INDEPENDENT FOLLOW-UP ORIGINALITY AND VALUE REVIEW
October 18, 2026, America/Chicago

Paper: A sharp lower bound for adjacent-edge correlations in random subtrees
Author: Scott Schubr
Scope: Later and equivalent-result literature refresh. A separate reviewer is
responsible for obtaining and comparing the complete final Luo-Xu-Tian article.
No package, original manuscript, shared registry or publication state was edited.
This is AI-assisted assessment, not external human refereeing.

BOUNDED VERDICT
No matching prior proof or stronger result implying the strict finite bound was
found in this fresh search. The identifiable increment remains an elementary
all-n proof of the lower-bound conjecture in the identified public author
manuscript. Conditional on the separate final-article comparison not finding a
prior proof, this has modest but legitimate specialist-note value. It does not
invent the constant 3/4, the probability model, Cayley/forest enumeration, or
Jensen's inequality. Absolute priority is not certified by a negative search.

The later-source refresh is complete within its stated coverage. This report
does not itself clear the complete-final-journal-source obligation. A searchable
publisher preview is not the complete article, and its lack of a finite-bound
proof cannot establish what appears in the omitted sections.

EXACT CLAIM AND NORMALIZATION
T is uniformly selected from all nonempty tree SUBGRAPHS of labeled K_n, including
all n singletons, not just induced trees, rooted trees, or spanning trees. For
every n>=3 and distinct adjacent edges e,f,
  P(e in T | f in T) > (3/4) P(e in T).
Equivalently P(e,f in T)/(P(e in T)P(f in T)) > 3/4. Sharpness uses the prior
Luo-Xu-Tian limit. Excluding singleton trees changes the model and already makes
the strict assertion false at n=3. This convention was verified against the
public author manuscript in the prior full review and reread here.

MATERIALS READ
- Shared README, CURRENT_WORK, WORKFLOW, exact subtree registry record and
  mathematical-assessment skill/rubric.
- publisher_review_subtree_20261018/full-assessment.txt,
  originality-and-value.txt and originality-independent.txt in full.
- Entire current main.tex at
  D:/LUMINARY ODDITIES LLC/AI Research/subtree_prepublication_package_Riemann_A_20261018/manuscript/main.tex
  Identified prior hash: 9901457eac1ada48976d34919283f08d5e39f7b83512ebb36632fd1110545829.
  This subreview did not execute the computational checks again. Their earlier
  fresh replay is accurately described by the preserved review, not counted as
  a new replay here.

PRIMARY SOURCE LEDGER AND PRECISE COMPARISONS

1. Zuwen Luo, Kexiang Xu and Jing Tian, Random subtrees and unimodal sequences in
graphs, public 20-page author manuscript, posted August 2, 2023.
https://www.researchgate.net/publication/372825398_Random_subtrees_and_unimodal_sequences_in_graphs
Freshly reread full relevant Section5 discussion, Conjecture5.1, printed p18,
and surrounding theorem statements/model. The conjecture is exactly the strict
finite >3/4 lower bound. The discussion reports numerical verification through
n=200 and explains why its upper-bound proof method does not directly work for
this lower bound. Thus the current manuscript's attribution to THIS version is
well supported. The ratio limit and upper inequality are already theirs.
This uploaded version has20 pages, and was not silently treated as the final
13-page journal text.

2. Luo-Xu-Tian final journal record/primary publisher preview:
Discrete Mathematics347(1) (January2024),113654,
https://doi.org/10.1016/j.disc.2023.113654
https://www.sciencedirect.com/science/article/pii/S0012365X23003400
The preview was available through indexed search content in this pass; direct
web-reader opening also returned an internal retrieval error. Read the complete
available preview including abstract/introduction/model/layout. It confirms
uniform sampling over all subtrees and describes the adjacent-edge upper-bound
proof and asymptotic three-quarters ratio. Its claim to solve Chin et al.'s
Conjecture1.2 refers to the UPPER inequality, not automatically the new lower
inequality. Complete final Sections3 and5 remain outside this subreview's read
scope. Do not equate a preview or its abstract with full final-source clearance.

3. Stijn Cambie, Jorik Jooken, Stephan Wagner, On the extrema of the mean subtree
order of graphs, arXiv2508.20593v2, September16,2026; v1August28,2025.
https://arxiv.org/abs/2508.20593
https://arxiv.org/html/2508.20593v2
Freshly read introductory main statements, Section3 and the complete-graph
calculations/conditional-mean propositions of Sections4-5. Thev2 addition proves
that the clique maximizes mean subtree order. Theorem1.2 proves the minimum at
the path; Proposition1.3 compares spanning and almost-spanning counts; Theorem1.4
and Corollary3.6 prove the maximum at the clique. Proposition5.7 states that in
a vertex- and edge-transitive connected host, conditioning on a fixed edge raises
the mean order more than conditioning on a fixed vertex. These are mean-order
and counting comparisons, not a lower bound on the pair-edge joint probability.
The complete-graph fixed-edge asymptotics in Section4 are consistent with known
ingredients and do not establish strict correlation for every finite n. No
implicit immediate subsumption of the current theorem was identified. Importantly,
the newer v2 was read, not the older v1 abstract still displayed by some indices.

4. Stephan Wagner and Ruoyu Wang, The distribution of subtrees in dense graphs
and the roots of the subtree polynomial, arXiv2605.03583v1, May5,2026.
https://arxiv.org/html/2605.03583v1
Freshly read main theorems and their method/proof sections. Theorem2 gives uniform
near-spanning coefficient asymptotics under linear minimum degree; Theorem3 gives
complex-root bounds. The LXT citation is to unimodality. Neither an asymptotic
order law nor a root-modulus bound supplies the finite strict adjacent-edge
correlation inequality. The spanning-tree concentration used here is explicitly
for the spanning-tree measure, a different random object.

