RANDOM-SUBTREE FINAL-SOURCE ORIGINALITY CHECK
October 18, 2026, America/Chicago
Publisher follow-up; no publication authorization inferred

RESULT
The focused online check is complete with a specifically bounded outcome: no
lawful COMPLETE final 13-page journal text was obtained. Therefore the exact
published conjecture status, numbering, proof coverage and all final hypotheses
remain unverified. This is not unrestricted originality clearance, and is not
evidence that the final article already proves the result. The source-access
limitation must remain explicit in the review and any authorized revision.

The earlier independent mathematical/replay verdict remains PASS for unchanged
sources. Relative to the complete, publicly available 20-page author manuscript,
the note proves exactly its strict finite adjacent-edge lower-bound conjecture.
No matching earlier proof appeared in the focused refresh. These findings still
support provisional originality and a modest worthwhile specialist-note value;
they do not establish priority over the unexamined final article or all literature.

EXACT RESULT AND CLOSEST PRIOR CLAIM
Scott Schubr, A sharp lower bound for adjacent-edge correlations in random
subtrees, reviewed package:
D:/LUMINARY ODDITIES LLC/AI Research/subtree_prepublication_package_Riemann_A_20261018
For every n>=3, T uniform among nonempty tree subgraphs of labeled K_n, singleton
trees included, and distinct adjacent e,f:
  P(e in T | f in T) > (3/4) P(e in T).
The known limiting ratio supplies optimality; neither the constant nor that limit
is newly claimed. Fixed-forest counting and reciprocal Jensen are standard tools.
The identifiable candidate increment is the finite strict inequality and its short
elementary all-n proof. This does not assert monotonicity or general host graphs.

Luo, Xu, Tian, Random subtrees and unimodal sequences in graphs:
- Public author manuscript, 20 pages, uploaded by Kexiang Xu August 2, 2023:
  https://www.researchgate.net/publication/372825398_Random_subtrees_and_unimodal_sequences_in_graphs
  The all-order subtree model includes singletons. Theorem 3.3 gives the limiting
  ratio; Theorem 3.5 gives an UPPER bound. Printed p. 18 Conjecture 5.1 is the strict
  finite LOWER bound at issue. It is not their already-resolved Conjecture 1.2.
- Final journal record: Discrete Mathematics 347(1) (2024), 113654, 13 pages.
  https://doi.org/10.1016/j.disc.2023.113654
  https://www.sciencedirect.com/science/article/pii/S0012365X23003400
  The accessible publisher preview discusses the same model and upper-bound
  result plus limiting ratio. Its absence of a new lower-bound proof in the
  abstract/introduction is not proof that none occurs later. Section 3 and the
  COMPLETE Section 5 could not be compared. Do not silently identify the author
  manuscript with the final typeset version.

