虚次元を文学し、数学し、哲学する

存在の構造を、現時点で意味を持つ構造的側面の総体である実次元（D）と、それに伴う非意味・非顕在・非定義のままの構造的余剰である虚次元（iD）の重ね合わせ Z = D + iD として記述する概念的枠組みを提示する。五公理を中核として、実次元の非閉鎖性・内在性・直交性・記述の非最終性・境界の動性を規定し、本シリーズの存在論的基盤を据える。

Presents a conceptual framework that describes the structure of existence as a superposition Z = D + iD: the real dimension (D), the totality of structural aspects that currently bear meaning, and the imaginary dimension (iD), the structural surplus that accompanies it while remaining non-meaningful, non-manifest, and undefined. Centred on five axioms — the non-closure, immanence, orthogonality, non-finality of description, and mobility of boundaries of the real dimension — it lays the ontological foundation of this series.

@article{muranushi2026eint,
  author    = {Muranushi, Yuma},
  title     = {Extended Imaginary Number Theory: A Conceptual Framework for the Dual Structure of Existence},
  journal   = {ï.Fragmenta},
  volume    = {1},
  year      = {2026},
  publisher = {i.Institute},
  doi       = {10.5281/zenodo.20095255},
  url       = {https://doi.org/10.5281/zenodo.20095255}
}

第一論文が存在の二重構造そのものを記述したのに対し、本稿は「起こり」——虚次元由来の微細振動が認知空間上で気づきとして主体に捕捉される事象——を主題とする。意図的把握と「起こり」を排他的様式ではなく虚次元との関係における質感のグラデーションとして位置づけ、「起こり」寄りの極が前景化する事態を現象学的に記述する。「成立を許す」構え、気づきの事後性、「起こり」を阻む実次元側の三つの構造を析出し、その精度を視座・純度の二軸として整理する。

Whereas the first paper described the dual structure of existence itself, this paper takes as its subject “arising” — the event in which subtle vibrations originating from the imaginary dimension are captured by the subject as awareness within cognitive space. It positions intentional grasping and arising not as exclusive modes but as a gradient of texture in their relation to the imaginary dimension, and phenomenologically describes situations in which the pole closer to arising comes to the foreground. It draws out three structures — the posture of “allowing to hold,” the aposteriority of awareness, and the real-dimensional aspect that obstructs arising — and organises their precision along the two axes of perspective and purity.

@article{muranushi2026arising,
  author    = {Muranushi, Yuma},
  title     = {The Structure of Arising: Passive Aposteriority and the Posture of Allowing to Hold},
  journal   = {ï.Fragmenta},
  volume    = {2},
  pages     = {1--14},
  year      = {2026},
  publisher = {i.Institute},
  doi       = {10.5281/zenodo.20254107},
  url       = {https://doi.org/10.5281/zenodo.20254107}
}

本稿は拡張虚数理論の第三論文として、第二論文「『起こり』の構造論」が整理した「起こり」の上位概念 ──「透」── を主題とする。第二論文の「起こり」が、捕捉する主体と捕捉される出来事の分離を前提とした離散的事象であったのに対し、透はその分離が解消し、主体が起こりの絶え間ない自己生起の媒体となる極限を指す ── 起こりの続編ではなく、その反転的完成である。本稿の中心的主張はこの主体の反転 ── 捕捉する者から媒体への転回 ── にある。

As the third paper of the Extended Imaginary Number Theory, this work takes as its subject Tōh — the higher-order concept of arising organised in the second paper, “The Structure of Arising.” Whereas the arising of the second paper was a discrete event premised on the separation between the capturing subject and the captured event, Tōh designates the limit at which that separation dissolves and the subject becomes the medium of arising’s continuous self-emergence — not a sequel to arising but its inverted completion. The central claim of this paper rests on this inversion of the subject — the turn from one who captures to a medium.

@article{muranushi2026toh,
  author    = {Muranushi, Yuma},
  title     = {T{\=o}h: Undistorted Mediation, the Culmination of Prayer},
  journal   = {ï.Fragmenta},
  volume    = {3},
  pages     = {1--22},
  year      = {2026},
  publisher = {i.Institute},
  doi       = {10.5281/zenodo.20509278},
  url       = {https://doi.org/10.5281/zenodo.20509278}
}

本稿は、「世界は記述され尽くせる」という暗黙の存在論を実数主義（R‑ealism）と定義し、その立場が自らの内的論理を貫徹したときに突き当たる構造的限界を論証する。実数主義とは、実在的であることを形式的記述可能性──その代表形としての R‑記述可能性──に等値する立場であり、近代以降の自然科学と形而上学を貫いてきた。どれほど精緻に記述しても、対象には必ず、まだ意味として立ち上がっていない余剰が残る。本稿が示すのは、実数主義はその論理を極限まで貫いたとき、経験・意味・出来事という三つの局面で、記述が立ち上がりの手前を必ず取り残すこと──記述の非閉鎖性──に突き当たる、という事態である。この取り残される余剰を、実数主義を否定せず包含する形で位置づける枠組みとして、本稿は拡張虚数理論 Z = D + iD を素描し、その余剰を虚次元 iD として実在の側に回復する拡張実在論を提示する。結論は一文に集約される──実数主義は誤っているのではなく、狭いのである。

This paper defines as R-ealism the tacit ontology on which the world is exhaustively describable, and argues for the structural limit this position meets when it carries its own inner logic to the end. R-ealism equates being real with being formally describable, with R-describability as its representative form. However precisely we describe an object, the description always leaves a surplus that has not yet risen into meaning. Pursued to its limit, R-ealism runs up against the non-closure of description: in three regions—experience, meaning, and event—description necessarily fails to capture the arising that precedes its result. As a framework that positions this surplus without negating R-ealism, the paper sketches Extended Imaginary Number Theory (Z = D + iD) and proposes Extended Realism, which restores that surplus as the imaginary dimension iD on the side of the real. The conclusion: R-ealism is not false, but narrow.

@article{muranushi2026realism,
  author    = {Muranushi, Yuma},
  title     = {R-ealism at Its Limit: Beyond Reductive Physicalism},
  journal   = {ï.Fragmenta},
  volume    = {4},
  pages     = {1--21},
  year      = {2026},
  publisher = {i.Institute},
  doi       = {10.5281/zenodo.20676271},
  url       = {https://doi.org/10.5281/zenodo.20676271}
}