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.

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.

View Formalization Target →
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.

View Formalization Target →
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.

View Formalization Target →
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.

View Formalization Target →
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.

View Formalization Target →
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 Verification Status

Pending
ModuleObserverBoundary.lean
Proof Statusnot started
Remaining Goals4
Imports
MathlibTopologyGraphTheory

Counterexample Ledger

PASS

No counterexamples or failure modes identified in current search space.

View Formalization Target →
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 Verification Status

Compiles
ModuleScaleFreeTopology.lean
Proof Statusin-progress
Remaining Goals12
Imports
MathlibGeometryFractal

Counterexample Ledger

PENDING
Identified Failure Modes:
  • Boundary singularity unhandled at limit R->0
View Formalization Target →

Lemmas ​

Lemmas provide intermediate topological and algebraic bridges between axioms and theorems.

LEM-004active

A boundary enclosing zero stress density resolves to a singularity.

Dependencies:AX-003
LEM-009active

Scale factors commute across discrete fractal steps.

Dependencies:AX-002

Core Axioms ​

The foundational postulates upon which the formalization engine is built.

AX-001active

The Observer Boundary is strictly conserved across scale invariances.

∀ (O : Observer) (S : Scale), Conserved(Boundary(O, S))
AX-002active

Fractal dimension cascades propagate field information without loss.

AX-003active

A minimal fabricon stress tensor constitutes an elementary observer context.

∃ T : Tensor, Minimal(T) → IsContext(T)