Formal Proof & Verification Dashboard
STATUS BOUNDARY: The formalization layer transforms canonical mathematical documentation into machine-verifiable proofs via Lean 4. Statuses reflect internal development progress on building the Formal Knowledge Graph. A "verified" state indicates the local Lean compiler has verified the proof obligations; it does not indicate external acceptance.
Verification Program
The GILC verification pipeline strictly requires:
- Every mathematical claim is extracted to an isolated
Theoremnode. - Every theorem depends cleanly on
AxiomsandLemmas(DAG). - Every theorem defines its formal language mapping (Lean 4).
- Counterexample search parameterizes potential failure modes before formalizing.
Active Theorem Pipeline
Formalization candidate for EQ-03-04-network-self-healing-security-0
Dependencies
Counterexample Ledger
PENDINGNo counterexamples or failure modes identified in current search space.
Formalization candidate for EQ-05-00-governance-overview-0
Dependencies
Counterexample Ledger
PENDINGNo counterexamples or failure modes identified in current search space.
Formalization candidate for EQ-05-04-governance-mathematical-ethics-ai-0
Dependencies
Counterexample Ledger
PENDINGNo counterexamples or failure modes identified in current search space.
Formalization candidate for EQ-06-04-economics-feedback-loops-value-generation-0
Dependencies
Counterexample Ledger
PENDINGNo counterexamples or failure modes identified in current search space.
Formalization candidate for EQ-07-02-apps-decentralized-supply-chain-yellowchain-0
Dependencies
Counterexample Ledger
PENDINGNo counterexamples or failure modes identified in current search space.
Observer Boundary Conservation
Dependencies
AX-001LEM-004LEM-009Proof Readiness Score
Lean 4 Verification Status
ObserverBoundary.leanMathlibTopologyGraphTheoryCounterexample Ledger
PASSNo counterexamples or failure modes identified in current search space.
Scale-Free Topology Invariance
Dependencies
AX-002LEM-009Proof Readiness Score
Lean 4 Verification Status
ScaleFreeTopology.leanMathlibGeometryFractalCounterexample Ledger
PENDINGIdentified Failure Modes:
- Boundary singularity unhandled at limit R->0
Global Proof Dependency Graph
Theorem Dependency DAG
Axioms → Lemmas → Theorems → Equations