FINAL QUALIFIED PUBLICATION ASSESSMENT
October 18, 2026, America/Chicago

APPROVE AS A QUALIFIED SPECIALIST AUTHOR PREPRINT, subject to final sealing checks.
The complete mathematical proof and ordinary exact replay pass. Exactly one
footnote changes: the requested short unavailable-final-text/no-priority notice.
The theorem/proof, scope, AI disclosure, bibliography and supplied checker remain
unchanged. All three rebuilt PDF pages were independently inspected by the
coordinating Publisher and pass legibility/layout checks.

The novel finite strict inequality is established relative to the identified
2023 Luo-Xu-Tian author-manuscript conjecture. Novelty remains provisional because
the complete final journal text was not obtained or compared. No priority over
results established there is claimed. The short proof has modest specialist
value; classical counting, Jensen and the limiting constant remain credited.
No other proof, value or inspected-literature blocker has been identified.

Scott conditionally authorized delivery of approved papers and explicitly
accepted a small disclosure for this remaining source limitation. The earlier
unrestricted-originality hold is not erased; qualified preprint readiness and
unqualified priority clearance are separate judgments. Current supporting
decision, source-access receipts and followup/disclosure scope reviews are
included alongside this assessment. Historical reviews under baseline/ retain
their original dates and states.

Ordinary assertions were active for the acceptance replay. The -O run provides
supplemental execution and output compatibility only, with assertions disabled.
Finite checks corroborate the analytic all-n proof. This is AI-assisted review,
not external human refereeing or proof-assistant formalization.

Once manifest, ZIP/source-ZIP and preservation checks pass, the exact sealed
qualified package is authorized for coordinating Publisher delivery to Luminary
Research Archive as one note. No prior package is replaced or deleted, and no
public release is claimed by this preparation record.
