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Mathematics · Preprint

Ordered Polynomial Crossings in Balanced Partition Models

Reciprocal interpolation and Foregger’s root-ordering conjecture

Candidate resolutionMF-PRISM-MATH-2026-16 / v1.1

Uses reciprocal interpolation and unimodality to order the crossing roots of balanced-partition marginal polynomials. The construction also identifies identical profiles and an exact selection rule within the stated model.

Read the paper Release & files
Cover of Ordered Polynomial Crossings in Balanced Partition Models
Current public editionv1.1 · 2026-09-12
Identifier
MF-PRISM-MATH-2026-16
Series
Mathematics
Edition
Version 1.1
Length
14 pages
Reserved DOI
10.5281/zenodo.22728342 (record reserved)
01
The question

What is this paper trying to establish?

Are the crossing roots in Foregger’s balanced-partition model ordered as conjectured?

02
The contribution

The central idea.

Uses reciprocal interpolation and unimodality to order the crossing roots of balanced-partition marginal polynomials. The construction also identifies identical profiles and an exact selection rule within the stated model.

Current status

Candidate proof of the stated root-ordering conjecture; no empirical education-outcome claim.

This manuscript presents a candidate resolution. Publication is not verification: independent specialist review remains necessary before the result should be treated as established.

03
Why it matters

What changes if the method holds?

A proof would settle the stated structural ordering question inside the mathematical model while avoiding unsupported claims about real educational outcomes.

04
Independent review

Where scrutiny should concentrate.

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

  1. 01
    Reciprocal interpolation across floor-function discontinuities.
  2. 02
    Unimodality under interval averaging and uniqueness of simple crossings.
  3. 03
    Identical-polynomial exceptions, betweenness inequalities, and the original Foregger conjecture.
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.22728342
Canonical record
MF-PRISM-MATH-2026-16
Metriq PRISM Laboratory, Ordered Polynomial Crossings in Balanced Partition Models, Metriq PRISM Laboratory Mathematics Research Paper MF-PRISM-MATH-2026-16, Version 1.1, 2026. Corresponding contributor: Daniel H. Jeffery, ORCID 0009-0001-1200-6042. DOI: 10.5281/zenodo.22728342.