PUBLICATION DECISION ASSESSMENT
October 18, 2026, America/Chicago

Decision: retain this project and advance the existing three-page note to human
mathematical review. Do not submit yet. No extra theorem or broader research
program is necessary to justify that next step. Do not claim a breakthrough,
new correlation machinery, or confirmed worldwide priority.

What was actually reassessed
1. A new reviewer read main.tex without earlier audits and checked all proof
   dependencies, normalization and endpoints. No gap found. Root inspected
   that review and the proof. This is AI-assisted review, not human peer review.
2. A separate reviewer checked closest primary results and attempted to reduce
   the claim to existing counting, local/global mean and negative-association
   theorems. No inspected published comparison subsumes the finite lower bound.
3. Root refreshed primary-source readings and resolved a concrete literature
   gap: full OA publisher text of Yang et al. (2025), DOI10.1016/j.ic.2025.105353,
   is now accessible and its claims concern diameter-constrained enumeration
   in tree hosts, not this finite adjacent-edge inequality.
4. Fredes-Marckert's69page author PDF was checked at its complete-graph and
   edge-correlation discussions. It explains fixed-size uniform Cayley sampling
   and standard spanning-tree negative association, not the target finite lower
   bound for the uniform mixture over all subtree orders.

Validity judgment
The proof establishes R_n>3/4 for n>=3 in the stated uniform-all-nonempty-
subtrees model. Conditional counts, reciprocal Jensen, the four-vertex mean
bound, the factorization and the direct n=3 case are valid. Strictness does not
depend on numerical experiments. Optimality uses the predecessor's known limit.

Difference from Luo-Xu-Tian
Their inspected author manuscript proves the finite upper bound R_n<=1 and
the limit R_n->3/4. Its Conjecture5.1p18 asks for R_n>3/4 at each finite order.
Our theorem supplies that missing finite comparison. A limit alone permits
approach from either side, so it cannot provide this conclusion. The new result
is substantive relative to that manuscript, with modest and focused significance.
The final13page journal text has not been obtained; this comparison must not be
silently relabeled as a direct comparison against the complete final article.

Method and result originality
The enumeration, conditioning, Jensen inequality and general size-bias ideas
are standard. The argument is an elementary consequence of classical counts
plus a useful moment reduction and mean threshold, not a new general method.
That does not eliminate a potential result-level contribution: proving a precise
previously posed finite inequality can warrant a concise note with classical tools.
No matching earlier resolution or directly subsuming theorem was identified in
the sources inspected. This supports provisional originality, not a certificate.

Publication value and feasibility
The natural product is one theorem and a short proof, approximately2-4pages.
Its value is a clean resolution of the explicit finite lower-bound question and
completion of the sharp constant's finite inequality. Scope is narrow; expected
interest is specialist graph enumeration/probability. Acceptance is not assured.
The appropriate next investment is source clearance and human review, not more
decimal calculations, speculative generalizations or unrelated mathematical work.

Remaining obligations
- Acquire final journal text lawfully and compare Section5 and all relevant
  Section3 results. Exact numbering alone is less important than whether the
  finite statement remained conjectural or was resolved/changed before publication.
- Refresh later results using the verified final statement and inspect any
  potentially overlapping theorem directly. Inaccessible/unindexed work remains
  a limit; no finite web search guarantees worldwide priority.
- Obtain a human graph theorist's assessment of proof correctness, literature
  overlap and specialist significance. A source-author response would be useful
  evidence about version/history but would not alone prove global priority.
- Human author review should confirm authorship, references and AI disclosure.

Practical decision rule
If final text and later work leave the inequality unresolved and human review
finds the proof sound, submit a carefully scoped short note. If a previous proof
already exists, reassess whether this proof has enough expository merit; do not
market the theorem as new. If a real proof gap emerges, withdraw the resolution
claim until repaired. Current evidence does not trigger either rejection case.

Paper disposition
The mathematical text needs no repair from these reviews. The existing version
caveat remains correct and is retained. No final-version claim was upgraded.
No publication, submission, outside message or author contact occurred.

Supporting records
evidence/ADVERSARIAL_PROOF_ASSESSMENT.txt
evidence/CLOSEST_RESULTS_ASSESSMENT.txt
evidence/YANG_2025_PRIMARY_RETRIEVAL_UPDATE.txt
evidence/EXPANDED_SOURCE_AND_PUBLICATION_ASSESSMENT.txt

Primary comparison sources
https://www.researchgate.net/publication/372825398_Random_subtrees_and_unimodal_sequences_in_graphs
https://www.researchgate.net/publication/324905745_Subtrees_of_graphs
https://www.labri.fr/perso/marckert/Graph_Subtrees.pdf
https://www.sciencedirect.com/science/article/pii/S0890540125000896
https://arxiv.org/html/2508.20593v2
https://arxiv.org/html/2605.03583v1
