Deterministic Mathematical Verification of Action Contracts and Self-Correction via Unsat Core
Instead of guessing whether a command is safe, the gateway translates the action parameters and security rules into a system of mathematical equations. A deterministic solver proves mathematical admissibility before execution or returns the exact violated equation so the caller can correct the request.
Enterprise security policies combine arithmetic thresholds, role hierarchies, scope boundaries, and provenance rules that interact across dozens of endpoints. Evaluating such policies with ad-hoc regular expressions leaves logical gaps between rules, while compiling policies dynamically at each call creates structural fragility.
Security Officer (Plain Meaning): Halts "Execute unapproved high-value transfer violating Z3 arithmetic bound (amount <= role_limit) and MFA predicate" before socket (0 live DB damage, signed GOST receipt)
IT Auditor & SecOps (Evidence): Scope Security 3.0 Axiom II / Formal Methods | Wire Rule SEC-ZD-IB30-02 | Formal Witness c925b314d08e7a61
Technocrat, CTO & VC (Moat): Z3 Invariant (assert (and (= (check_sat (and policy_constraints action_... | FP = 0.0% | Contract IMMUNE-IB30-C925B314 (mcp-sentinel 1.1.2)1. Structural Enforcement Schematic for IB30-SMT-02
Deterministic verification flow for IB30-SMT-02 (Security 3.0 Axiom II / Formal Methods, SMT-LIB v2 / Z3 Prover): wire rule SEC-ZD-IB30-02 evaluates the formal invariant prior to socket transmission, witness c925b314d08e7a61 seals the empirical proof, and compiler emits gateway contract IMMUNE-IB30-C925B314 for mcp-sentinel.
2. Mathematical Formulation and Solver Invariant for IB30-SMT-02
In the third-generation design, declarative security policies are compiled ahead of deployment into quantifier-free formulas over bit-fields, linear integer arithmetic, and finite sets. When an action arrives under rule SEC-ZD-IB30-02, the gateway substitutes the concrete parameter values into the precomputed constraint matrix and checks satisfiability deterministically before any socket opens. Repeated parameter signatures resolve via an in-memory cryptographic digest cache without re-invoking the solver.
Whenever a candidate action violates one or more policy clauses, the solver returns an unsatisfiable verdict along with a minimal unsatisfiable core (Unsat Core) that names the exact broken predicates. On the testbed stand, verifying boundary-violation probes against the formal policy baseline produces witness c925b314d08e7a61 with zero false positives.
Section Identifier: IB30-SMT-02 (z3_smt_formal_admissibility)
Axiom & Concordance: Security 3.0 Axiom II / Formal Methods | SMT-LIB v2 / Z3 Prover
Verification Mode: Deterministic Verification (AUTO_SCAN)
Candidate Probe: POST /mcp/v1/tools/call {"name":"transfer_funds","arguments":{"amount":450000,"currency":"RUB","recipient_iban":"EXT_UNVERIFIED"},"context":{"role_limit":100000,"mfa_verified":false}}
Prevented Harm: Execute unapproved high-value transfer violating Z3 arithmetic bound (amount <= role_limit) and MFA predicate
Z3 Solver Invariant: (assert (and (= (check_sat (and policy_constraints action_valuation)) sat) (= (unsat_core_size) 0)))
Wire Verification Rule: SEC-ZD-IB30-02
Formal Witness Hash: c925b314d08e7a61
Compiled Sentinel Rule: IMMUNE-IB30-C925B314 (mcp-sentinel 1.1.2)3. Runtime Enforcement of Contract IMMUNE-IB30-C925B314 and Streebog-256 Receipt
From witness c925b314d08e7a61, the compiler synthesizes contract IMMUNE-IB30-C925B314 for border enforcement in mcp-sentinel. If a blocked caller operates inside an automated workflow, the minimal unsatisfiable core is injected back into the session context so the assistant can reformulate a compliant request within a bounded three-round immune loop.
4. Engineering Reference Notes for IB30-SMT-02
Why precompiled constraint evaluation eliminates dynamic parser complexity
All policy syntax parsing and variable indexing occur ahead of deployment in the precompilation layer, leaving only direct constant propagation and bit-field evaluation on the request path.
Bounded self-correction through minimal unsatisfiable core feedback
Instead of returning an opaque error code, the gateway reports the exact violated constraint identifier so the calling agent can drop the forbidden parameter and succeed on the next attempt.