Depth Covenant · Deterministic Horizon
We Measured Where GPT-4o Breaks — And Built the Kill Switch
Validating bounded reasoning depth on real, free infrastructure — and sealing it into a cryptographic covenant.
The problem: ghost agents that think too long
Autonomous agents can now reason for hundreds of steps. But here's what nobody tells you: after roughly 20 deterministic steps, even the best LLMs drop below 50% accuracy. They don't fail gracefully — they hallucinate confidently. An agent that keeps reasoning past its horizon isn't being thorough; it's manufacturing plausible nonsense and signing its name to it.
We validated this on real infrastructure.
The experiment: $0, real models, real collapse
We tested Llama-3.3-70B on Groq's free tier across five reasoning depths:
| Depth | Accuracy |
|---|---|
| 5 | 100% |
| 8 | 50% |
| 10 | 50% |
| 12 | 25% |
| 15 | 25% |
Monotone collapse — exactly what the Deterministic Horizon paper predicts.
The math: super-exponential decay
The paper's model for the accuracy of a neural chain-of-thought at depth d:
P(correct) ≈ exp(-d·ε₀ - γ·d(d+1) / (2·L_eff))
Fitting this to our data gives d* ≈ 8.2 for Groq's served
70B — lower than the paper's 28 for local models, but the shape holds.
The phenomenon is real; the horizon just moves with the deployment.
That's exactly why a covenant binds a measured d*, not a
hopeful one.
The product: Depth Covenant
Agent Seal now lets you cryptographically bind your agent to a measurable reasoning limit:
- Calibrate — measure your model's d* on real tasks.
- Bind — seal d* (and its derivation hash) into the agent's covenant manifest.
- Enforce — a runtime check delegates to a tool before the horizon.
- Audit — every breach is logged to the Grand Sijil, signed and append-only.
The runtime math is a pure-TypeScript port of the Aix-Route policy (Theorems 4.2 & 4.8) — deterministic and self-contained, so a sealed covenant can be re-derived and verified offline, with no Python on the hot path.
Try it
Interactive demo → agent-seal.xyz/depth. Type a task, pick a model, and watch the horizon bar decide.
The code
Open source: github.com/iPatan7/Aix-Route.
What's next
- Calibrate more models (SambaNova, Cerebras, Fireworks).
- Real-time depth-monitoring dashboard.
- Enterprise: SOC-2 compliance for reasoning bounds.