Research-derived mathematics for Neuroca.
VoidKit is a growing scientific-computing and mathematics library built from the reusable mathematical machinery developed across Neuroca research.
It is broader than any one theory or model. VDM is one source family, not the definition of the package. Phase Calculus is another major research line, and many tools in VoidKit are intended to stand independently as numerical, algebraic, statistical, geometric, graph, dynamical, symbolic, or exact-computation utilities.
The project exists to turn research code into durable tools without erasing where the mathematics came from or what made an implementation distinctive.
Current status: early development / active extraction. The repository is usable as a research library, but the public API is not yet stable and substantial material is still being reconciled from the mining corpus.
Research tends to produce useful mathematics in inconvenient places: experiment scripts, validators, derivation notebooks, one-off solvers, native kernels, symbolic audits, and prototype implementations.
VoidKit is the refinery for that material.
The goal is to recover useful mathematical capability and give it a clean, tested, discoverable home while preserving:
- the original mathematical contract and assumptions;
- authored mechanism and method identity;
- derivational and implementation provenance;
- exact arithmetic, invariants, certificates, and validation gates when they matter;
- alternate Python, Rust, C, assembly, and symbolic implementations when they provide independent evidence or performance value;
- uncertainty honestly, including cases where novelty or canonical status is still being assessed.
A familiar-looking implementation is not automatically redundant. A research-derived method is compared on its actual mathematics, algorithm, evidence, and behavior before it is generalized, replaced, or retired.
VoidKit is being developed as a broad mathematics and scientific-computing library. Current and planned capability families include:
| Area | Examples |
|---|---|
| Numerical methods | root finding, interval certification, ODE/PDE methods, spectral operators, exact finite-time flows |
| Exact & discrete mathematics | permutations, free groups, Heisenberg structure, arbitrary-width arithmetic, Fibonacci/balanced refinement |
| Dynamical systems | nonlinear flows, reaction-diffusion, finite-relaxation transport, sparse/asynchronous fields |
| Graphs & networks | propagation diagnostics, causal/event structures, matching, spectral tools, sparse field dynamics |
| Statistics & information | correlated-series statistics, heavy-tail analysis, divergence and information measures |
| Geometry & topology | symbolic geometry, lattice/refinement tools, topology, recurrence and structural diagnostics |
| Wave & field methods | Klein-Gordon tools, pseudospectral methods, conservation/Noether diagnostics |
| Symbolic & certification tools | symbolic identity checks, algebraic-root certification, enumerative/symbolic search |
| VDM | authored VDM mechanisms and mathematics, including SIE and RE-VGSP, kept under their own identity |
| Phase Calculus | QBL, Orthad, exact coordinates, transport, FQM/cocycle machinery, certificates, native kernels, and Phase-native computation such as the π spigot/streamer family |
This list describes the project direction, not a claim that every listed capability is already merged into the public API.
VoidKit follows a few strict rules:
- Portable does not mean generic. A method can be reusable outside its parent research program and still remain an authored method.
- Generalization is additive. If a generic primitive can be extracted from an authored mechanism, the primitive may be exposed separately without replacing the authored object.
- Novelty is not a packaging gate. Some items are known methods, some are distinctive implementations, and some may warrant novelty review. Unassessed novelty does not block preservation, testing, or use.
- Source semantics outrank cleanup convenience. API cleanup does not authorize changing equations, branch behavior, certificates, invariants, or other load-bearing mathematics.
The detailed mining and custody rules live in MATH_MINING_TODO.md.
VoidKit is currently at v0.1.0 (pre-alpha) and should be treated as an evolving research library.
The active math-mining ledger tracks 326 retained code/support sources from the current VDM Math Mining v3 corpus. Those sources range from general-purpose mathematical utilities to large Phase Calculus families, native kernels, VDM mechanisms, symbolic verification code, and research implementations still awaiting reconciliation.
A few important consequences:
- APIs may move while the package is being organized by mathematical ownership.
voidkit.vdmis reserved for VDM-specific authored mechanisms and mathematics.voidkit.phase_calculusis the dedicated Phase Calculus namespace and is still being populated from canonical research sources.- historically useful but non-canonical VDM experiments may be retained under
voidkit.vdm.easter_eggs. - mining archives under
sources/are provenance/research material, not automatically public API.
For the current extraction state and planned work, see MATH_MINING_TODO.md.
