The Komorebi Methodology
Mathematical Discovery, Realization, and the Discipline of Proof
Author: Komorebi P.
Series: Realization Calculus / Mathematical Essays
This is the reviewed full essay, not an outline. The reader contains 28 physical
pages, nine chapters, a conclusion, a preface, three reproducible figures, source
notes, and references. The main text contains 7,611 words under
texcount -1 -sum essay.tex, including countable headings. The approved dark-plum
monograph cover, white interior, serif typography, and restrained gold accents remain.
Read and edit
Start with Komorebi_Methodology.pdf.
The essay follows one argument: realization makes a question accessible, obstruction gives failure mathematical content, admissible correction supplies a constructive response, verification establishes scope, and mathematical memory supports reuse. The returning-coordinate example now continues through an exact memory formula and its all-time induction proof rather than ending at the failed simplification.
Editable files:
Komorebi_Methodology.tex: design, cover, title page, preface, contents, assembly.essay.tex: nine chapters and conclusion.sources.tex: source notes, scope, and bibliography.figures.py: three vector diagrams and their PNG previews.
The PDF contains no administrative checkpoint labels. PROGRESS_LEDGER.md and
audit/REVIEW_REPORT.md preserve the editorial history separately.
Verification and its boundaries
The recorded run passes 40/40 exact-check groups with 665 finite cases and 17/17 manifest-validator controls. The former cover exact matrix calculations, finite factorization and continuation tests, rational memory recurrences, arithmetic transforms, obstruction witnesses, and the declared proof-field illustration. These are cases in a test suite, not counts of new mathematical theorems. The validator controls are separately counted actual command-line executions against isolated fixtures. They include genuine negative controls and check the intended diagnostics.
The final three-pass typesetting build contains no reported overfull/underfull boxes, LaTeX warnings, or missing-character messages. All 28 pages were rendered and reviewed. The structural audit found no out-of-page text spans, unresolved reference markers, replacement glyphs, invalid internal links, or bookmark-title mismatches. All 27 bookmarks were checked against their destination pages.
A source-only rebuild under the same installed environment reproduced all 28 pages with matching extracted text, bookmarks, and rendered pixels at 72 dpi using the same renderer. Its exact-calculation and integrity-control records also match. This is reproducibility, not an independent implementation of the tools. PDF byte identity is not asserted. The visual editorial review used separate 145-dpi page renders.
No new Lean compilation or corpus-wide formal audit was performed. The continuation and memory identities have written proofs. The unbounded tower and infinite Hilbert-space example also rely on their written arguments, not on finite tests. Historical Lean records remain attributed to their source documents. The comparison of research workflows is a proposed study, not a completed experiment.
audit/CLAIM_MAP.json connects the major exposition claims to these evidence types.
The source package does not bundle the full companion monographs or Lean projects.
Verify the delivered package first
In the freshly extracted directory, before creating or rebuilding files, run:
python verify_manifest.py
The verifier requires the complete file inventory in MANIFEST_SHA256.txt and
checks its SHA-256 digests. It rejects empty or incomplete inventories, extra or
missing files, modified payloads, duplicates, and unsafe paths. A metadata file added
by an operating system can therefore trigger a strict unlisted-file diagnostic.
Inspect that diagnostic rather than silently weakening the check.
The previous validator incorrectly accepted an empty manifest. That defect was
reproduced, recorded, and corrected. The original package's nonempty hash check is
not thereby invalidated. See audit/review_baseline_finding.json.
Integrity is relative to the supplied manifest. It is not authentication of the author and not a mathematical correctness proof. Regeneration changes files and creates build artifacts, so a delivery manifest is not expected to pass afterward. Do not overwrite the delivered manifest to disguise those changes.
Run the standard-library checks
python exact_checks.py
python integrity_checks.py
These require Python 3.10 or later but no third-party Python packages or TeX.
Both produce readable and machine-readable records in audit/. The integrity
controls use temporary fixtures and do not mutate the delivered inventory.
Rebuild the PDF
Install the figure dependencies and use the shared build entry point:
python -m pip install -r requirements.txt
python build.py
PowerShell: ./build.ps1. Unix-like shell: ./build.sh.
build.py runs both check suites, regenerates the figures, and performs three
pdflatex passes. It preserves compiler output in audit/build_pass_*.log and
returns failure when a command or the checked final-log classes fail. Visually inspect
the rebuilt PDF after editorial changes. Command success is not visual review.
Use a TeX distribution providing newpxtext, newpxmath, mathtools, microtype,
tikz, tcolorbox, titlesec, fancyhdr, hyperref, bookmark, and dependencies.
The display family is TeX EB Garamond (EBGaramond-LF) and the sans-serif family is
TeX Gyre Heros (qhv). Install these using TeX Live or MiKTeX. No font binaries
are distributed in the ZIP. Fonts embedded in the PDF are part of normal typesetting.
The actual environment is recorded in audit/build_environment.json. Dependency
ranges are not a fully locked environment. Different toolchain or font versions may
alter pagination or metadata.
Optional PDF and reproduction checks
python -m pip install -r requirements-review.txt
python review_pdf.py
python reproduce.py
The optional scripts use PyMuPDF. The first checks PDF structure and navigation. The second starts from sources in a temporary directory with no inherited PDF, figures, or calculation receipts, rebuilds, and compares to the current reader. It still uses the same installed tools. Neither is a proof of the essay's methodological effectiveness or an independent mathematical review.
Audit records and continuity
audit/REVIEW_REPORT.md explains the substantive changes and corrected failures.
audit/QA_REPORT.json summarizes current checks. audit/SOURCE_REGISTER.md identifies
bibliographic editions and public documentation. audit/provenance.json binds the
current source and PDF to the baseline. PROGRESS_LEDGER.md states the restart point.
audit/history/editorial-01/ preserves the first full-essay receipts as historical
evidence. Its page counts, hashes, and scope apply to that earlier artifact, not to
this reader. Current evidence is directly under audit/.
This package does not change a project-wide licensing decision or relicense third-party material. The public source PDFs and font distributions are not bundled.