Vortex Mathematics Engine
High-dimensional tensor acceleration, modulo-9 digital root invariants, and non-decaying geometric flux paths for academic research, universities, and students.
Geometry, Rhythm, and the Invariant Flow of Information.
Modern numerical methods treat numbers as continuous scalar magnitudes distributed along an arbitrary linear coordinate axis. In contrast, Vortex Mathematics demonstrates that the decimal number system is not arbitrary, but rather a self-contained, discrete geometry governed by modulo-9 invariants and toroidal symmetry.
Modulo-9 Digital Root Invariance
DR(n) = 1 + ((n - 1) \pmod 9)
Every natural integer projects onto a 9-element finite topological field. Digital root reduction is invariant across polynomial addition and multiplication, forming a discrete state machine that governs dimensional projection without loss of relational geometry.
The Doubling Circuit Flux Path
2^k \pmod 9 \in \{1, 2, 4, 8, 7, 5\}
Successive powers of 2 (1, 2, 4, 8, 16, 32, 64...) reduce under digital root arithmetic to an infinite repeating sequence {1, 2, 4, 8, 7, 5}. In VME, this circuit represents closed, non-decaying kinetic flux propagation around a torus manifold.
Polar Oscillation & Singularity Triad
3^k \equiv 9 \pmod 9, \; 6^k \equiv 9 \pmod 9
The triad {3, 6, 9} never participates in the doubling circuit. Instead, 3 and 6 oscillate as polar counterweights across the central singularity of 9. In physical simulations, this triad acts as a potential field mediator and energy valve.
Toroidal Coordinate Manifolds
X(u,v) = (R + r\cos v)\cos u + \Phi(DR(u,v))
VME maps continuous physical equations onto a discrete 3D torus where geodesic paths follow digital root gradient flows. This collapses algorithmic time complexity from classical dense matrix calculations into polynomial-time harmonic circulation.
The VME Computation Stack
Engineered from scratch for deterministic execution, zero-copy memory transfers, and SIMD vector hardware saturation across Intel, AMD, ARM, and Apple Silicon.
libvme-core
High-throughput SIMD primitives for modulo-9 tensor transformations, discrete toroidal metric tensors, and SIMD-vectorized digital root reductions running at memory bus saturation speed.
vme-harmonics
Accelerated discrete Fourier and toroidal harmonic transforms that decompose continuous wavefields into 9-harmonic phase streams, bypassing classical dense matrix multiplications.
vme-soliton
Non-linear differential equation solver for continuous plasma, fluid vorticity, and electromagnetic soliton propagation constrained to toroidal energy-conservation boundaries.
vme-neuro-bridge
Direct bridge linking VME toroidal descriptors directly to biological EEG/ECoG sensor streams via the Vortex Programming Language runtime and neuro_io interface.
Toroidal Flux Invariant
Simulated telemetry fixture — demo values, not real measurements.
# Initialize high-dimensional VME Toroidal Field
import torch
import redeaux_vme as vme
# 1. Allocate a 3D toroidal descriptor (rank 3: X, Y, T)
torus = vme.TorusDescriptor(
major_radius=4.8,
minor_radius=1.6,
modulo_base=9,
dimensions=(256, 256, 32),
device="cuda:0"
)
# 2. Inject continuous field state and compute digital root circulation
field_input = torch.randn(256, 256, 32, device="cuda:0")
flux_projection = torus.project_harmonic_stream(field_input)
# 3. Execute doubling circuit traversal (1-2-4-8-7-5) with O(N) complexity
kinetic_flow = vme.doubling_circuit_flow(flux_projection, cycles=1024)
# 4. Extract polar singularity moments along 3-9-6 axis
singularity_moments = torus.evaluate_singularity_axis(kinetic_flow)
print(f"[VME] Torus Invariance Check: {singularity_moments.is_invariant()}")
# Output: [VME] Torus Invariance Check: True (Energy conserved within 10^-14 tolerance)Research Grants & Thesis Projects for Universities & Students
We actively collaborate with university departments, computational physics institutes, neuroscience faculties, and graduate researchers around the world. Here are active research avenues currently underway using the VME math library:
Toroidal Solitons & Plasma Confinement
Using VME doubling-circuit magnetic flux vectors to model magnetohydrodynamic (MHD) equilibrium in compact stellarators and tokamak divertors with reduced simulation runtime.
Post-Quantum Lattice Manifold Invariants
Evaluating modular torus coordinates and digital root cyclic permutations as trapdoor mechanisms and hardness assumptions against Shor and Grover quantum attacks.
Brainwave Phase-Locking Synchrony via neuro_io
Connecting high-density scalp and intracranial electrophysiology into VME toroidal space to extract real-time phase synchronization and epileptic seizure precursor signatures.
Lossless Semantic Compression Manifolds
Applying VME harmonic decomposition to multi-terabyte scientific telemetry and sensor arrays, achieving high compression ratios with zero loss of topological invariants.
Bring Vortex Mathematics to Your Lab
Whether you are a university professor seeking computational tooling for your department, a graduate student formulating a doctoral thesis, or an undergraduate researcher exploring non-linear topology, REDEAUX provides complimentary access to the VME SDK, documentation, and hardware test clusters.