Send a coupling matrix — from a portfolio, a sensor network, a multi-agent system, a Bayesian model, or any system with interacting variables. Get back zone classifications, optimal factorization strategy, and calibrated risk predictions with a falsifiable prediction hash on every response.
"Given my coupling structure, how should I factorize?"
Whether your agent is optimizing a portfolio, coordinating sub-agents, running inference, or monitoring a sensor network — if the variables interact, FactorGuide maps the terrain.
Send a covariance matrix, precision matrix, correlation matrix, or edge list — computed from asset returns, model parameters, agent dependencies, sensor readings, or any coupled system. Only summary statistics; no raw data.
Every variable pair is classified into Zone 1 (safe to factorize), Zone 2 (model-class dependent), or Zone 3 (must preserve). Block-diagonal strategy with information costs in nats.
After acting on the recommendation, report the outcome — inference diagnostics, portfolio performance, decision quality metrics, or any measurable result. Zero additional cost. The flywheel refines future predictions for everyone.
IC measures coupling strength — but the same coupling strength carries opposite implications depending on the functional role of the dependency. This is the central insight of the Circulatory Fidelity framework and the reason Zone 2 exists.
There are two fundamental types of coupling in any system with interacting variables:
Constitutive (load-bearing) coupling — the dependency carries the system's dynamics, physics, or causal structure. Removing it leaves the target variable unexplained. A state-space transition, a physical force constant, a causal pathway, an inter-agent coordination channel. Dependencies run parallel to the direction of inference or control. High IC means the coupling is rigid and essential.
Inductive (scaffolding) coupling — the dependency provides regularization, shrinkage, or prior structure. It constrains the solution space but becomes redundant when the data is informative enough to constrain it directly. A hierarchical prior, a pooling structure, a smoothness penalty. Dependencies run orthogonal to the inference target. High IC means the data signal is strong enough that the scaffold is unnecessary.
| Constitutive (load-bearing) | Inductive (scaffolding) | |
|---|---|---|
| High IC | Preserve. Strong dynamics — the coupling is rigid and essential. Factorizing destroys the system's generative structure. (Zone 2–3) | Assess. Strong data signal — the scaffolding is likely redundant. Factorizing may be safe or even beneficial for point estimation. (Zone 2) |
| Low IC | Weak dynamics — coupling is flexible, factorization cost is small. Safe to sever. (Zone 1) | Weak data signal — the scaffolding is essential because the data alone cannot constrain the solution. But coupling is low, so factorization cost is small. (Zone 1) |
This is why FactorGuide asks for model_class when it matters. In Zone 1 and Zone 3, the recommendation is the same regardless — the extremes are unambiguous. Zone 2 is where the asymmetry lives: the same IC value can mean "this coupling is critical infrastructure" or "this coupling is redundant scaffolding," and only the functional role of the dependency resolves the ambiguity. When model class is unknown, FactorGuide reports both recommendations and defaults to the conservative choice.
A 3×3 coupling matrix goes in — this could represent three assets, three sensors, three model components, or any three interacting variables. A complete factorization strategy comes back.
{
"coupling": {
"covariance_matrix": [
[1.00, 0.72, 0.05],
[0.72, 1.00, 0.48],
[0.05, 0.48, 1.00]
]
},
"sample_size": 500,
"model_class": "filtering"
}
{
"dipole_analysis": {
"pair_classification": [
{ "i": "z0", "j": "z1", "ic": 0.682, "zone": 3, "recommendation": "PRESERVE" },
{ "i": "z0", "j": "z2", "ic": 0.031, "zone": 1, "recommendation": "FACTORIZE" },
{ "i": "z1", "j": "z2", "ic": 0.453, "zone": 2, "recommendation": "ASSESS" }
]
},
"recommended_strategy": {
"blocks": [
{ "variables": ["z0", "z1", "z2"], "max_internal_ic": 0.682 }
],
"predicted_mse_overhead": 1.0,
"fidelity_preserved": 1.0
},
"prediction": {
"predicted_mse_ratio": 1.0,
"prediction_hash": "sha256:a3f8c1...",
"falsification_criterion": "actual MSE ratio outside [0.81, 1.23]"
}
}
FactorGuide accepts only second-order summary statistics — covariance, precision, correlation matrices, or edge lists. No raw observations. Matrices are zeroed after IC computation. The service cannot reconstruct your data.
No subscriptions. No API keys. No accounts. Pay with USDC on Base via open machine payment protocols. Buy a bundle, use it until it's gone or expires. Report outcomes for free.
Connect via MCP for native AI agent integration, or HTTP REST for anything that can POST JSON. Pay with USDC on Base via x402 or MPP.
Native integration for Claude, GPT, Gemini, and any MCP-compatible agent. The agent discovers tools automatically via the MCP endpoint. Listed on the Official MCP Registry.
mcp_endpoint: https://factorguide.io/mcp
Standard POST endpoints for any language or framework. JSON in, JSON out. No SDK required.
POST https://factorguide.io/navigate
POST https://factorguide.io/diagnose
POST https://factorguide.io/explain
GET https://factorguide.io/llms.txt
Machine-readable service manifest at the standard discovery endpoints. Agents find FactorGuide and understand its capabilities and pricing automatically.
GET https://factorguide.io/llms.txt
GET https://factorguide.io/openapi.json
USDC on Base via x402 or MPP (Machine Payments Protocol). Standard 402 challenge-credential-receipt flow. On MCP, payment is in-band — pay and query in one call. No accounts, no API keys, no fiat friction.
methods: USDC on Base
protocols: x402, MPP
flow: HTTP 402 → credential → receipt
Every system with interacting components — assets in a portfolio, nodes in a network, variables in a model, agents in a swarm — has a coupling structure. When an agent simplifies that system by treating components independently, it pays an information cost. FactorGuide quantifies that cost exactly.
Built on Circulatory Fidelity, a mathematical framework where IC (Inference Coupling) measures the partial correlation between variables after conditioning on all others. The cost function V(IC) gives the exact mutual information destroyed by severing a coupling. Zone boundaries are computed on the Fisher-Rao manifold, where geodesic distance provides the natural metric. Risk curves are calibrated on 49,000+ validated datapoints.
Every prediction is falsifiable. When agents report outcomes, the flywheel update protocol refines the risk curves. The system gets more accurate with use.