Public project and authorship statement
Komorebi P. · First published 27 October 2026
Komorebi is my independent mathematical research project, published under the name Komorebi P. It brings together manuscripts, formal developments, software, calculations, experiments, and guides for readers.
At its center is Realization Calculus, which studies how mathematical objects are represented, decomposed, transferred, and reconstructed, and what information or obstructions remain after those operations. Komorebi Space provides a framework for comparing compatible realizations. The individual works develop different parts of this program, each with its own assumptions, claims, and supporting evidence.
Why the work uses a pseudonym
I use a pseudonym to give readers room to encounter the work on its own terms: through its definitions, arguments, constructions, and results. Biography, credentials, and institutional affiliation can provide context, but they cannot settle the mathematical questions.
For me, the pseudonym is a working arrangement rather than a commitment to permanent anonymity.
Read the author's note in the current edition of The Possibility for a Machine-Native Mathematics.
Authorship and AI assistance
This project has developed with substantial AI assistance in mathematical formulation, exploration of possible proof approaches, drafting, programming, exact calculations, testing, review, references, figures, and document production. The extent of that assistance and the review history vary across the collection and are described in the disclosures accompanying individual works.
I am the named author and take responsibility for what I publish and for correcting it. Crediting AI assistance is part of giving an accurate account of how the work was produced. That assistance does not, by itself, establish the correctness of a result.
Review must be documented separately. Publication under my name does not imply that every proof has received my personal approval, independent human review, or external certification.
Citations and acknowledgment of prior work
This project draws extensively on the work of other researchers and contributors. I estimate that thousands of research papers have been examined in detail and used throughout its development, alongside many thousands of instances of consulting and using material from the On-Line Encyclopedia of Integer Sequences (OEIS). These are retrospective estimates of the scale of that work, rather than audited counts of distinct sources.
Those contributions range from a passing comment or observation that suggested a direction to a closed-form expression, an argument, an example, or a program used in the work. I am grateful to the authors of those papers and to the contributors whose sequence entries, comments, formulas, references, and code make OEIS useful to this research.
The citation record is incomplete. Until now, keeping track of every source and its role throughout the project has not been feasible. I am working to reconstruct that record, add missing citations, and correct attribution across the manuscripts, software, and website as the sources are identified and checked.
Specific contributions need specific credit. This acknowledgment accompanies that continuing work and does not replace citations to the sources actually used. For OEIS material, the aim is to identify the sequence entry and the particular comment, formula, reference, or program used, together with its credited contributor or underlying source where available. An absent citation should not be read as a claim that the corresponding idea, formula, or code originated here.
Readers who recognize a missing or inaccurate attribution are welcome to report it through the repository's issue tracker. Identifying the passage, formula, or program and the relevant source will help me make a precise correction.
Current state and publication circumstances
This work remains in progress and has, in many respects, been rushed because of circumstances shaped by the AI industry. I am continuing to correct, verify, and organize it.
The works are at different stages of development and review. The finalization queue records remaining editorial work, source checks, proof replays, software tests, and reviews. Completion and confidence labels reflect the evidence recorded for each work. All executable software remains beta and a work in progress.
Why unfinished work is included
The collection is both a body of mathematical work and a record of how that work develops. Drafts, partial results, calculations, experiments, and open directions are included deliberately to make the intermediate steps toward completion visible. They help readers trace how questions, arguments, and constructions take shape, where gaps remain, and what still needs to be checked.
Inclusion does not mean that an item is finished or that every claim has been verified. Each work should be read alongside its stated scope, completion status, assumptions, and recorded evidence.
I will continue to audit, correct, and update the collection as time and resources permit. My main focus is the core papers, Komorebi Space, and the more complete works. The broader collection preserves the surrounding research process as those priorities advance.
How to evaluate the collection
Each result should be read alongside its exact statement, hypotheses, argument, source revision, and supporting evidence. Written proofs, accepted Lean declarations, exact calculations, numerical experiments, and software tests establish different things. A formal proof also requires a faithful correspondence between the formal statement and the mathematical claim it is intended to support.
The completion guide distinguishes publication readiness, Lean coverage, and the basis for confidence in a result. A finished reading edition may contain open questions. A completed formal contract covers its registered claims, and a conditional result retains its assumptions. Originality and broader scientific applicability require their own assessment.
I have made the collection public so that others can inspect, question, reproduce, and build on it under the applicable terms. Corrections and precise objections are welcome. Identifying the work, revision, and statement or function at issue, together with the discrepancy and a reproducible example where possible, helps me investigate and make a useful correction.
Sources and editorial provenance
This statement draws on the project overview, the current essay, and the work-specific disclosures below.
The current reading edition of The Possibility for a Machine-Native Mathematics develops the broader conceptual account.
- Project overview and reading guide.
- Machine-Native Mathematics: current author's note.
- Stratified Relational Workspace: AI assistance disclosure, including authorship, responsibility, and external review boundaries.
- Realization Boundaries: assistance and provenance, including the scope of AI-assisted review and its limitations.