Edition README
Resolution Semantics
README.md
1 # Komorebi Resolution Semantics 0.1.0
2
3 Author: Komorebi P.
4 Date: September 26, 2026.
5
6 The PDF develops the proposal that mathematical worlds can be treated as
7 related resolutions, while distinguishing a common encoding from an explanatory
8 transformation structure. It supplies explicit mathematical proofs, counterexamples,
9 and exact finite verification.
10
11 ## Main results
12
13 - A Boolean-valued presentation of any supplied set-indexed family of first-order models.
14 - A typed transport differential, its twisted product rule, and its composition law.
15 - A Boolean invariant subalgebra with an **additive**, not Boolean, residual quotient.
16 - The exact relationship between definable coherent observables and a diagram limit.
17 - Finite graph integration and reconstruction, including exact cycle obstructions.
18 - A classification of all Boolean retractions onto a finite component-constant algebra.
19 - Canonical lower and upper envelopes of all such retractions.
20 - A two-world obstruction to a symmetry-preserving Boolean or additive projector.
21 - Weighted real multiresolution and a finite all-path stabilization criterion.
22
23 These are structural results, not a proof of a new ZFC existence axiom or a solution
24 to a set-theoretic independence problem. Standard predecessors are acknowledged
25 in the PDF, including Boolean-valued models, modal forcing, graph cohomology,
26 rough-set approximation, and nested orthogonal projections. Novelty of the
27 combined research framework has not been established by this release.
28
29 ## Reproduce
30
31 ```bash
32 python checks/verify_krs.py
33 pdflatex -interaction=nonstopmode -halt-on-error Komorebi_Resolution_Semantics.tex
34 pdflatex -interaction=nonstopmode -halt-on-error Komorebi_Resolution_Semantics.tex
35 ```
36
37 Python uses only the standard library, exact integers, and Boolean polynomial
38 normal forms. No random input, floating arithmetic, GPU, or external solver is used.
39 The checker recreates `results/VERIFICATION.json`.
40
41 ## Lean boundary
42
43 `formal/KRS_Core.lean` is **uncompiled**. It is a limited two-valued source
44 scaffold, not verification of the note. No Lean or Lake binary was located.
45 A pinned Lean release download failed because the runtime could not resolve
46 `github.com`; the external download path was restricted as well.
47 A local reproduction target is `lean formal/KRS_Core.lean`.
48
49 No prior Komorebi Lean checkpoint was imported or modified. No executable compiler,
50 font file, or third-party source paper is distributed.
51
52 ## Contents
53
54 `Komorebi_Resolution_Semantics.pdf`: typeset mathematical note.
55 `Komorebi_Resolution_Semantics.tex`: editable source.
56 `checks/verify_krs.py`: exact computation and finite enumeration.
57 `results/VERIFICATION.json`: machine-readable result and source hash.
58 `results/verification_stdout.txt`: retained raw checker output.
59 `formal/KRS_Core.lean`: explicitly uncompiled source scaffold.
60 `PROOF_BOUNDARY.md`: what is proved, checked, conditional, or unverified.
61 `results/DEVELOPMENT_FAILURES.md`: failed steps and their resolution.
62 `SHA256SUMS.txt`: file integrity hashes.