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Mathematics · Preprint

Scaling Obstructions in the Multigeometric Residue Problem

Composite-base counterexamples and a complete base-four classification

Candidate resolutionMF-PRISM-MATH-2026-12 / v1.1

Constructs scaling counterexamples to residue completeness in every composite base and classifies the four-digit base-four case. Primitive normalization separates the literal obstruction from a stronger corrected problem.

Read the paper Release & files
Cover of Scaling Obstructions in the Multigeometric Residue Problem
Current public editionv1.1 · 2026-09-12
Identifier
MF-PRISM-MATH-2026-12
Series
Mathematics
Edition
Version 1.1
Length
11 pages
Reserved DOI
10.5281/zenodo.22728334 (record reserved)
01
The question

What is this paper trying to establish?

Does residue completeness survive scaling in composite bases, and what remains after primitive normalization?

02
The contribution

The central idea.

Constructs scaling counterexamples to residue completeness in every composite base and classifies the four-digit base-four case. Primitive normalization separates the literal obstruction from a stronger corrected problem.

Current status

Candidate counterexamples to the literal composite-base statement; primitive base-four normalization is treated separately.

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?

It separates a literal statement defeated by scaling from the stronger normalized problem that carries the real mathematical content.

04
Independent review

Where scrutiny should concentrate.

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

  1. 01
    Whether the source question intended primitive normalization or its literal printed hypotheses.
  2. 02
    The composite-base scaling construction and the four-subset-sum block classification.
  3. 03
    The two-adic parity criterion and the precise normalized base-four conclusion.
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.22728334
Canonical record
MF-PRISM-MATH-2026-12
Metriq PRISM Laboratory, Scaling Obstructions in the Multigeometric Residue Problem, Metriq PRISM Laboratory Mathematics Research Paper MF-PRISM-MATH-2026-12, Version 1.1, 2026. Corresponding contributor: Daniel H. Jeffery, ORCID 0009-0001-1200-6042. DOI: 10.5281/zenodo.22728334.