Draft:Quaternion Autocontained Framework

Submission declined on 17 February 2026 by Lynch44 (talk).

This draft appears to contain text generated by a large language model (such as ChatGPT). You cannot use LLMs to generate article content.

LLM-generated pages with certain obvious signs of being machine generated may be deleted without notice.

These tools are prone to specific issues that violate our policies:

hallucinations: they often invent false information and cite non-existent references.
unencyclopedic tone: they tend to be vague, promotional, or essay-like, rather than neutral and factual.
copyright issues: they may closely paraphrase existing text, leading to copyright violations.

Instead, only summarize in your own words a range of independent, reliable, published sources that discuss the subject.

See the advice page on large language models for more information.

If you would like to continue working on the submission, click on the "Edit" tab at the top of the window.
If you have not resolved the issues listed above, your draft will be declined again and potentially deleted.
If you need extra help, please ask us a question at the AfC Help Desk or get live help from experienced editors.
Please do not remove reviewer comments or this notice until the submission is accepted.

Where to get help

If you need help editing or submitting your draft, please ask us a question at the AfC Help Desk or get live help from experienced editors. These venues are only for help with editing and the submission process, not to get reviews.
If you need feedback on your draft, or if the review is taking a lot of time, you can try asking for help on the talk page of a relevant WikiProject. Some WikiProjects are more active than others so a speedy reply is not guaranteed.

How to improve a draft

Wikipedia:Contributing to Wikipedia – a basic overview on how to edit Wikipedia.
Help:Wikitext – how to use the markup
Help:Referencing for beginners – how to include references
Wikipedia:Article development – how to develop your article
Wikipedia:Writing better articles – how to improve your article
Wikipedia:Verifiability – make sure your article includes reliable third-party sources

You can also browse Wikipedia:Featured articles and Wikipedia:Good articles to find examples of Wikipedia's best writing on topics similar to your proposed article.

Improving your odds of a speedy review

To improve your odds of a faster review, tag your draft with relevant WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags.

Add tags to your draft

Editor resources

Easy tools: Citation bot (help) | Advanced: Fix bare URLs

Declined by Lynch44 4 months ago. Last edited by Lynch44 4 months ago. Reviewer: Inform author.

Resubmit

Please note that if the issues are not fixed, the draft will be declined again.

Comment: In accordance with Wikipedia's Conflict of interest guideline, I disclose that I have a conflict of interest regarding the subject of this article. Marcoaureliodecunha (talk) 21:19, 17 February 2026 (UTC)

Quaternion Autocontained Framework

Quaternion Autocontained Framework (QAF) is a proposed theoretical framework that aims to unify elements of quantum mechanics, general relativity, and cosmology using quaternionic algebra and an autocontainment principle. According to its author, QAF is formulated around a norm-preserving constraint on a fundamental tensor object and seeks to derive physical laws and dimensionless constants from a small set of structural postulates.^[1]

Wikipedia summarizes topics based on independent reliable sources and does not evaluate the correctness of scientific claims. This article describes the framework as presented in its publications and any available independent commentary.

Overview

QAF proposes that physical observables should be built from quadratic (norm-based) invariants rather than from amplitudes defined on an external background. In the framework's presentation, a single autocontainment constraint is used to motivate a unified structure from which both local relativistic behavior and nonlocal quantum behavior are interpreted as different projections or regimes.^[2]

Mathematical structure

In the author's formulation, QAF uses the algebra of quaternions and group-theoretic structures associated with symplectic and spin groups (e.g., $Sp(2)$ and $Spin(5)$ ). The framework emphasizes invariants and projection maps between a higher-dimensional internal structure and observed four-dimensional physics.^[3]

Use of quaternions

Quaternions are commonly used in mathematics and physics to represent rotations and to encode non-commutative algebraic structure. QAF extends this use by treating quaternionic structure as foundational rather than merely representational.^[4]

Spin and symplectic groups

The groups $Sp(2)$ and $Spin(5)$ appear in mathematical physics in contexts including representation theory and geometry. Background on these structures can be found in standard references on Lie groups and spin geometry.^[5]^[6]

Claimed physical applications

The author has presented QAF as applicable to both microphysical and cosmological phenomena, including proposed derivations of dimensionless constants and characteristic cosmological scales.^[7]

Cosmology

In the QAF presentation, the cosmic microwave background (CMB) and the baryon acoustic oscillation (BAO) scale are discussed using geometric and thermodynamic arguments and are related to fundamental constants via closed-form expressions. These claims are described in the framework's preprints.^[7]

Background on the CMB and BAO within standard cosmology is covered in widely used cosmology references.^[8]^[9]

Quantum mechanics and relativity

QAF is presented as deriving or reproducing core structures of quantum mechanics and relativity from a single algebraic constraint and projection rules.^[3] Background on the standard formulations can be found in widely cited texts.^[10]^[11]

Publications

The framework has been primarily disseminated through preprints and independent publications by its author, including technical supplements and topical papers.^[1]^[2]^[3]^[7]

Reception

As of 2026, QAF has limited coverage in independent reliable secondary sources. Wikipedia inclusion and article acceptance depend on the availability of significant independent discussion and analysis in reliable publications.

