Academic Platform 'ï.Fragmenta (Fragments of the Imaginary Dimension)' Officially Launched — Fragments of an Incomplete System Describing Existence as Z = D + iD

ï.Fragmenta — Fragments of the Imaginary Dimension | Fragments of an Incomplete System.

il Inc. (Headquarters: Tokyo, Founder: Yuma Muranushi) has officially launched 'ï.Fragmenta — Fragments of the Imaginary Dimension,' a scholarly essay platform operated by i.Institute (Institute of the Imaginary Dimension), its academic division, on June 16, 2026. URL: https://iii-iii.com/i.fragmenta/

ï.Fragmenta serves as a dissemination hub that aggregates and publishes a series of essays connected to the 'Extended Imaginary Number Theory'—an ontological framework systematized by Founder Yuma Muranushi. These essays are published with DOIs obtained from the international academic repository Zenodo, bilingual Japanese-English PDFs, citation formats (APA/Chicago/BibTeX), and explanations of key concepts.

◆ 'Literature, Mathematics, and Philosophy of the Imaginary Dimension' — What is ï.Fragmenta?

ï.Fragmenta is a series of essays centered on 'that which cannot fully become meaning, yet possesses structure before language.' Under a framework that conceptualizes existence as the superposition Z = D + iD—where D represents the real dimension (structural aspects with current meaning) and iD the imaginary dimension (structural surplus of non-meaning, non-presence, and non-definition)—the series expands its contours from a space that transcends literature, mathematical rigor, and philosophical inquiry, belonging to no single discipline.

Each paper is not a fragment of a closed whole, but a fragment of an ever-expanding totality. The subtitle 'Fragments of an Incomplete System' embodies this very stance.

◆ Dual-Layered Naming — 'FRAGMENTA' and 'Fragments of the Imaginary Dimension'

The platform's name is designed with two layers.

'FRAGMENTA' carries a philosophical gravitas, aligning with the fragments (fragmenta) of lost ancient works, such as those of Heraclitus.

'Fragments of the Imaginary Dimension' provides accessible understanding for a general audience.

This dual-layered structure harmonizes specialized inquiry with public openness within a single name.

◆ Published Essays — Extended Imaginary Number Theory Series Vol. I–IV

At launch, the platform features the following essays. Volumes I–IV have been assigned DOIs on Zenodo and are openly accessible under CC BY 4.0. Additional papers will be released periodically.

Vol. I Extended Imaginary Number Theory — Z = D + iD as the Dual Structure of Existence (2026.05.09 / DOI: 10.5281/zenodo.20095255)
Establishes the ontological foundation of the series by defining five axioms: non-closure, immanence, orthogonality, non-finality of description, and dynamic boundaries of the real dimension.

Vol. II Structural Theory of 'Occurrence' — Passive Posteriority and the Attitude of 'Allowing Emergence' (2026.05.17 / DOI: 10.5281/zenodo.20254107)
Phenomenologically describes 'occurrence'—subtle vibrations from the imaginary dimension captured as awareness in cognitive space—as a gradient of texture between intentional grasp and passive reception.

Vol. III Transparency — The Ultimate Prayer of Unmediated Mediation (2026.06.01 / DOI: 10.5281/zenodo.20509278)
Explores 'transparency,' the limit where the separation between the perceiving subject and the perceived event dissolves, and the subject becomes a medium for the continuous self-emergence of occurrences. Not a sequel to 'occurrence,' but its inverted completion.

Vol. IV The Northernmost Point of Realism — At the End of Reductive Physicalism (2026.06.13 / DOI: 10.5281/zenodo.20676271)
Names the implicit ontology that 'the world can be fully described' as 'Realism (R-ealism),' and demonstrates the non-closure of description when this stance follows its internal logic to its conclusion. Proposes an extended realism that restores surplus into the real as the imaginary dimension iD.

◆ Platform Features

- Aggregated design allowing an overview of all essays in the Extended Imaginary Number Theory series
- Clear bibliographic information for each essay: DOI, status, license, page count, etc.
- Bilingual Japanese-English PDFs and mobile-optimized viewing versions for smartphone users
- Standard citation formats (APA/Chicago/BibTeX) for each paper
- Explanations of key concepts such as 'imaginary dimension,' 'perspective,' 'tolerance of contradiction,' 'future-oriented ontology,' and 'loneliness as a prime number,' with cross-links to i.Encyclopedia and the imaginary dimension media 'Perspective Plus'
- Integration with author identifiers including ORCID, Google Scholar, PhilPeople, Wikidata, OpenAlex, and SSRN

◆ Founder Profile

Yuma Muranushi (Muranushi Yuma)

Independent Researcher (i.Institute)

ORCID: 0009-0004-3697-4197

Born July 28, 1982, in Tokyo. Philosopher, investor, and philanthropist. Developed the original theoretical system 'Extended Imaginary Number Theory,' which expands the structure of human and world existence through the use of imaginary numbers. Continuously questions the structure of the world across literature, mathematics, and philosophy, expanding the boundary between D and iD. Also designs and operates educational and humanitarian support networks across over 60 countries.

◆ Overview of ï.Fragmenta

Name: ï.Fragmenta — Fragments of the Imaginary Dimension
URL: https://iii-iii.com/i.fragmenta/
Launch Date: June 16, 2026
Publisher: i.Institute (Institute of the Imaginary Dimension)
Publication Location: Shibuya-ku, Tokyo
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Currently Published Essays: Extended Imaginary Number Theory Series Vol. I–IV

◆ Company Overview

Company Name: il Inc. (il)
Representative: Yuma Muranushi (Founder)
Headquarters: Minato-ku, Tokyo
Business Activities: Philosophical and ideological research; planning and operation of humanitarian implementation projects; construction and operation of media based on philosophical thought

[Related URLs]

ï.Fragmenta: https://iii-iii.com/i.fragmenta/
ï Project: https://iii-iii.com
Imaginary Dimension Media 'Perspective Plus': https://iii-iii.com/i.media/

[Inquiries]

il Inc., Representative: Yuma Muranushi (Muranushi Yuma)
Email: iii@iii-iii.com