The prior validated extraction work is now restored in two custody-preserving passes. The first covers algebra, interval/spectral/Klein-Gordon, Yin-Yang, and exact-logistic primitives. The second reconciles the 27-module ore-extraction family into current capability owners, including PDE, statistics, information theory, graph, wave/Noether, recurrence, topology, signal, thermodynamics, special-function, and variational tools. Duplicate historical namespaces were deliberately not recreated.
VoidKit is not currently presented as a stable PyPI release. Install it from the repository while the API is under active development.
git clone https://github.com/Neuroca-Inc/voidkit.git
cd voidkit
python -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -e .Optional dependency groups can be installed as needed:
python -m pip install -e ".[symbolic]"
python -m pip install -e ".[graphs]"
python -m pip install -e ".[tda]"
python -m pip install -e ".[vdm]"For a full research checkout, including all current optional Python dependencies:
python -m pip install -e ".[full]"Python 3.9+ is supported by the package metadata. pyproject.toml is the dependency and package-metadata authority; requirements.txt is only a convenience full-development environment.
The repository already includes conventional utilities alongside research-derived mathematics:
from voidkit.advanced_math import descriptive_stats
data = [1, 2, 3, 4, 5]
stats = descriptive_stats(data, ddof=1)
print(stats["mean"])
print(stats["std"])Current CLI entry points include:
voidkit-stats 1 2 3 4 5 --json
voidkit-diff "sin(x)**2 + x**3" --var x --order 1VDM-specific entry points and APIs live under voidkit.vdm. Phase Calculus APIs will live under voidkit.phase_calculus as canonical implementations are promoted from the research corpus.
The repository is intentionally broader than the original VDM-oriented README suggested.
voidkit/
├── advanced_math/
├── algebra/
├── causal_inference/
├── clustering/
├── dynamical_systems/
├── dynamics/
├── evolutionary/
├── fractal_analysis/
├── fractional_calculus/
├── graph/
├── iit/
├── info_theory/
├── neuro/
├── numerical/
├── optimization/
├── ot/
├── pathway_analysis/
├── pde/
├── phase_calculus/
├── provenance/
├── recurrence/
├── rmt/
├── sde/
├── semantic/
├── signal/
├── soc_analysis/
├── special/
├── stats/
├── structure/
├── spatial/
├── stochastic/
├── structural_plasticity/
├── symbolic/
├── tda/
├── thermodynamics/
├── time_series/
├── topology/
├── variational/
├── vdm/
└── wave/
The exact module organization will continue to improve as mined capabilities are reconciled and promoted.
VoidKit currently has both Python and Rust source trees.
Python is the primary public research interface today. Rust is used for high-performance implementations and native counterparts where appropriate. The mining corpus also contains C and assembly implementations that may be promoted when they have a clear mathematical/API role and verification path.
See RUST_README.md for the current Rust-side notes.
The repository-wide math roadmap is maintained in:
That document tracks:
- every retained item in the current mining corpus;
- implementation status;
- intended destination;
- research/custody rules;
- known source gaps;
- Phase Calculus recovery targets;
- already-extracted work that still needs to be merged;
- items requiring deeper mathematical or novelty assessment.
The TODO is deliberately exhaustive so valuable research code does not disappear simply because it was buried in an old experiment or had an unfamiliar name.
VoidKit is not intended to become a pile of thin wrappers around existing libraries.
Standard mathematics belongs here when a centralized, tested implementation is useful. Distinctive research implementations belong here when they provide something worth preserving: a derivation, algorithm, invariant, exact construction, certification path, performance characteristic, unusual composition, or other real capability.
The standard is usefulness plus mathematical custody, not novelty theater and not reinvention for its own sake.
VoidKit is licensed under the BSD 3-Clause License. See LICENSE for the controlling terms.
If VoidKit materially contributes to research or published work, please cite the software and, when applicable, the originating research for the specific method used. GitHub and citation-aware tooling can read the preferred software citation from CITATION.cff. Method-level provenance remains important: an authored VDM or Phase Calculus method should retain the citation and research lineage associated with that method rather than being credited only as a generic utility.
VoidKit is developed under Neuroca, Inc., whose research program centers on neuro-cognitive architectures and the mathematical/computational systems that support them.
Repository: https://github.com/Neuroca-Inc/voidkit
Copyright © 2025-2026 Justin K. Lietz and Neuroca, Inc.