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Claim. The account sallerk, in a comment of 31 August 2026 (the claim's date) on the site's discussion thread, reports that every connected graph on at most $11$ vertices can be partitioned into at most $\lceil n/2\rceil$ edge-disjoint paths: $11{,}716{,}571$ graphs at $n=10$ and $1{,}006{,}700{,}565$ at $n=11$ were decided, with no counterexample and no graph left undecided. The check is over simple paths, not trails, as the statement of Problem 583 requires. Each sweep is split into shards and accepted only when the shard counts sum to the number of connected graphs on $n$ vertices (OEIS A001349), which the comment presents as its exhaustiveness certificate. A second decider written from the definition agrees with the fast one on all $992$ connected graphs on $4$ to $7$ vertices; beyond $n=7$ the result rests on the fast decider and the count alone. The comment argues the range is not vacuous, since from $n=7$ upward a growing share of the connected graphs ($36$ of $853$ at $n=7$, $6{,}666{,}730$ of $11{,}716{,}571$ at $n=10$) is reached by none of the six partial results the site lists. The code, run records and a reproduction note are in a public repository, and the comment discloses that the searches and computations were done with AI assistance. The repository link is pinned to the revision of 31 August 2026 that the comment posted; the folder was pruned on 7 September 2026.

Independent reproduction. A comment of 17 September 2026 by the account herong reproduces the $n\le11$ result with an independent decider; it has its own page, herong's check.

Covers. Connected graphs on at most $11$ vertices. Nothing for $n\ge12$: the comment says the $n=12$ sweep leaves $35{,}633{,}639$ graphs its heuristic cannot decide, and the problem asks about every $n$, so neither a proof nor a counterexample follows.

Depends on. Nothing in this wiki.

Standing. Claimed: a forum computation with provenance, which the site does not verify; reproduced by a second forum computation (herong's, above), not reviewed and given no credit by this corpus, which has not run either check. The claim is partial, so the problem's standing is unchanged by it.