Background and foundational sources

The following references provide background mathematics and physics relevant to quaternionic formalisms, spin/symplectic groups, gauge theory, and standard cosmology (they do not constitute independent coverage of QAF):

Hamilton (1844) on quaternions.^[4]
Standard references on Lie groups and spin geometry.^[5]^[6]
Standard references on quantum mechanics and general relativity.^[10]^[11]
Standard references on cosmology, CMB, and BAO.^[8]^[9]

References

1 2 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "QAF Technical Supplement A (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)
1 2 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Quaternion Autocontained Framework (one-page summary, preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)
1 2 3 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Derivations of quantum-mechanical and relativistic structures in QAF (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo/OSF/arXiv). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)
1 2 Hamilton, W. R. (1844). "On Quaternions; or on a new system of imaginaries in algebra". Philosophical Magazine. 3. 25: 489–495. doi:10.1080/14786444408644914.
1 2 Knapp, Anthony W. (2002). Lie Groups Beyond an Introduction (2nd ed.). Birkhäuser. ISBN 978-0817642593. {{cite book}}: Check |isbn= value: checksum (help)
1 2 Lawson, H. Blaine; Michelsohn, Marie-Louise (1989). Spin Geometry. Princeton University Press. ISBN 978-0691085425.
1 2 3 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Cosmology in the Quaternion Autocontained Framework (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo/OSF/arXiv). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)
1 2 Dodelson, Scott (2003). Modern Cosmology. Academic Press. ISBN 978-0122191411.
1 2 Weinberg, Steven (2008). Cosmology. Oxford University Press. ISBN 978-0198526827.
1 2 Sakurai, J. J.; Napolitano, Jim (2017). Modern Quantum Mechanics (3rd ed.). Cambridge University Press. ISBN 978-1108473224.
1 2 Wald, Robert M. (1984). General Relativity. University of Chicago Press. ISBN 978-0226870335.

Primary sources and preprints

The following entries are preprints and working papers by the proposer(s) of the Quaternion Autocontained Framework (QAF). These items are cited in the text as sources for the framework’s definitions and claims. They are included here as primary sources.

Marco Aurelio De Cunha. "Quaternion Autocontained Framework – Reality on One Page". Zenodo. Retrieved 17 February 2026.

Marco Aurelio De Cunha. [REPLACE_WITH_DOI_OR_URL_OF_SPECIFIC_PDF "Exact Value of the Fine Structure Constant by Geometric Derivation (QAF)"]. Zenodo. Retrieved 17 February 2026. {{cite web}}: Check |url= value (help)

Marco Aurelio De Cunha. [REPLACE_WITH_DOI_OR_URL_OF_SPECIFIC_PDF "Cosmology in the Quaternion Autocontained Framework"]. Zenodo. Retrieved 17 February 2026. {{cite web}}: Check |url= value (help)

Marco Aurelio De Cunha. [REPLACE_WITH_DOI_OR_URL_OF_SPECIFIC_PDF "GR and QM from QAF"]. Zenodo. Retrieved 17 February 2026. {{cite web}}: Check |url= value (help)

Marco Aurelio De Cunha. [REPLACE_WITH_DOI_OR_URL_OF_SPECIFIC_PDF "Particles and Interactions in QAF"]. Zenodo. Retrieved 17 February 2026. {{cite web}}: Check |url= value (help)

[QAF-suppA-1] 1 2 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "QAF Technical Supplement A (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)

[QAF-onepage-2] 1 2 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Quaternion Autocontained Framework (one-page summary, preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)

[QAF-QMGR-3] 1 2 3 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Derivations of quantum-mechanical and relativistic structures in QAF (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo/OSF/arXiv). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)

[Hamilton1844-4] 1 2 Hamilton, W. R. (1844). "On Quaternions; or on a new system of imaginaries in algebra". Philosophical Magazine. 3. 25: 489–495. doi:10.1080/14786444408644914.

[Knapp2002-5] 1 2 Knapp, Anthony W. (2002). Lie Groups Beyond an Introduction (2nd ed.). Birkhäuser. ISBN 978-0817642593. {{cite book}}: Check |isbn= value: checksum (help)

[LawsonMichelsohn1989-6] 1 2 Lawson, H. Blaine; Michelsohn, Marie-Louise (1989). Spin Geometry. Princeton University Press. ISBN 978-0691085425.

[QAF-cosmology-7] 1 2 3 REPLACE_WITH_AUTHOR_NAME (REPLACE_WITH_DATE). [REPLACE_WITH_URL "Cosmology in the Quaternion Autocontained Framework (preprint)"]. REPLACE_WITH_HOST (e.g., Zenodo/OSF/arXiv). Retrieved {{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAME}} {{subst:CURRENTYEAR}}. {{cite web}}: Check |url= value (help); Check date values in: |access-date= and |date= (help)

[Dodelson2003-8] 1 2 Dodelson, Scott (2003). Modern Cosmology. Academic Press. ISBN 978-0122191411.

[Weinberg2008-9] 1 2 Weinberg, Steven (2008). Cosmology. Oxford University Press. ISBN 978-0198526827.

[SakuraiNapolitano2017-10] 1 2 Sakurai, J. J.; Napolitano, Jim (2017). Modern Quantum Mechanics (3rd ed.). Cambridge University Press. ISBN 978-1108473224.

[Wald1984-11] 1 2 Wald, Robert M. (1984). General Relativity. University of Chicago Press. ISBN 978-0226870335.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]