How the Komorebi works fit together
Project overview · Three demonstrations · Browse every work · Current work queue
Use this map to choose a route through the collection. It covers the twelve core papers and selected connecting books. The complete catalogue also includes research continuations, software and experiments.
Read the relationships carefully. The cards show subject groups and a suggested learning order. The table under documented connections identifies specific uses named in retained source text. Neither is a complete graph of theorem dependencies or a new review of those dependencies.
Begin with the finite foundations
For a first mathematical reading, the suggested order is Paper I → Paper II → Paper III. Vectors, matrices, linear maps, kernels and images provide a useful starting background. Individual chapters state additional algebraic and analytic assumptions.
1. Describe the parts
Paper I: Typed systems and exact packet coordinates
Seeds, operator actions, packet families and reconstruction.
2. Compare resolutions
Paper II: Refinement, transfer and integral separation
Coarse and fine coordinates, weighted paths and lattice constraints.
3. Track compatibility
Paper III: Typed transfer and obstructions
Composable operations, chosen connections, nonlinear coordinates and defects.
Realization Calculus collects the core development. Komorebi Space develops the broader setting for comparing realizations. Their pages identify the relevant editions and evidence.
Choose an application or extension
The groups below organize subjects. They do not assert that every paper in one group is a formal prerequisite of the next group.
Functions, signals and evolution
IV: Cyclic analytic functions and reciprocal families
VI: Transfer semigroups and their realizations
Begin with series, signal indexing or linear evolution as appropriate. Analytic convergence and probability assumptions belong to the selected result.
Quantum and computation
VIII: Packet algorithms and exact compilation
Packet algebra connects to finite quantum examples and algorithms. Physical interpretation, performance and hardware behavior need their own evidence.
Arithmetic and comparison
IX: Arithmetic packets and local deformation
X: Residual seeds and conditional completion
XI: Arithmetic realization and conditional comparison
XII: Patching support and conditional automorphic completion
Use each work's algebraic and arithmetic hypotheses. A finite construction does not discharge an open arithmetic premise.
For an example before a paper, use the core-paper example index. Paper XI's Conjecture 66 obligations remain open. Paper XII retains its original and amended claim distinction and explicit arithmetic inputs.
Connect the books by the question you are asking
| Question | Starting works | Concrete introduction |
|---|---|---|
| What can a representation retain or recover? | Realization Boundaries, Information Realization, Sufficient Resolution | Recovery demonstration, then kernels. |
| How can an obstruction be repaired? | Constructive Repair, Grounded Abstraction | Repair directions and reusable calibration. |
| How should a proof or inference retain its evidence? | Proof Path Theory, Komorebi Methodology, Certified Inference | Proof certificates and a Gaussian update. |
| How do finite constructions enter models? | Special Functions, Large Signal Model, Quantum and Circuits, Physics | Start with the relevant paper example, then inspect the model's assumptions. |
| What changes with hidden state or interacting systems? | Machine Societies, Machine Native Reasoning | Hidden memory, followed by each work's recorded review scope. |
These are subject connections. A shared term such as “residual” or “packet” is not sufficient to transfer a theorem between different settings.
Documented connections
The following source passages support narrower statements than the broad reading map. Read the linked statement and its hypotheses before using a result.
| Earlier work → later use | What the source actually records | Source |
|---|---|---|
| Paper I → Paper III's starting framework | The introduction credits Paper I with typed seeds, operator grammars, exact projector packets, generated hulls and reconstruction. This is a statement of background use. | Paper III, purpose and formal status. |
| Paper II → Paper III's coordinate transport | The canonical triangle holonomy result names the inherited refineCoordinates_comp and refineCoordinates_self declarations. This is an explicit inherited formal dependency recorded by the manuscript. |
Result and inherited names, then the refinement boundary. |
| Earlier finite contracts → Paper III's release scope | The manuscript distinguishes its thirty original result environments from definitions and interfaces, and separates Paper III declarations from inherited results. | Finite contract and its denominator. |
The coordinate-transport boundary matters: two complete coordinate presentations are being compared. Discarding data or learning a coarse model introduces extra structure. The inherited result does not automatically cover those operations.
This map records what the source says. It does not certify the source's proof or rerun the inherited Lean projects. For exact formal declarations and replay evidence, use the work's Lean and Evidence sections.
Software routes
Komorebi Math contains Python implementations of selected finite constructions. Polyphase Float provides C arithmetic with explicit precision and rounding on its supported platform. The three standalone demonstrations need neither library. First runs provides their separate installation routes.
Keep the current records together
Use the finalization queue for remaining work and completion criteria, the status catalogue for each component's evidence, and the records guide for dated reviews and their source bindings. These remain the maintained status records. This map does not introduce a competing completion score.
Project overview · Three demonstrations · Choose a reading route