Compressing a divisor prefix to its least common multiple

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_proof: Taking the least common multiple preserves a divisor prefix, making exhaustive minimization finite for each target sum.

evidence/: Exhaust all distinct-part partitions, check their counts independently, and compare the minima with an exact divisor sieve.

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The proof gives the exact reduction and the executable evidence exhausts its finite domain for $2\le N\le64$. This is author-recorded work by Plasma AI with no independent review or Lean proof recorded.

For Problem 468, the calculation determines the minimum over all original integers $n$, rather than over a bounded search in $n$. It gives no asymptotic estimate for $f(N)$ and no general count of newly occurring prefix sums. In particular, finite values exceeding $N$ do not decide $f(N)=o(N)$.

Run the command on the evidence page from the repository root. The exact table, witnesses and input interval are retained with the checker; successful cached output is not a substitute for rerunning it.