merged; double counting | Construct collision; prove soundness/completeness |
| C2: sequence contracts | A2, P6–P7, Lab A | Non-strict LIS or invalid alignment accepted | Trace equality and verify original identities/strings |
| C3: capacity/versioning | A3, P4/P8, Lab B | Reused 0/1 item; impossible treated as zero | Restore layers and reconstruct a fresh case |
| C4: interval/tree combination | A4, P11–P14, Lab C | Invalid split cost or unvalidated tree | Derive boundary costs and independent child states |
| C5: subset constraints | A5, P15–P16, Lab D | Missing closure or repeated city; exponential cost hidden | Enumerate tours and count states/transitions |
| C6: digit semantics | A6, P17, Lab E | Padding, zero or bound cache changes counted set | Compare tiny ranges to enumeration |
| C7: optimization choice | A7, P19–P20, capstone | Greedy asserted without proof; budget ignored | Counterexample and augmented state |
| C8: engineering evidence | A8, contracts, every lab | Value-only tests, false space/time claims | Witness checker, oracle and measured resource record |
Levels
- 0 — missing or invalid: no usable explanation or a critical failure remains.
- 1 — assisted: can follow a familiar trace but requires hints to define state, repair assumptions or justify output.
- 2 — independent: correct contract, derivation, proof outline, boundary cases, witness and cost analysis; passes a fresh equivalent task without the key.
- 3 — transfer: independently adapts to a changed constraint, explains failed alternatives and defends the new proof/resource tradeoff.
For a clerical arithmetic error, identify whether the model remains sound and recheck a new numeric case. For a conceptual error, do not pass the competency until a fresh task demonstrates repair. The scoring key lists what each task must establish, while source/code review checks properties that finite tests cannot establish, including independence and asymptotic behavior.
Lab acceptance
All eight APIs must satisfy documented contracts, not merely fixture values. Record the tested environment, preserved attempt, checks, source reasoning and help used. Untouched starter code must fail; an implementation importing the reference does not meet independent implementation requirements. Different tied witnesses are valid. Reject illegal objects even when their reported value is right.
Remediation and delayed transfer
Within the failed competency, use one minimal counterexample, repair the state or invariant and solve a fresh problem. After 7–14 days, attempt a changed requirement without solutions: exact-fill selection, a digit occurrence property, an additional scheduling budget, or a tree-distance reroot task. Record assistance and score the affected competencies again. Passing the original fixture twice is not delayed transfer.
Workload estimates and grading reliability still need learner pilots and reviewer agreement; use the instructor guide to collect that evidence.