CNVS Formal Verification Report — Lean 4 Test

Test Target:
Information Density — Weighted Density Model.

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 invalid theorem constructions.
* No circular definitions.
* No tautological proof structure.

Formal Properties Successfully Verified:

1. Nodal Density:
   ρ_N = I_F / I_N

2. Global Density:
   ρ_G = I_F / I_G

3. Weighted Combined Density:
   ρ_C = α ρ_N + β ρ_G

4. Weight Constraint:
   α + β = 1

5. Non-Negativity:
   Lean verified that ρ_N, ρ_G, and ρ_C are non-negative under positive information denominators.

6. Upper Bound:
   If I_F ≤ I_N and I_F ≤ I_G, then:
   ρ_C ≤ 1

7. Concrete Numerical Model:
   Lean verified a finite example with:
   I_F = 20
   I_N = 100
   I_G = 1000
   α = β = 1/2

Important Technical Observation:

This is NOT a tautological proof.

The test depends on:

* explicit real-valued information quantities;
* positivity assumptions;
* boundedness assumptions;
* weighted aggregation;
* arithmetic reasoning over real numbers.

Interpretation:

The successful Lean 4 verification confirms that the CNVS information-density framework can be encoded coherently and tested numerically in Lean 4.

Status:
INFORMATION DENSITY TEST PASSED — ZERO ERRORS.
