Competencies, Evidence, and Remediation
Complete each competency independently. Finishing the book list or implementing one traversal does not establish the whole module's outcomes.
| Competency | Evidence | Repair path |
|---|---|---|
| C1: model and representation | A1, P1–P4, lab contracts | Concepts 1–4; preserve edge identities and isolated vertices |
| C2: traversal and structure | A2, Lab A, P5–P8 | Concepts 5–8; finish events, mutual reachability, cycle versus downstream |
| C3: nonnegative routes | A3, Lab B, P9–P10 | Dijkstra proof, stale heap entries, parent-edge validation |
| C4: signed route statuses | A4, Lab B, P11–P12 | Snapshot/in-place distinction and source-cycle-target reachability |
| C5: forest optimum | A5, Lab C, P13–P16 | Respecting cuts, tied exchanges, forest coverage |
| C6: feasible and optimal flow | A6, Lab D, P17–P19 | Residual cancellation, capacity/conservation, equal cut bound |
| C7: reduction correctness | A7, Lab E, P20 | Both matching/flow directions and integrality |
| C8: engineering transfer | A8, dependency capstone | Resource assumptions, error behavior, independently checked outputs |
Per-competency rubric
- 0: absent work or a fundamentally wrong model, result or contract.
- 1: partly correct output but a material proof, witness or cost error.
- 2: correct output, valid witness where requested, sound proof sketch and explicit preconditions/cost model; minor omissions are repairable.
- 3: level 2 plus independent changed-assumption reasoning, an effective counterexample, and a clear explanation of the algorithm's practical limits.
Initial completion requires at least level 2 in every competency, all five lab contracts passing checks, source review of the implementation/proof obligations, and a complete evidence record. Finite tests cannot certify asymptotic complexity or independent authorship. Equivalent valid optima must be accepted when ties are outside the output contract.
Critical errors block the affected competency: losing isolated vertices or edge identity; confusing reachability with SCCs; using discovery as weighted finality; marking all pairs unbounded because any negative cycle exists; excluding every tied maximum cycle edge from all MSTs; infeasible flow or missing cancellation; equating maximal with maximum matching; or presenting critical-path duration as an unrestricted resource-constrained scheduling guarantee.
Repair and delayed recheck
Retain the original attempt, score, assistance, counterexample, repaired invariant and fresh task. Use the named repair lesson, then attempt a changed graph without viewing the key. Do not average away a missing competency or impose an arbitrary number of invented mistakes.
After 7–14 days, attempt a 60–90 minute unseen transfer task with changed edge direction, weight domain, witness requirement or assignment capacity. Require at least level 2 in each competency it exercises. A reviewer should ask why the previous algorithm or proof stopped applying, not just whether new code runs.
The workload and thresholds are author estimates pending independent review and learner pilots. Passing one module does not certify an elite professional percentile.