Semester 2 Common Failure Modes

Use a minimal counterexample and a fresh recheck. This table targets specific failures, not a quota of mistakes or generic advice to “add more evidence.”

Failure	Separating example or check	Repair
Numeric magnitude mistaken for input length	Large B written with few bits creates a huge DP table	S1: bit model, table-cell budget, explicit decline
Sorted values hide lost identity	Equal-key records A,C swap or disappear	S2: stable record oracle and tie rule
Endpoint convention changes in prose only	Two intervals touch at time 2	S2/S4: predecessor, proof and witness tests updated together
BFS levels substituted for readiness	Unequal task durations on a diamond graph	S3: weighted longest predecessor finish and certificate
Cycle returns a partial result	Back edge leaves unprocessed vertices	S3: complete coverage or explicit rejection
Correct objective paired with invalid schedule	Duplicate IDs, overlaps or budget overspend	S4: validate witness independently of the reported value
Greedy choice has no exchange argument	Earliest-finish fixture yields 11 instead of 18	S4: derive sufficient state or prove a valid greedy rule
Zero cost causes unbounded reuse	One cost-0 job repeatedly selected	S4: prefix decreases on every inclusion
Latest version used instead of requested version	Two forks from version 0 have different deletions	S5: recheck every retained version against copied models
Shallow copy leaks nested mutations	Caller appends to returned prerequisite list	S5: ownership contract and isolation checks
Invalid batch consumes an ID or publishes partial work	Valid delete followed by missing-key delete	S5: validate working snapshot before publication
Amortized bound sold as request latency	Append at full capacity copies old elements	S5: actual/potential ledger and per-call distinction
Current-only filter hides historical key	A deleted key remains in version 0	S5/S6: supported population, safe rebuild, exact confirmation
Timing or random seed presented as theorem	One run, one input family	S6: measured scope, proof assumptions and repetition
Unsafe search pruning	Low-value partial branch still has a high-value completion	S6: upper bound for maximization or explicit approximation

Record affected competency, failed assumption, repair and changed-case result. Use the rubric to decide whether the error blocks completion.