Apex Zero Loop — Development skill for Claude Code

Apex Zero Loop (AZL)

**Sub-Millisecond Zero-Iteration Agent Verification and Hoare Logic Kernel in Pure Python 3.10+**

[](LICENSE) [](pyproject.toml) [-success.svg)](pyproject.toml) [](tests/)

`ai-agents` • `agentic-ai` • `formal-verification` • `guardrails` • `llm-safety` • `infinite-loop` • `hoare-logic` • `autonomous-agents` • `runtime-verification` • `langgraph` • `crewai` • `autogen` • `python` • `zero-dependency`

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1. System Architecture

AI coding agents (Hermes, Cursor, Claude Code, Devin) frequently enter expensive retry death loops: generating code, executing it, encountering a runtime exception or contract violation, calling an upstream LLM to fix it, and repeating 5 to 10 times ($0.50 to $2.00 per loop, 30 to 60s latency).

`Apex Zero Loop` eliminates this loop by intercepting agent payloads before execution:

1. Proving Hoare logic weakest preconditions $\mathrm{wp}(C, Q)$ using pure Python DPLL SAT.
2. Tracing symbolic runtime hazards (division by zero, None dereferences, KeyErrors) in microseconds.
3. Auditing agent state machines for deadlocks and livelocks using Tarjan's SCC algorithm.
4. Synthesizing deterministic local AST patches in sub-500 microseconds without calling any LLM.

flowchart TD
    Agent["AI Coding Agent Payload
(Hermes / Cursor / Claude)"] --> Gate["ZeroLoopGate Interceptor"]

    subgraph VerificationKernels["Formal Verification Core"]
        Gate --> AST["Python AST Parser"]
        AST --> Hoare["Hoare wp Engine
Dijkstra Calculus (237.98 us)"]
        AST --> SymExec["Symbolic Hazard Tracer
Exception Paths (35.45 us)"]
        AST --> State["State Machine Auditor
Tarjan SCC (2