5. Wang Ruoyu, Subtrees in Graphs: Statistics, Extrema and Asymptotics,
Uppsala Dissertations in Mathematics151,2026; defense August27,2026.
https://uu.diva-portal.org/smash/get/diva2%3A2058439/FULLTEXT01.pdf
https://uu.diva-portal.org/smash/person.jsf?pid=authority-person%3A109982
Fresh access returned indexed primary PDF content/abstract; direct PDF openings
failed and the record page presented a bot challenge. The earlier independent
review read the44-page physical thesis summary, not appended papers. This pass
checked its current author repository summary of all four articles. Topics are
edge contraction of tree hosts, local mean/density, local convergence and dense
graph subtree-size/root asymptotics. None is identified as a finite adjacent-edge
3/4 result. This is a limited fresh check; do not count it as a second full-PDF
read or infer that unprovided appended papers were read.

6. Yu Yang et al., Exact counting of subtrees with diameter no more than d in
trees: A generating function approach, Information and Computation307 (2025),
105353; DOI10.1016/j.ic.2025.105353.
https://www.sciencedirect.com/science/article/pii/S0890540125000896
Freshly read primary publisher abstract through indexed content. This is an
enumeration algorithm for diameter-restricted subtrees of a TREE host, including
rooted constraints, not all tree subgraphs of a complete graph. No matching
statement was identified. This pass did not read its full proof sections. The
earlier review's primary retrieval/read-depth record is preserved separately.

7. Xian'an Jin, Tianlong Ma and Yi Wang, A proof of a conjecture on subtree roots,
arXiv2608.07898v1, August8,2026.
https://arxiv.org/abs/2608.07898
https://arxiv.org/html/2608.07898v1
New lead in this refresh. Freshly read abstract/introduction, Theorem1.3 and
the generating-function setup, proof outline and concluding stronger conjecture.
This proves Brown-Mol root-region conjectures for subtree polynomials of TREE
hosts. It does not give a complete-host fixed-two-edge lower correlation bound.
Do not confuse this different newly resolved subtree conjecture with LXT5.1.
No independent validity certification of this preprint is made here.

8. Malwina Luczak and Peter Winkler, Building uniformly random subtrees,
Random Structures & Algorithms24(4) (2004),420-443.
https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20011
Fresh primary abstract checked because the title and appearance in the mean-order
paper are plausible alternative terminology. It constructs size-n uniform rooted
subtrees of a rooted d-branching tree. That host, rooting and fixed-order measure
differ from the present all-order complete-graph measure. No claimed implication.

SEARCH COVERAGE AND LIMITS
Fresh indexed-web queries used the exact LXT title/DOI and author combinations,
publication years2024-2026, adjacent-edge/adjacent edges plus subtree and lower
bound/correlation/conditional probability, random subtree plus three-quarters or
3/4, lower-bound conjecture, and the exact Conjecture5.1 formulation. Irrelevant
phylogenetic, lattice-tree, random-forest and subtree-root results were rejected
by reading primary scopes, not by assuming words with similar names refer to
the same theorem.

The current author-upload page displays Citations(5), but the display contains
duplicate local/global sub-k-tree records and additional recommendations. It is
not an exhaustive or deduplicated citation graph. Earlier Google Scholar five-
record inspection is preserved evidence, not a fresh Scholar live check here.
No matching later resolution appeared in the inspected primary texts or fresh
exact/equivalent search. This cannot exclude unpublished proofs, unindexed
papers, inaccessible sources or differently formulated implications.
No access controls were bypassed, no account/login or paid acquisition used,
and no authors or other people were contacted.

STRONGEST HONEST CONTRIBUTION AND VALUE
The note gives a short complete proof of the finite lower-bound question stated
by Luo-Xu-Tian in their public author manuscript, with sharpness credited to their
prior asymptotic result. The method exposes the role of a reciprocal moment of
subtree order and needs only classical counts, Jensen and elementary bounds.
The contribution is narrow but inspectable and pedagogically useful. No broader
graph/weighted-model theory, ratio monotonicity, new constant or application has
been established. A short specialist research note is proportionate if the final
predecessor text confirms it did not already prove the assertion. Even if a prior
proof later emerges, any publication would need reframing around a demonstrably
different/simpler proof rather than retaining a new-theorem claim by inertia.

MINIMAL DISCLOSURE RECOMMENDATIONS
If complete final journal text remains unavailable, retain one short footnote:
  "Conjecture numbering refers to the publicly posted author manuscript;
  the complete final journal version has not been verified."
The abstract should continue identifying the conjecture as belonging to that
author manuscript. Credit for the model, counts and limiting constant already
appears correctly; do not add duplicate disclaimers throughout the note. Keep
the current scope paragraph and AI-assisted-review distinction. A competing-
interests declaration is a separate author fact and should not be invented.

If the separate final-text review succeeds, replace the obsolete access caveat
with the verified final theorem/conjecture location and correct its citation.
No access disclaimer is then necessary solely because novelty searches are
bounded. Proportionate language is "We prove the finite lower bound conjectured
by Luo, Xu and Tian" with the precise verified reference; avoid "first ever,"
"completely novel method," or any claim that 3/4 was discovered here.

This report does not authorize or perform publication. The user requested a
report before publication; the final-source finding and this follow-up should
be reconciled before the parent review gives its final decision.
