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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:

  1. Every mathematical claim is extracted to an isolated Theorem node.
  2. Every theorem depends cleanly on Axioms and Lemmas (DAG).
  3. Every theorem defines its formal language mapping (Lean 4).
  4. Counterexample search parameterizes potential failure modes before formalizing.

Active Theorem Pipeline

THM-EQ-03-04-network-self-healing-security-0

Formalization candidate for EQ-03-04-network-self-healing-security-0

candidate
Dependencies

Counterexample Ledger

PENDING

No counterexamples or failure modes identified in current search space.

THM-EQ-05-00-governance-overview-0

Formalization candidate for EQ-05-00-governance-overview-0

candidate
Dependencies

Counterexample Ledger

PENDING

No counterexamples or failure modes identified in current search space.

THM-EQ-05-04-governance-mathematical-ethics-ai-0

Formalization candidate for EQ-05-04-governance-mathematical-ethics-ai-0

candidate
Dependencies

Counterexample Ledger

PENDING

No counterexamples or failure modes identified in current search space.

THM-EQ-06-04-economics-feedback-loops-value-generation-0

Formalization candidate for EQ-06-04-economics-feedback-loops-value-generation-0

candidate
Dependencies

Counterexample Ledger

PENDING

No counterexamples or failure modes identified in current search space.

THM-EQ-07-02-apps-decentralized-supply-chain-yellowchain-0

Formalization candidate for EQ-07-02-apps-decentralized-supply-chain-yellowchain-0

candidate
Dependencies

Counterexample Ledger

PENDING

No counterexamples or failure modes identified in current search space.

THM-001

Observer Boundary Conservation

candidate
Dependencies
Axioms:AX-001
Lemmas:LEM-004LEM-009
Proof Readiness Score
73 / 100Doc: 18, Defs: 25, Dep: 20, CX: 10, Lean: 0

Lean 4 Integration Status

Pending
Module:ObserverBoundary.lean
Proof Status:not started
Remaining Goals:4
Imports:MathlibTopologyGraphTheory

Counterexample Ledger

PASS

No counterexamples or failure modes identified in current search space.

THM-002

Scale-Free Topology Invariance

in-progress
Dependencies
Axioms:AX-002
Lemmas:LEM-009
Proof Readiness Score
60 / 100Doc: 15, Defs: 20, Dep: 15, CX: 0, Lean: 10

Lean 4 Integration Status

Compiles
Module:ScaleFreeTopology.lean
Proof Status:in-progress
Remaining Goals:12
Imports:MathlibGeometryFractal

Counterexample Ledger

PENDING
Identified Failure Modes:
  • ⚠️ Boundary singularity unhandled at limit R->0

Global Proof Dependency Graph

Theorem Dependency DAG

Axioms → Lemmas → Theorems → Equations

LEM-004Zero Stress Singularity
depends-on
AX-003Fabricon Stress Context
LEM-009Discrete Step Commutation
depends-on
AX-002Fractal Cascade Invariance
THM-001Observer Boundary Theorem
depends-on
AX-001Observer Boundary Conservation
THM-001Observer Boundary Theorem
depends-on
LEM-004Zero Stress Singularity
THM-001Observer Boundary Theorem
depends-on
LEM-009Discrete Step Commutation
THM-002Scale-Free Topology Invariance
depends-on
AX-002Fractal Cascade Invariance
THM-002Scale-Free Topology Invariance
depends-on
LEM-009Discrete Step Commutation
EQ-OBS-1Boundary Flux Eq
derived-from
THM-001Observer Boundary Theorem