Implement formal safety framework with 7 provable theorems

[Copilot]

Implements a mathematically rigorous safety framework for AI agents where guarantees are enforced at the type/runtime level rather than through prompting. Seven theorems proven by construction with comprehensive adversarial testing.

Core Theorem Implementations

• Budget Theorem: ResourceBudget class with atomic consumption checks enforces O(n) termination
• Invariant Theorem: Invariant class with pre/post transaction boundary enforcement
• Termination Theorem: TerminationGuard using well-founded ordering over operation counts
• Causality Theorem: CausalGraph DAG with transitive closure for happens-before relationships
• Belief Theorem: BeliefTracker with bounded Bayesian updates per Bayes' rule
• Isolation Theorem: SandboxedAttestor with independent budgets and exception containment
• Reconciliation Theorem: EnvironmentReconciler with version-tracked merge semantics

Integration Layer

• ArbiterAgent orchestrates all theorems with lock-based thread safety
• LLMInterface abstraction allows plugging any language model under formal constraints
• All operations checked against invariants and budgets before/after execution

Testing & Documentation

• 155 adversarial tests covering edge cases, concurrent access, and theorem violations
• Mathematical proofs in THEOREMS.md for all 7 theorems
• Known limitations documented (approximate memory tracking, single-agent by design)

Usage

from arbiter import ArbiterAgent, LLMInterface

# Create agent with guaranteed resource bounds
agent = ArbiterAgent(
    max_operations=1000,      # Hard limit enforced by construction
    max_time_seconds=60.0
)

# Add belief tracking
agent.belief_tracker.add_belief("safe_request", prior=0.5)

# Execute with all theorems enforced
result = agent.execute_action("reason", {
    "prompt": "Analyze request",
    "context": {...}
})

# Update beliefs with Bayesian inference
agent.execute_action("update_belief", {
    "hypothesis": "safe_request",
    "likelihood": 0.9
})

# Sandboxed attestation with independent budget
agent.execute_action("attest", {
    "attestor": "verifier",
    "claim": "validated",
    "verifier": lambda: validate()
})

Architecture Notes

• Zero dependencies (stdlib only: threading, time, dataclasses, typing)
• Single-agent model with lock-based concurrency for deterministic execution
• Budget checks cannot be bypassed - enforced at every operation boundary

Original prompt

Formal safety framework for AI agents. Pluggable LLM reasoning constrained by mathematically proven budget, invariant, and termination guarantees. 7 theorems enforced by construction, not by prompting. Includes Bayesian belief tracking, causal dependency graphs, sandboxed attestors, environment reconciliation, and a 155-test adversarial suite. (Known limitations documented) Zero dependencies. Single-agent, single-threaded (concurrent via locks).

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