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Methods, results, and limitations belong together.

This library provides versioned technical reports, protocols, software references, datasets, and clear notices when work is preliminary.

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RecordTypeStatus

Slavin Mirror Arithmetic and the Prime Mirror Spectrum Theorem

A reconstruction theorem for centered modular correlation spectra. The paper proves that, for an odd prime, an unlabeled spectrum determines its multiplier up to multiplicative inversion, using reflection symmetry, a parity anchor, and a Dedekind-sum congruence.

David A. Slavin · September 13, 2026 · Version 1.0.0 · Zenodo · CC BY 4.0

Slavin, D. A. (2026). Slavin Mirror Arithmetic and the Prime Mirror Spectrum Theorem (Version 1.0.0) [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.22738384

Related mathematical fields

This work connects number theory, modular arithmetic, finite fields, centered least residues, correlation spectra, reflection and inverse symmetry, reconstruction problems, and Dedekind sums. The archived package includes the paper, editable source, exact verification code, and recorded tests for every odd prime through 101.

View publication on Zenodo (DOI) →Open the interactive Mirror Analyzer →

Preprint

Published

Slavin Magic Hypercube: Construction, Transit-Detection Pipeline, and Applications

Version 1.0.1 of the Slavin Magic Hypercube software package, including its construction, transit-detection pipeline, and applications. Permanently archived and citable through Zenodo.

David A. Slavin · 2026 · Version 1.0.1 · Zenodo

Slavin, D. A. (2026). Slavin Magic Hypercube: Construction, Transit-Detection Pipeline, and Applications (v1.0.1) [Software]. Zenodo.

Related mathematical fields

This construction relates to combinatorics and combinatorial design theory through its constrained arrangement of integers; modular arithmetic through the wraparound Siamese construction; number theory through the identification and distribution of prime-valued cells; matrix analysis through row, column, and diagonal invariants; and computational mathematics through reproducible generation, verification, and integrity testing.

View publication on Zenodo (DOI) →

Software

Published

Discrete 31-Based Magic Structures: The 31×31 Square, 31×31×31 Cube, and 31⁴ Hypercube

A rigorous treatment of finite 31-based structures using affine coordinate mappings over ℤ/31ℤ, with exact line-sum formulas, sufficient conditions for axis-line balance and toroidal panmagic behavior, reproducibility requirements, and a critical assessment of physical interpretations. The paper retains the verified classification of the original Siamese square as magic but not fully panmagic, while distinguishing it from the stronger general affine construction.

David A. Slavin · September 1, 2026 · CC BY 4.0

Working paper

Zenodo publication in progress

Slavin 31×31 Prime-Highlighted Siamese Magic Square — 36 at Row 1, Column 16

A reproducible 31×31 Siamese-method magic square with complete CSV data, a prime-highlighted SVG, construction and verification code, verification results, documentation, licensing information, and SHA-256 integrity checks.

David A. Slavin · August 30, 2026 · Version 1.0 · CC BY 4.0

Related mathematical fields

This construction relates to combinatorics and combinatorial design theory through its constrained arrangement of integers; modular arithmetic through the wraparound Siamese construction; number theory through the identification and distribution of prime-valued cells; matrix analysis through row, column, and diagonal invariants; and computational mathematics through reproducible generation, verification, and integrity testing.

View publication on Zenodo (DOI) →

Research dataset

Published

Research charter

Scope, terminology, evidence classes, authorship, versioning, and publication standards.

Foundational document

In preparation

Verified Perception architecture

System contracts for observation, evidence, validation, confidence, contradiction checking, correction, and verified state.

Technical report

In preparation

MM² structured-redundancy methods

Definitions, construction rules, proposed error-detection uses, simulation protocols, and comparison criteria.

Exploratory methods note

Testing

GlyphLab structural repair

Geometry-aware stencil construction, continuity scoring, controlled correction, and preservation tests.

Software methods report

In preparation

Researcher identifier

David A. Slavin

ORCID: 0009-0008-6376-0871

Publication policy

No preliminary document is presented as peer-reviewed.

Each future release will identify its author, date, version, evidence level, methods, limitations, and revision history. Independent review and formal peer review will be labeled only when they have actually occurred.