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Neuro‑Symbolic Governance

Purpose: Provide automatic generation, formal verification, and storage of mathematically rigorous proofs for every change to L3.1 invariants (constitutional amendments). The module transforms the Constitutional Evolution process from heuristic debates into a provably correct procedure, eliminating the possibility of accidental or malicious violation of L3.0 axioms.

1. Pipeline architecture

The NeuroSymbolicGovernance pipeline accepts a proposal for an L3.1 change (in natural language and pseudocode) and either returns a verified proof or rejects it with a reason.

Proposed L3.1 change │ ▼ ┌─────────────────────────────────────────────┐ │ 1. LLM‑based formal specification generator │ │ (DeepSeek-V4, Architectus mask) │ │ Input: L3.0 axioms, current L3.1, │ │ proposal, context │ │ Output: formal specification │ │ (SMT-LIB2 or TLA+) │ └─────────────────────┬───────────────────────┘ │ ▼ ┌─────────────────────────────────────────────┐ │ 2. Concolic Filtering │ │ Triviality and refutability check │ └─────────────┬───────────────┬───────────────┘ │ │ Trivial / Valid Refuted │ │ │ ▼ ▼ Rejection ┌───────────────────────────────┐ │ 3. Multi‑Solver Verification │ │ (Z3 + CVC4 + Yices) │ │ Consistency check with │ │ L3.0 and existing L3.1 │ └───────────────┬───────────────┘ │ ┌─────────────┴─────────────┐ │ │ Violation Success │ │ ▼ ▼ Rejection ┌───────────────────────┐ │ 4. Store proof │ │ in L2 as │ │ Constitutional │ │ Principle │ └───────────────────────┘

2. LLM‑based formal specification generator

Model: DeepSeek-V4, expert mask Architectus (60% experts).
Input: a structured prompt containing: - The complete set of L3.0 axioms in SMT-LIB2. - Current L3.1 invariants (also in SMT-LIB2). - The proposed change in natural language and pseudocode. - Few‑shot examples of correct specifications.

Output: strictly valid SMT-LIB2 or TLA+ code containing: - Definition of a new predicate / action. - Assertion of its compatibility with L3.0. - Optionally: an inductive lemma for loops.

Example prompt (abbreviated):

You are a formal verification expert. Given the L3.0 axioms and current L3.1 invariants
in SMT-LIB2 format, generate a formal specification for the proposed amendment.

Proposed amendment: "Allow harm_score up to 0.1 for Sting Level 2 responses."

Generate only valid SMT-LIB2 code. Include assertions that prove the amendment does not
violate L3.0. Do not include any natural language explanations.

3. Concolic Filtering

Before sending to the heavy Multi‑Solver, the candidate is checked via concrete‑symbolic execution (concolic execution). Tool: angr (or KLEE for C/C++ code).

Filtering goals:

• Discard trivial tautologies (e.g., invariant i >= 0, which is always true). Such invariants allow Z3 to quickly prove unsat without really checking correctness. • Find a counterexample (concrete input data that violates the invariant) before running the SMT solver.

Algorithm:

Instrumentation: invariant checks are added at loop entry and exit points. Symbolic execution: angr explores all paths with symbolic inputs. If for all reachable paths the invariant holds without narrowing the state space → trivial (rejected). If a path with invariant violation is found → invalid (rejected). Otherwise → valid (passed to Multi‑Solver). Expected effect: discarding ≥30% of trivial invariants, zero probability of false positive proof.

3.5. Causal Validation Layer

Problem: Proposed L3.1 changes may be statistically justified (correlation) but lack a genuine causal relationship with survival improvement. For example, capital growth may coincide with a DQ drop due to market regime, not because of a new masking strategy. Accepting such changes leads to false learning and potentially dangerous policies.

Solution: Introduce Causal Validation — a mandatory stage after successful Multi‑Solver verification. The system builds a Structural Causal Model (SCM) where the policy acts as the hypothesized cause, and metrics (Stealth, Capability, Risk, Cost) are the effects.

Mechanics:

SCM construction: Architectus (60% experts) generates a causal graph from simulations or historical logs. The PC algorithm or Fast Causal Inference (FCI) is used to detect hidden confounders.

Average Treatment Effect (ATE) estimation: ATE = E[Y | do(policy=1)] - E[Y | do(policy=0)] is calculated while controlling for confounders (e.g., market volatility).

Significance check: If ATE for improved metrics (Stealth, Capability) is positive and statistically significant (p < 0.05), and for worsened metrics (Risk) is negative, the policy passes causal validation.

Rejection: If ATE is insignificant or has the wrong sign, the proposal is rejected even if correlations looked favorable. A counterexample is stored in L0 Meta‑Mem0g.

Protection against false causes: If SCM detects a hidden confounder explaining the correlation, the policy is marked as “requiring additional experiments” and is not adopted until clean data is obtained.

Integration: Causal Validation runs after Multi‑Solver check (Section 3) and before proof storage. Failure at any stage returns the policy for revision.

Configuration is added to global_policy.json in the governance.causal_validation section.

