FINAL-SOURCE VERIFICATION RECORD
October 18, 2026, America/Chicago

Status: NOT VERIFIED AGAINST COMPLETE FINAL JOURNAL TEXT.
This is a specific unresolved source obligation, not a mathematical proof gap.

Verified article identity
Zuwen Luo, Kexiang Xu, Jing Tian, Random subtrees and unimodal sequences in
graphs, Discrete Mathematics347(1)(2024),113654.
DOI: https://doi.org/10.1016/j.disc.2023.113654
Publisher: https://www.sciencedirect.com/science/article/pii/S0012365X23003400
zbMATH: https://zbmath.org/7756925 (final article13-page s).

Verified full-text source used for the conjecture
https://www.researchgate.net/publication/372825398_Random_subtrees_and_unimodal_sequences_in_graphs
Author-uploaded20-page  manuscript, Kexiang Xu, August 2, 2023 (upload notice).
Conjecture 5.1, printed p. 18. Exact statement, with typesetting normalized:
"If e and f are adjacent edges of a complete graph K_n, then"
  P[e subseteq T | f subseteq T] > (3/4) P[e subseteq T].
The manuscript's definitions select uniformly among all nonempty tree subgraphs
of K_n, including singleton trees. This matches our theorem. Theorem 3.3 supplies
the limiting ratio; Theorem 3.5 supplies the finite upper bound. Conjecture 1.2 is
the earlier upper-bound conjecture, not the lower bound proved in our note.

Final-version search and access outcomes
Google/Scholar, exact title/DOI/PII/filename/statement searches, Chinese author
and institutional queries, repositories, citation indexes, archives and message
boards did not produce an accessible complete final copy. No claim is made
that every website or nonindexed deposit has been searched.
Scholar's three versions: ScienceDirect; ACM abstract entry; same author PDF.
Current publisher and ordinary linked PDF requests return a preview/access box.
Crossref VOR-linked Elsevier API supplies metadata only without body in the
public XML response; PDF request restricted. OpenAlex and OpenAIRE indicate
closed access and no repository file. Semantic Scholar's BRONZE flag points
only to DOI; current access does not substantiate an available PDF.
oaDOI redirects to preview. Internet Archive Fatcat reports no accessible files
and only one release. CORE retrieval provided no usable result; Wayback CDX
timed out. These last failures are access limits, not evidence of no holdings.
Author institutional pages list the publication but supply no target file.
MathOverflow, Math StackExchange, Reddit/r/Scholar, PubPeer, Zhihu and Tieba
queries surfaced no matching final copy or resolution. No posting occurred.
Latest preparation refresh returned the same author manuscript and publisher
record; it did not clear the final-source hold.

Closest-source checks
Chin et al., Subtrees of graphs (2018), doi10.1002/jgt.22359, Theorem 6.5:
classical fixed-subtree counts; Section 7Conjecture 7.3 is the upper bound.
https://www.researchgate.net/publication/324905745_Subtrees_of_graphs
Fredes-Marckert, Models of random subtrees of a graph: fixed-size sampling and
spanning-tree negative association; no matching all-order finite lower bound
identified in relevant discussions.
https://www.labri.fr/perso/marckert/Graph_Subtrees.pdf
Yang et al.(2025), doi10.1016/j.ic.2025.105353, full OA publisher text now read:
diameter-constrained counting in tree hosts, no matching correlation theorem.
https://www.sciencedirect.com/science/article/pii/S0890540125000896
Latest checked followups:
https://arxiv.org/html/2508.20593v2 (mean-order extrema; different Conj5.1)
https://arxiv.org/html/2605.03583v1 (dense-host distributions/roots)
No matching earlier resolution found in inspected sources. This supports
provisional result novelty, not absolute priority certification.

How to close the hold
Obtain the final13-page PDF or full published HTML through library/document
delivery, lawful public deposit, or author-provided copy. Compare definitions,
Section 3 and the complete Section 5: exact lower-bound statement, strictness,
quantifiers, numbering and whether its status changed before publication.
Record source URL/access route, version, relevant page and bytes/hash when
available; update attribution only after the comparison. Then refresh later
literature with that exact statement and obtain human mathematical review.

No purchase, external contact, public posting or access-control bypass occurred.
