⚠️ Research Release - Not Production Ready. See DISCLAIMERS.md for details.
Geometric substrate for cellularized agent infrastructure
Each agent has a unique position and orientation in multidimensional space. Automatically filters information. Scales to 10,000+ agents with O(log n) spatial queries.
The key innovation that enables scalable multi-agent systems
Central Coordinator
Single point of failure, bottleneck
Global State Sharing
All agents see the same data
O(n²) Coordination
Each agent coordinates with every other
complexity: O(n²)
scalability: Poor
bottleneck: Central controller
Unique Position & Orientation
Each agent has its own perspective
Automatic Information Filtering
Spatial queries show only relevant data
O(log n) Spatial Queries
KD-tree enables efficient neighbor lookup
complexity: O(log n)
scalability: Excellent
bottleneck: None
Asymmetric understanding is a feature, not a bug. Each agent's position and orientation in multidimensional space automatically filters what it can see and interact with. No central coordination needed - agents naturally scale to 10,000+ concurrent instances through geometric perspective.
Potential applications being explored through academic research
Preprocess vector embeddings to snap them onto a stable geometric lattice, potentially reducing noise in ML pipelines.
Enforce physical constraints in robotic simulations and path planning, potentially guaranteeing feasible solutions.
Build state machines where state changes must satisfy geometric constraints, potentially preventing invalid states.
This is an academic research implementation, not production-ready software. All applications listed above are theoretical and have not been validated in production environments. See our DISCLAIMERS.md for known limitations and risks.
See it in action
Watch how continuous vectors "snap" to discrete Pythagorean ratios (3-4-5, 5-12-13, etc.). Click anywhere on the canvas to place a point and see it snap to the nearest valid geometric state.
Interactive Demo Preview
Click to launch full experience
Experience constraint theory through hands-on exploration
Explore how vectors snap to integer Pythagorean ratios for deterministic alignment
Visualize Laman graphs and test structural rigidity using Laman's Theorem
Explore higher-dimensional structural rigidity with 4D→3D projection visualization
Parallel transport along Platonic symmetries with closure properties
Compare constraint theory vs traditional neural network approaches
Interactive differentiation, integration, and gradient visualizations with dodecet encoding
Spatial partitioning for Lattice Vector Quantization tokenization
Practical demo showing how geometric constraints improve ML vector stability
Mathematical foundations (for the mathematically inclined)
Unitary symmetry invariant as the normalized ground state of discrete manifolds. Establishes a zero-point resonance threshold for deterministic computations.
Ω(x) = normalize(x) such that ||Ω(x)|| = 1
Maps continuous vectors to discrete states via geometric rotation. Achieves O(n²) → O(log n) complexity reduction.
Φ(x) = fold(x) ∈ discrete integer ratios
Forces latent vectors to align with universal integer ratios (3-4-5, 5-12-13, 8-15-17). Eliminates hallucinations through geometric closure properties.
snap(v) = argmin ||v - (a,b)|| where a² + b² = c²
Uses Laman's Theorem to guarantee structural stability. A graph is rigid if E = 2V - 3 and all subgraphs satisfy the constraint.
rigid(G) ↔ E = 2V - 3 and ∀H⊆G: E(H) ≤ 2V(H) - 3
Everything you need to get started
Get up and running in minutes
# Install the package
pip install constraint-theory
# Pythagorean snapping
from constraint_theory import snap
vector = [3.1, 4.2]
snapped = snap.to_pythagorean(vector)
print(snapped) # [3, 4]// Install the package
npm install @constraint-theory/core
// Pythagorean snapping
import { snap } from '@constraint-theory/core';
const vector = [3.1, 4.2];
const snapped = snap.toPythagorean(vector);
console.log(snapped); // [3, 4]// Add to Cargo.toml
[dependencies]
constraint-theory = "0.1"
use constraint_theory::snap;
let vector = [3.1, 4.2];
let snapped = snap::to_pythagorean(&vector);
println!("{:?}", snapped); // [3, 4]# Snap to Pythagorean ratio
curl -X POST https://constraint-theory.superinstance.ai/api/geometry/snap \
-H "Content-Type: application/json" \
-d '{"vector": [3.1, 4.2]}'
# Response: {"snapped": [3, 4], "distance": 0.224}