A SHARP LOWER BOUND FOR ADJACENT-EDGE CORRELATIONS IN RANDOM SUBTREES
Scott Schubr - qualified publication candidate - October 18, 2026

Start with manuscript/main.pdf and RELEASE_STATUS.txt. This revision replaces
one source-version footnote by the brief final-text-unavailable/no-priority
disclosure authorized by Scott. The theorem, complete proof and supplied checker
are unchanged. Earlier sealed package and its ZIP are preserved under baseline/.

The result proves the strict finite lower bound P(e in T|f in T) > (3/4)P(e in T)
for n>=3 under uniform selection over all nonempty tree subgraphs of labeled K_n,
including singleton trees. The limiting constant and classical counting methods
are credited to prior work. No arbitrary-host or monotonicity claim is made.

Originality remains provisional against the inaccessible final journal text.
The exact lower-bound conjecture is verified in Luo-Xu-Tian's publicly available
2023 author manuscript. The complete final 13-page journal text was not obtained;
the note claims no priority over results established there. The disclosure does
not resolve that source gap or certify worldwide novelty.

Fresh verification:
  python -B verification/independent_check.py
The unchanged checker performs exact-rational checks for n=3..200 and independent
edge-subset enumeration for n=3..5. It uses assert: run ordinarily for acceptance
gates; -O disables those assertions. This revision records both ordinary and -O
executions with identical saved outputs. The all-n analytic proof is primary;
finite tests corroborate it. No external human refereeing is claimed.

Compile manuscript/main.tex with a current LaTeX distribution or Tectonic.
Current review/ records describe this qualified revision. Historical assessment
and no-release records under baseline/ remain historical, not current authority.
MANIFEST.sha256.json identifies file bytes; hashes do not prove mathematics.
No license grant, journal submission or already-completed publication is implied.
