PUBLISHER DECISION -- OCTOBER 18, 2026, AMERICA/CHICAGO

A sharp lower bound for adjacent-edge correlations in random subtrees
Scott Schubr

Approve a qualified specialist author preprint after the disclosed new revision
passes source/PDF/package checks. This is a publication-form decision, not a
declaration that the missing final-source comparison has succeeded.

The complete elementary proof and earlier independent exact computational review
passed and remain authenticated to the unchanged mathematical source. The current
online follow-up found no matching prior finite strict lower-bound proof in the
inspected accessible sources. The correct contribution is an all-n proof of the
specific question stated in the identified 2023 Luo-Xu-Tian author manuscript.
Classical counting, Jensen's inequality, the model and asymptotic constant 3/4
remain credited to their predecessors. This is modest, useful specialist work.

The complete final13-page journal article remains unavailable for comparison.
The retrieval search is complete within the recorded routes; comparison of the
unobtained text is NOT complete. Novelty remains provisional and no priority is
claimed over results in that article. All unrestricted-originality/first-proof
clearance remains withheld. No other proof, value or inspected-literature blocker
has been identified.

Scott's latest direct instructions permit a small disclosure for this sole
remaining limitation and direct delivery of papers approved by this assessment.
The new subtree revision will replace its source-version footnote with exactly:

  Conjecture numbering refers to the 2023 author manuscript. The complete final
  journal text was unavailable for comparison; we claim no priority over results
  established there.

The abstract must continue specifying the author-manuscript conjecture. Retain
the existing scope and AI-assistance paragraphs; do not duplicate this disclosure
throughout the manuscript or invent a competing-interests declaration.

Release conditions: original package/ZIP preserved; exact proof and checker
unchanged; footnote verified in the compiled PDF; ordinary and optimized exact
checker replay passed; source-bound change record and complete manifest/ZIP
identity checks. Once those pass, root is authorized to send the exact qualified
package to Luminary Research Archive as one specialist note. No earlier broad
originality HOLD is erased: it is superseded only for this explicitly qualified
publication form following Scott's acceptance of the disclosed limitation.

Supporting current reviews: final-source-assessment.txt; followup-review.txt;
disclosure-release-scope-addendum.txt; assessment-summary.json. Earlier complete
proof/replay: ../publisher_review_subtree_20261018/full-assessment.txt and
proof-and-replay.txt. Current revision verification is recorded separately and
must identify the exact final TeX/PDF/ZIP before delivery.

Independent AI-assisted assessment; not external human refereeing, proof-assistant
formalization, an exhaustive priority guarantee, or observed publication.
