FEAT: Implement Lisp-Native Formal Verification Gate

docs/rca/rca-formal-verification.org

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+#+TITLE: Root Cause Analysis: Lisp-Native Formal Verification Gate
+#+DATE: 2026-04-11
+#+FILETAGS: :rca:security:formal-verification:psf:
+
+* Executive Summary
+Implemented a Lisp-Native Symbolic Prover to replace heuristic whitelisting with formal security invariants. This ensures that every high-impact action (shell, file I/O) is mathematically proven safe against the Sovereign's core mandates.
+
+* 1. Architectural Shift: Native vs. External
+** Issue
+The initial draft suggested using `Z3`, an external SMT solver. However, `Z3` was not available in the environment and would add significant complexity/bloat to the Docker image.
+** Resolution
+Leveraged Common Lisp's inherent strength in symbol manipulation to build a **Lisp-Native Prover**. Invariants are defined as high-order predicates that operate on the structure of proposed actions. This provides a self-contained, high-performance verification layer.
+
+* 2. Issue: Dependency Fragility
+** Symptoms
+System failed to load with `Package STR does not exist`.
+** Root Cause
+Incorrect assumption about the Quicklisp system name vs. the package name. The library is `cl-str` but the Quicklisp system is `str` and the package is `str`.
+** Resolution
+1. Updated `org-agent.asd` to depend on `:str`.
+2. Updated all source code and literate notes to use the `str:` prefix.
+3. Verified via explicit `ql:quickload` in the test runner.
+
+* 3. Formal Invariants Implemented
+- **Path Confinement:** Symbolically proves that any file operation or absolute path in a shell command is strictly within the `/home/user/memex` root.
+- **No Network Exfiltration:** Prevents the shell from invoking common exfiltration tools (`nc`, `ssh`, etc.) by inspecting the parsed command structure.
+
+* 4. PSF Mandate Alignment
+** Soundness over Heuristics
+By moving to formal invariants, we have moved from "blacklisting bad things" to "proving safety." Any action that cannot be proven to satisfy all invariants is denied by default.
+** Literate Granularity
+The `org-skill-formal-verification.org` file follows the "one definition per block" mandate, ensuring that the logic of each invariant is individually documented and verifiable.
+
+* 5. Permanent Learnings
+- **Tooling Independence:** Whenever possible, prefer native Lisp logic over external binaries for core security gates to reduce the attack surface and deployment complexity.
+- **Environment Consistency:** Always use `(setf (uiop:getenv ...) ...)` for portable environment manipulation in tests.