Komorebi Resolution Semantics 0.1.0
Author: Komorebi P.
Date: September 26, 2026.
The PDF develops the proposal that mathematical worlds can be treated as related resolutions, while distinguishing a common encoding from an explanatory transformation structure. It supplies explicit mathematical proofs, counterexamples, and exact finite verification.
Main results
- A Boolean-valued presentation of any supplied set-indexed family of first-order models.
- A typed transport differential, its twisted product rule, and its composition law.
- A Boolean invariant subalgebra with an additive, not Boolean, residual quotient.
- The exact relationship between definable coherent observables and a diagram limit.
- Finite graph integration and reconstruction, including exact cycle obstructions.
- A classification of all Boolean retractions onto a finite component-constant algebra.
- Canonical lower and upper envelopes of all such retractions.
- A two-world obstruction to a symmetry-preserving Boolean or additive projector.
- Weighted real multiresolution and a finite all-path stabilization criterion.
These are structural results, not a proof of a new ZFC existence axiom or a solution to a set-theoretic independence problem. Standard predecessors are acknowledged in the PDF, including Boolean-valued models, modal forcing, graph cohomology, rough-set approximation, and nested orthogonal projections. Novelty of the combined research framework has not been established by this release.
Reproduce
python checks/verify_krs.py
pdflatex -interaction=nonstopmode -halt-on-error Komorebi_Resolution_Semantics.tex
pdflatex -interaction=nonstopmode -halt-on-error Komorebi_Resolution_Semantics.tex
Python uses only the standard library, exact integers, and Boolean polynomial
normal forms. No random input, floating arithmetic, GPU, or external solver is used.
The checker recreates results/VERIFICATION.json.
Lean boundary
formal/KRS_Core.lean is uncompiled. It is a limited two-valued source
scaffold, not verification of the note. No Lean or Lake binary was located.
A pinned Lean release download failed because the runtime could not resolve
github.com; the external download path was restricted as well.
A local reproduction target is lean formal/KRS_Core.lean.
No prior Komorebi Lean checkpoint was imported or modified. No executable compiler, font file, or third-party source paper is distributed.
Contents
Komorebi_Resolution_Semantics.pdf: typeset mathematical note.
Komorebi_Resolution_Semantics.tex: editable source.
checks/verify_krs.py: exact computation and finite enumeration.
results/VERIFICATION.json: machine-readable result and source hash.
results/verification_stdout.txt: retained raw checker output.
formal/KRS_Core.lean: explicitly uncompiled source scaffold.
PROOF_BOUNDARY.md: what is proved, checked, conditional, or unverified.
results/DEVELOPMENT_FAILURES.md: failed steps and their resolution.
SHA256SUMS.txt: file integrity hashes.