Theorem Registry
The Theorem Registry is the unified ledger of mathematical facts backing the theoretical corpus. It establishes the dependency Directed Acyclic Graph (DAG) between axioms, lemmas, and theorems.
Primary Theorems
Theorems are the high-level formalization targets that directly satisfy research claims in the corpus.
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 Integration Status
PendingObserverBoundary.leanMathlibTopologyGraphTheoryCounterexample Ledger
PASSNo counterexamples or failure modes identified in current search space.
Scale-Free Topology Invariance
Dependencies
AX-002LEM-009Proof Readiness Score
Lean 4 Integration Status
CompilesScaleFreeTopology.leanMathlibGeometryFractalCounterexample Ledger
PENDINGIdentified Failure Modes:
- Boundary singularity unhandled at limit R->0
Lemmas
Lemmas provide intermediate topological and algebraic bridges between axioms and theorems.
A boundary enclosing zero stress density resolves to a singularity.
AX-003Scale factors commute across discrete fractal steps.
AX-002Core Axioms
The foundational postulates upon which the formalization engine is built.
The Observer Boundary is strictly conserved across scale invariances.
∀ (O : Observer) (S : Scale), Conserved(Boundary(O, S))Fractal dimension cascades propagate field information without loss.
A minimal fabricon stress tensor constitutes an elementary observer context.
∃ T : Tensor, Minimal(T) → IsContext(T)