プレプリントと研究報告
This page collects mathematical preprints and research reports made available on this website.
このページでは、このホームページで公開している数学のプレプリントと研究報告を紹介します。
These reports present raw material for further research developed with AI assistance: results, ideas, examples, and open questions. They may later be developed into full papers.
AIの支援を利用して得られた結果・アイデア・例・未解決の問いなど、研究の原石に当たるものをまとめた報告です。 これらをもとに、通常の論文へと発展させることもあります。
This report constructs real Banach spaces and a bijection that preserves all pairwise distances on every closed ball of radius 1/4 but is not a global isometry, providing a counterexample to Scottish Book Problem 155. OpenAI Codex assisted with mathematical exploration, literature searches, language editing, and LaTeX preparation. The author verified the arguments and assumes sole responsibility for the contents.
Download the report (PDF)
Download the TeX source archive (ZIP)
PDF SHA-256:
6391e63add5473dca696e5ce542603616727ac83d557f7520bf6a36d056db8c2
Source ZIP SHA-256:
80e6bdec1fddd44f8d41285425c7b3e188e12056cdd90a5333e0dd25c34bee56
BibTeX:
@report{Ishiki2026ScottishBook155,
author = {Ishiki, Yoshito},
title = {AI-Assisted Research Report: A counterexample
to Scottish Book Problem 155},
institution = {Zenodo},
type = {AI-Assisted Research Report},
version = {1.0},
date = {2026-08-30},
doi = {10.5281/zenodo.22168214},
url = {https://doi.org/10.5281/zenodo.22168214},
urldate = {2026-08-30}
}
Plain-text citation:
Yoshito Ishiki, “AI-Assisted Research Report: A counterexample to Scottish Book Problem 155,” version 1.0, Zenodo, 30 August 2026. https://doi.org/10.5281/zenodo.22168214.
This report records mathematical results, constructions, computations, and open directions developed with assistance from OpenAI Codex. The author selected the included material and assumes sole responsibility for the contents.
Download the report (PDF)
Download the TeX source archive (ZIP)
PDF SHA-256:
62fdfbd9d57487384e394ad810c894b9a12eab0f81d344f8623ee20287cff62f
Source ZIP SHA-256:
4352109f71c9c0a45fbbf09e21b685af74f64233e1df6913f107c9df8d5f84de
BibTeX:
@report{Ishiki2026AIReport,
author = {Ishiki, Yoshito},
title = {AI-Assisted Research Report: Finite Hausdorff
Hyperspaces and Gromov--Hausdorff Geometry},
institution = {Zenodo},
type = {AI-Assisted Research Report},
version = {1.0},
date = {2026-08-13},
doi = {10.5281/zenodo.21913552},
url = {https://doi.org/10.5281/zenodo.21913552},
urldate = {2026-08-13}
}
Plain-text citation:
Yoshito Ishiki, “AI-Assisted Research Report: Finite Hausdorff Hyperspaces and Gromov–Hausdorff Geometry,” version 1.0, Zenodo, 13 August 2026. https://doi.org/10.5281/zenodo.21913552.
Preprints written in the usual paper format and made available here, but not on arXiv. This category is independent of whether AI was used in their preparation.
通常の論文形式でまとめ、このホームページで公開している、arXiv未掲載のプレプリントです。 AIの使用の有無によらず、この区分に掲載します。
No preprints currently in this category. / 現在この区分のプレプリントはありません。
Preprints first shared here and now available on arXiv. The original website versions remain archived below.
このホームページで公開した後、arXivにも掲載されたプレプリントです。初回公開版の記録も保存しています。
Now available on arXiv:2609.29665.
arXiv掲載済みです。以下のZenodo DOI・PDF・引用情報は、2026年9月4日公開の保存版（version 1.0）に対応します。
A revised paper based on the AI-assisted research report above.
上記のAI支援研究報告をもとに、通常の論文形式にまとめた改訂版です。
Download the archived version 1.0 (PDF)
PDF SHA-256 (version 1.0):
f4b6bef18d3a8401c3270a699f46638a97ae7ae1e5d2117b35d2f7898706a428
BibTeX:
@misc{Ishiki2026ScottishBook155Preprint,
author = {Ishiki, Yoshito},
title = {A counterexample to Scottish Book Problem 155},
howpublished = {Zenodo},
note = {Preprint, version 1.0},
year = {2026},
date = {2026-09-04},
doi = {10.5281/zenodo.22422011},
url = {https://doi.org/10.5281/zenodo.22422011}
}
Plain-text citation:
Yoshito Ishiki, “A counterexample to Scottish Book Problem 155,” preprint, version 1.0, Zenodo, 4 September 2026. https://doi.org/10.5281/zenodo.22422011.
Now available on arXiv:2609.09639 (v3 HTML; v3 PDF). Version 3 was submitted on 13 September 2026.
arXiv掲載済みです（v3：2026年9月13日）。以下のZenodo DOI・PDF・引用情報は、2026年9月9日公開の保存版（version 1.0）に対応します。
The Gromov–Hausdorff space of isometry classes of nonempty compact metric spaces is homeomorphic to the real separable infinite-dimensional Hilbert space. The four parts develop continuous invariant full-support probability measures, continuous finite-dimensional local models, the absolute retract property, and discrete approximation.
空でないコンパクト距離空間の等長類からなるGromov–Hausdorff空間が、実可分無限次元Hilbert空間と同相であることを示します。不変全台確率測度の連続選択、有限次元局所モデル、絶対レトラクト性、離散近似の四部からなります。
Download the archived version 1.0 (PDF)
The manuscript includes a statement describing the use of OpenAI Codex and the author's verification and responsibility.
Concept DOI for all versions: 10.5281/zenodo.22676583
PDF SHA-256 (version 1.0):
1409244febaf05e4679af945480a04232f22dea2917deeab9b7bc6c08288005c
@misc{Ishiki2026TopologyGHSpace,
author = {Ishiki, Yoshito},
title = {The topology of Gromov--Hausdorff space},
howpublished = {Zenodo},
note = {Preprint, version 1.0},
doi = {10.5281/zenodo.22676584},
year = {2026},
date = {2026-09-09},
url = {https://doi.org/10.5281/zenodo.22676584}
}
Yoshito Ishiki, “The topology of Gromov–Hausdorff space,” preprint, version 1.0, Zenodo, 9 September 2026. https://doi.org/10.5281/zenodo.22676584