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Mathematics · Preprint

Rooted Weyl Alternants for the Graceful Tree Conjecture

Global alternants, extremal-edge flows, and exact pruning tests

Method & partial progressMF-PRISM-MATH-2026-10 / v1.2

An exact signed-enumeration framework for graceful tree labelings, with global alternants, directed edge classes, and two leaf recurrences. The reconstructed finite audit reproduces 7,812 rooted types and the pruning results through thirteen vertices.

Read the paper Release & files
Cover of Rooted Weyl Alternants for the Graceful Tree Conjecture
Current public editionv1.2 · 2026-09-12
Identifier
MF-PRISM-MATH-2026-10
Series
Mathematics
Edition
Version 1.2
Length
9 pages
Reserved DOI
10.5281/zenodo.22728328 (record reserved)
01
The question

What is this paper trying to establish?

Can graceful tree labelings be detected and pruned through exact signed alternants?

02
The contribution

The central idea.

An exact signed-enumeration framework for graceful tree labelings, with global alternants, directed edge classes, and two leaf recurrences. The reconstructed finite audit reproduces 7,812 rooted types and the pruning results through thirteen vertices.

Current status

Method and partial progress; the universal Graceful Tree Conjecture is not resolved.

This manuscript develops a method and finite evidence, but it does not resolve the full open problem. The unresolved boundary is part of the published result.

03
Why it matters

What changes if the method holds?

The framework turns parts of the graceful-labeling search into auditable algebraic certificates and exact finite pruning tests, while keeping the universal conjecture explicitly open.

04
Independent review

Where scrutiny should concentrate.

The paper identifies the following points as the highest-value targets for independent review.

  1. 01
    Orientation and inherited ordering conventions in the global and rooted identities.
  2. 02
    Validity of sibling-orbit reductions for every coefficient, not just endpoint counts.
  3. 03
    The distinction between finite nonvanishing certificates and a universal graceful-tree proof.
Publication record

An open, inspectable research artifact.

The public record links the manuscript to its release, source package, review materials, and persistent identifier. Status travels with the paper; a reserved DOI is not presented as a published Zenodo record.

GitHub release Source folder
Document
Preprint
Review status
Open for independent review
Published
2026-09-12
DOI status
Reserved · 10.5281/zenodo.22728328
Canonical record
MF-PRISM-MATH-2026-10
Metriq PRISM Laboratory, Rooted Weyl Alternants for the Graceful Tree Conjecture, Metriq PRISM Laboratory Mathematics Research Paper MF-PRISM-MATH-2026-10, Version 1.2, 2026. Corresponding contributor: Daniel H. Jeffery, ORCID 0009-0001-1200-6042. DOI: 10.5281/zenodo.22728328.