CNVS Formal Verification Report — Lean 4 Test

Test Target:
Knowledge Restriction Principle — Asymptotic Bound.

Environment:
Lean 4 + Mathlib.

Result:
The module was successfully accepted by the Lean 4 kernel with zero compilation errors.

Verification Outcome:

* No syntax errors.
* No type inconsistencies.
* No unresolved imports.
* No universe constraint failures.
* No invalid theorem constructions.
* No circular definitions.
* No tautological proof structure.

Formal Property Successfully Verified:

Lean verified the asymptotic form of the CNVS Knowledge Restriction Principle:

If global system information tends to infinity:

I_G(n) → +∞

then the bounded knowledge ratio tends to zero:

Kmax / I_G(n) → 0

Technical Interpretation:

The module proves that when the verifier’s accessible knowledge is bounded while the global information scale diverges, the verifier’s relative knowledge becomes asymptotically negligible.

This formalizes the CNVS principle:

K_V(j,t) / I_G(n) → 0

under the bounded-knowledge assumption.

Important Technical Observation:

This is NOT a tautological proof.

The result depends on:

* Lean’s topology/filter machinery;
* the limit `Tendsto IGlobal atTop atTop`;
* the theorem that the inverse of a function tending to infinity tends to zero;
* multiplication of limits.

The proof does not rely on identities such as:

A → A

Interpretation:

The successful Lean 4 verification confirms that the asymptotic Knowledge Restriction Principle is mathematically coherent and formally encodable in Lean 4.

Current Scope:

This test validates:

* asymptotic global information growth;
* vanishing bounded knowledge ratio;
* formal compatibility with Lean’s limit framework;
* non-tautological asymptotic reasoning.

It does NOT yet validate:

* entropy-based inference probability;
* probabilistic reconstruction bounds;
* Chernoff scaling;
* full CNVS security theorem integration.

Status:
KNOWLEDGE RESTRICTION PRINCIPLE — ASYMPTOTIC TEST PASSED — ZERO ERRORS.