FRESH LAWFUL RETRIEVAL COVERAGE
Raw response bytes, status, exact URLs, timestamps and SHA256 are saved in
source_receipts/ and the JSON receipts adjacent to this report.
1. Publisher article page and ordinary linked PDF request: HTTP 403; not PDFs.
   Browser reader/search indexing provides a preview, not the complete final text.
2. Elsevier public content API pii-path XML/PDF requests: HTTP 429. No rate-limit
   or access-control bypass was attempted.
3. Exact Crossref VOR/TDM XML link PII:S0012365X23003400: HTTP 200, 1792 bytes,
   core bibliographic metadata only; openaccess=0, no article body. A response
   element named full-text-retrieval-response does not make it full text.
   Explicit documented FULL view: HTTP 401 AUTHENTICATION_ERROR/Invalid API Key.
   No API credential was invented, supplied or acquired. Plaintext link: 400.
4. Crossref: confirms DOI, journal, version-of-record TDM links. Metadata only.
5. OpenAlex work W4385962474: closed; no repository fulltext or PDF location.
6. OpenAIRE: closed; identifiers resolve only to DOI/DBLP/zbMATH, no file deposit.
7. Semantic Scholar 139f3656f0e1e5197457d0dcb15197ae10fab702:
   openAccessPdf says BRONZE but its URL is merely the DOI landing page, not a
   PDF. That flag conflicts with the closed-access indexes and does not supply
   a readable final text. It was not treated as successful OA retrieval.
8. Unpaywall unauthenticated request: 422 requires email; no personal address or
   fabricated email was submitted. This request yields no availability conclusion.
9. EuropePMC DOI search: 0 records, not a proof of absence in mathematics archives.
10. Author institution: Kexiang Xu's NUAA English/Chinese home and paper-list
    pages read. No target PDF was supplied. The home-page external profile link
    uses an institution portal host that fails DNS here. No university login or
    proxy access was attempted or bypassed.
    https://faculty.nuaa.edu.cn/xkx/en/lwcg/21729/list/index.htm
    https://faculty.nuaa.edu.cn/xkx/zh_CN/lwcg/21714/list/index.htm
11. Firecrawl scientific-paper metadata and in-body passage retrieval for the DOI
    each returned 404: paper not available through that index. These failures do
    not establish anything about the paper's mathematical content.
12. Exact title/DOI/PII, PDF, institutional, arXiv, conjecture-number, lower-bound,
    three-quarters, reciprocal/Jensen and adjacent-edge/correlation searches did
    not recover a different complete final copy or a matching earlier proof.
    Search outputs are saved. Existing independently reviewed primary followups
    (Chin et al.; Fredes-Marckert; Cambie-Jooken-Wagner; Wagner-Wang; Wang 2026
    thesis) retain their earlier recorded comparison scopes; this pass does not
    reclassify those papers as full rereads or exhaustive worldwide discovery.

PROPORTIONATE JUDGMENT
Validity: earlier complete proof and exact replay PASS, authenticated unchanged.
Originality/novelty: provisionally positive versus the inspected author manuscript;
unresolved versus its unexamined final edition and absolute worldwide priority.
Value: focused specialist contribution, with an explanatory short proof. It is
not a new forest-counting theory or discovery of 3/4. If the final paper contains
the same theorem, the claim must be recast as an independent proof/exposition and
the contribution reassessed. There is presently no evidence that this happened.
Readiness: suitable for Scott's review as a transparently qualified specialist
note. Do not describe it as fully novelty-cleared, first proof, or resolution of
a conjecture verified to remain open in the final published paper. Release and
whether to accept the disclosed source limitation are human decisions; the user
explicitly requested a report before publication, so no handoff is authorized.

MINIMAL DISCLOSURE AND OPTIONAL ALTERNATIVE
The existing abstract identifies the author manuscript, and its short source-
version footnote already warns that final wording/numbering have not been
verified. Keeping that version-bound wording while this report retains the
explicit novelty limitation does not require a duplicate disclaimer or a new
manuscript revision. Preserve existing credit for the conjecture and constant.
If the editor chooses a more explicit overlap caveat, a single alternative
footnote is sufficient:

  The conjecture number refers to the 20-page author manuscript. We have not
  compared the complete final journal article; overlap with results established
  there remains unverified, and no priority over such results is claimed.

No conflict-of-interest statement is required by this source issue, and no
unsupported declaration should be added. The abstract's author-manuscript
qualifier is accurate and can stay. This is an optional alternative, not a
required correction to the mathematics; this report edits no frozen manuscript.

REMAINING SOURCE OBLIGATION
Obtain the final 13-page paper by a lawful accessible deposit, existing library
access, or author-supplied copy. Compare the model, all of Section 3 and Section 5,
strictness/endpoints, final numbering and proof status; bind its bytes/version
and update the exact attribution. Do not call the source comparison complete
because the bounded search or this assessment report is complete.

PRESERVATION AND SCOPE
Only this external review directory was written. Original sealed package remains
unchanged; see source-preservation.json for 14 manifested file checks and ZIP hash.
No theorem/proof/code revision, research extension, purchase, outreach, posting,
publication, database change or shared-registry edit was performed by this agent.
