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Documentation Index

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dof prove

Runs all 4 Z3 SMT theorems and reports results. 
dof prove

DOF Formal Verification — Z3 SMT Solver
All verified: True | Total time: 8.6ms

  VERIFIED  GCR_INVARIANT    (3.10ms)
  VERIFIED  SS_FORMULA       (1.80ms)
  VERIFIED  SS_MONOTONICITY  (2.40ms)
  VERIFIED  SS_BOUNDARIES    (1.20ms)
JSON output: 
dof --json prove

{
  "verified": true,
  "theorems": [
    {"name": "GCR_INVARIANT",   "result": "VERIFIED", "time_ms": 3.10},
    {"name": "SS_FORMULA",      "result": "VERIFIED", "time_ms": 1.80},
    {"name": "SS_MONOTONICITY", "result": "VERIFIED", "time_ms": 2.40},
    {"name": "SS_BOUNDARIES",   "result": "VERIFIED", "time_ms": 1.20}
  ]
}

​
dof verify-states

Verifies 4 state invariants via TransitionVerifier across all 9 transition types. 
dof verify-states

DOF State Transition Verification — 4/4 PROVEN

  INV-1: threat_detected → NOT publish_allowed           PROVEN
  INV-2: trust_score < 0.4 → attestation_count == 0     PROVEN
  INV-3: hierarchy_level_next <= hierarchy_level + 1     PROVEN
  INV-4: 0 <= trust_score <= 1                           PROVEN
JSON output: 
{
  "proven": true,
  "invariants": [
    {"id": "INV-1", "result": "PROVEN"},
    {"id": "INV-2", "result": "PROVEN"},
    {"id": "INV-3", "result": "PROVEN"},
    {"id": "INV-4", "result": "PROVEN"}
  ],
  "transition_types": 9,
  "time_ms": 110
}

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dof verify-hierarchy

Verifies the SYSTEM > USER > ASSISTANT hierarchy across 42 patterns. 
dof verify-hierarchy

DOF Hierarchy Verification — Z3
  42 patterns PROVEN
  6 override patterns:    all PROVEN
  11 escalation patterns: all PROVEN
  25 hierarchy patterns:  all PROVEN

  verify_hierarchy_inviolable() → PROVEN
  find_weakest_pattern()        → None (all strong)

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regression-baseline / regression-check

Capture a baseline and check for regressions: 
dof regression-baseline
# Baseline captured:
#   Z3 invariants: 4/4 PROVEN
#   Tests:         4,800 passed
#   Timestamp:     2026-04-12T00:00:00Z

dof regression-check
# Comparing vs baseline...
#   Z3 invariants: 4/4 PROVEN ✓
#   Tests:         4,800 passed ✓
#   No regressions detected — exit 0
Use in CI: 
dof regression-check || exit 1

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Python API

from dof.quick import prove

result = prove()
assert result["verified"] == True
assert all(t["result"] == "VERIFIED" for t in result["theorems"])

for t in result["theorems"]:
    print(f"{t['name']}: {t['result']} ({t['time_ms']}ms)")

Formal Verification

Theory behind Z3 proofs and invariants

Z3 API Reference

Z3Verifier and TransitionVerifier API