Mathematics · proofs · software

The Komorebi research collection

Explore the ideas.
Follow the evidence.

A place to read mathematics, inspect the reasoning, and try the calculations for yourself.

Start with the introduction Browse all works

Find a paper or book, choose a reading route, and follow the mathematics with its assumptions in view.

Explore papers and books See the project map

Follow a statement to its argument, inspect the formal sources, and see what the recorded evidence supports.

Examine a proof How verification works

Try a runnable example, change the inputs in an interactive diagram, and compare the results for yourself.

Try the software Open interactive diagrams

Extended case study Euler numbers

One sequence.
Several perspectives.

Follow packets, polynomial coordinates, and exact residual correction through one extended derivation.

E0
1
E2
−1
E4
5
E6
−61
E8
1385
Read the Euler derivation

Extended case study Wavelets

One signal.
Exact multiresolution.

Follow four Haar levels, transport a finite filter, and calculate the exact error from omitted interactions.

Read the wavelet and polyphase derivation

Extended case study Factorial lanes

One factorial.
Ten exact lanes.

Reconstruct 34!, then follow hypergeometric coordinates and an exact five-adic reciprocal calculation.

Read the factorial-lane derivation

Extended case study Quantum phase

One state.
Phase and measurement.

Change measurement settings, reconstruct a qubit, and calculate which coherence a discarded outcome removes.

Read the quantum phase and measurement study

Extended case study Counting families

One partition triangle.
Two families.

Start with set partitions, obtain Bell and ordered Bell numbers, and follow the signed inverse and reciprocal packets.

Read the Stirling, Bell, and Fubini derivation

Extended case study Polynomial packets

One polynomial.
Three character packets.

Project degrees with roots of unity, move into falling-factorial coordinates, and reconstruct an exact value.

Read the roots-of-unity and Newton derivation

Explore more of the site.

Experiment with code and proofs, compare pages, and keep a reading list.

Experiment

Recovery laboratory

Find what a linear measurement loses and the extra information needed to recover an answer.

Compare

Read side by side

Keep a statement beside its proof, or compare two reading pages.

Save

Saved reading

Collect useful works and passages in this browser, then return to them.

Calculate

Python playground

Choose a worked example, edit the code, and inspect the results.

Prove

Try a proof in Lean

Explore a proof from Paper XII, edit its steps, and see what Lean says.

A few useful tools.

Explore an idea, or find a specific passage.

Interactive diagramsChange the inputs. Follow the result. Search the collectionFind a work, statement, or passage. Look up notationFind symbols and their source context.

Future Developments

See what’s next

My future research will focus on Hilbert’s 12th and 24th problems, the Strong Artin conjecture, and the Langlands program. Refining my work on machine learning and reasoning is another priority.

Research directionsRefining the current workWebsite and GitHub improvements
Explore the collections and how they connect

Three repositories, one place to begin

Operation KOMOREBI
Papers, books, research programs, formal sources, and evidence.
Komorebi Math
A Python library for finite mathematical constructions and inspectable certificates.
Polyphase Float
A C library for arbitrary-precision binary floating-point arithmetic.

What connects the work?

Describe an object in parts, transfer operations through those parts, and account for what a change of representation preserves or loses.

How to read completion and verification

The collection records completion, formal coverage, and confidence separately. A linked file does not mean every claim has been verified. Software is beta.

Read the guide to evidence and status