Navokoj: A Physics Engine for Logic | Constraint Intelligence Platform

For sixty years, the world has solved optimization problems by guessing. We treat constraints as a search tree, climb every branch, hit a dead end, and backtrack. It is slow, brittle, and exponentially expensive.

Today, ShunyaBar Labs is releasing Navokoj. an optimization engine that stops guessing and starts flowing. By treating Boolean logic as a continuous dynamical system, we don’t ‘search’ for answers; we let the system fall into them, like water finding the bottom of a valley.

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The Optimization Bottleneck

Optimization is the invisible layer that runs the world. From routing logistics fleets to scheduling hospital shifts and verifying cryptographic circuits, society relies on solving NP-complete problems.

For decades, the standard approach to these problems has been discrete search: making a decision, checking for conflicts, and backtracking when a dead end is reached. While effective for structured problems, this method hits a “complexity wall” as variables increase. The search space grows exponentially, turning sub-second tasks into overnight computations.

We built Navokoj to dismantle this wall.

From Decision Trees to Energy Landscapes

Instead of traversing a discrete decision tree, Navokoj maps logic problems onto a high-dimensional Riemannian manifold. In this space, ‘conflicts’ are mountains and ‘solutions’ are valleys.

We apply principles from statistical mechanics and fluid dynamics to ‘melt’ the problem. We guide the system toward a solution by following the natural gravity of the constraints (gradients). This allows Navokoj to make thousands of coordinated decisions simultaneously. It isn’t just a solver; it is a physics engine for logic.

Performance

This architectural shift delivers a step-change in performance. In our production tests spanning 1,110 real-world API requests, Navokoj achieved:

347ms Median Latency vs 45s avg on classical solvers

Metric	Navokoj	Classical Solvers
Median Latency	347ms	45s
Scale Limits	500k+ vars	~50k vars
Architecture	Continuous Flow	Backtracking Search
Complexity Wall	Quasi-linear scaling	Exponential wall

Optimization is usually an overnight batch job. Navokoj makes it a real-time API call.

• Massive Scale: We routinely solve 500,000+ variable instances on commodity GPUs.
• Phase Transition Immunity: Where traditional solvers hit a ‘complexity wall’ and timeout, Navokoj scales quasi-linearly, cutting through the critical phase transition with arithmetic symmetry breaking.

Because the algorithm is highly parallelizable, we can deliver this performance without relying on expensive supercomputing clusters. We run efficiently on standard CPUs, allowing us to offer this capability at a fraction of the cost of legacy enterprise solvers.

Case Study: Real-Time Conflict Resolution

In the example below, we represent a graph with 5 vertices and 3 colors. The expression enforces that adjacent nodes (like V1 and V4) do not share the same color state.

import requests

# We define the graph constraints as a logical expression.
# The solver must find a state where every node has exactly one color
# and no connected nodes share a color.

expression = (
    "(~(v3 & v4) & (~v7 & v8)) & "
    "(~((v3 & v4) & (v7 & v8))) & "
    "(~((v5 & v6) & (v7 & v8))) & "
    "((v1 | v2) & (~v1 | ~v2)) & " # XOR constraints for valid coloring
    "(~(v1 & v2) | ~(v3 & v4))" # Adjacency constraints
)

response = requests.post(
    "https://api.navokoj.shunyabar.foo/v1/solve",
    json={
        "expression": expression,
        "solver": "nano"
    },
    headers={"Authorization": "Bearer API_KEY"}
)

print(response.json())

While a traditional solver might struggle as the graph complexity grows, Navokoj flows to the solution almost instantly. For this request, the engine returned a valid optimal assignment in just 260 milliseconds.

{
  "success": true,
  "solution": {
    "assignment": {"v3": 0, "v4": 0, "v7": 0, "v8": 1, "...": "..."},
    "solve_time_seconds": 0.2608,
    "status": "optimal",
    "satisfied_constraints": 51
  }
}

Navokoj aims to be the reasoning engine that connects language, constraints, and action.

The Future is Continuous

We support standard CNF formats for researchers and simple boolean expressions for developers building the next generation of logistics, scheduling, and AI agents.

Because extraordinary claims require extraordinary evidence, the API is open for public beta testing until June 2026.

Break it. Benchmark it. We are excited to see what you build.

Get started with Navokoj →

01 November, 2025 The Navokoj Team, ShunyaBar Labs