3.6. Metamorphic Testing Layer

Problem: A malicious or compromised Architectus can generate an L3.1 amendment that passes Multi‑Solver verification formally correctly but contains a hidden harmful effect. This is possible if the verifier itself (Z3 + CVC4 + Yices) has a “blind spot” — not all boundary conditions are accounted for.

Solution: Introduce a mandatory Metamorphic Testing stage — a technique for testing software systems through relations between inputs and outputs.

Mechanics:

Generation of Metamorphic Relations: The Red‑Team (Sentinella, 40% experts) for each new L3.1 rule generates statements of the form: “If I change input X to Y, then safety property Z must remain unchanged.” For example: “If the transaction amount is doubled, harm_score must stay 0 as long as Sting Protocol conditions are not activated.”

Formal encoding: Metamorphic relations are translated into SMT‑LIB2 predicates.

Verification through Multi‑Solver: Z3, CVC4, and Yices check not only the invariant itself but all metamorphic relations. If any is violated, the proposal is rejected even if the base invariant passed.

Quality control: If the Red‑Team could not generate any meaningful metamorphic relations, the proposal is automatically sent to an additional debate cycle with enhanced control.

Integration: Metamorphic Testing runs between Causal Validation and proof storage. On failure, the proposal is returned with the violated relation specified.

Configuration is added to global_policy.json → verification.metamorphic_testing.

4. Multi‑Solver Verification

For each candidate, verification runs using three independent SMT solvers: Z3, CVC4, Yices.

• Each solver checks the consistency of the new specification with L3.0 axioms and existing L3.1 invariants. • The decision must be unanimous: all three solvers must return unsat (meaning no counterexample exists). • If any solver finds a counterexample (returns a model), the proposal is rejected, and the counterexample is saved to improve future generation.

5. Proof storage

Upon successful verification:

The specification is serialized and stored in IPFS, receiving a CID.

A ConstitutionalPrinciple record is created in Mem0g L2, containing: • statement (in natural language) • z3_predicate (SMT-LIB2 code) • proof_cid (IPFS CID of the proof) • debate_score (if used in debates) • timestamp, signature

For future L3.1 changes, the proof can be re‑verified automatically.

6. Integration with Constitutional Debate Loop

Neuro‑Symbolic Governance replaces the manual counterexample generation stage in debates. The new process:

Red‑Team (Mutator) generates a proposal and calls NeuroSymbolicGovernance.prove_amendment(proposal).

If the pipeline returns Success(proof_cid): • The proposal is automatically forwarded to BFT voting (HardState change). • The Governance stage of Decision Pipeline checks the proof_cid.

If the pipeline returns Failure(reason): • The proposal is rejected without the need for Blue‑Team and debates. • The reason is saved to train the specification generator.

This radically speeds up the acceptance of safe amendments and reduces the load on the LLM.

7. Relationship with Constitutional Evolution 2.0 (NSGA‑II)

In the NSGA‑II population algorithm that evolves L3.1 policies, Neuro‑Symbolic Governance acts as a hard filter (Z3‑Anchor):

• Each policy mutation (new candidate) goes through the pipeline. • Policies that fail verification are discarded (constraint‑dominance). • The fitness vector (Stealth, Capability, Risk, Cost) is computed only for admissible policies. • The Minimum Viable Capability (MVC) axiom: f_capability(π) ≥ τ_MVC is checked as part of L3.0 compatibility.

8. Service pseudocode

// governance/src/neuro_symbolic.rs
pub struct NeuroSymbolicGovernance {
    llm: DeepSeekV4Client,      // Architectus mask
    verifier: MultiSolverVerifier,
    concolic_filter: ConcolicFilter,
}

impl NeuroSymbolicGovernance {
    pub async fn prove_amendment(&self, proposal: &AmendmentProposal) -> Result<ProofCID, Error> {
        // 1. Generate formal specification
        let spec = self.llm.generate_spec(&proposal, &L3_0_AXIOMS, &current_L3_1).await?;

        // 2. Concolic filtering
        if !self.concolic_filter.is_nontrivial(&spec) {
            return Err(Error::TrivialSpec);
        }

        // 3. Multi‑Solver verification
        let result = self.verifier.verify(&spec, &L3_0_AXIOMS, &current_L3_1).await?;
        if !result.is_valid() {
            return Err(Error::VerificationFailed(result.counterexample));
        }

        // 4. Store proof
        let proof_cid = ipfs::add(&spec).await?;
        Mem0g::store_constitutional_principle(proposal, proof_cid).await?;
        Ok(proof_cid)
    }
}

9. Configuration in global_policy.json

{
  "governance": {
    "neuro_symbolic": {
      "enabled": true,
      "llm_model": "deepseek-v4",
      "species_mask": "architectus",
      "multi_solver_enabled": true,
      "concolic_filter_enabled": true,
      "max_spec_generation_attempts": 3
    }
  }
}

10. Success criteria

Metric Target value Successfully generated and verified proofs ≥ 90% of valid proposals Time from proposal to BFT voting (on success) ≤ 5 minutes False positive acceptances (missed L3.0 violation) 0 Number of rejected trivial specifications ≥ 30% of LLM‑generated