CNVS Formal Verification Report — Lean 4 Test

Test Target:
Reconstruction Consistency and Non-Uniform Fragmentation.

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. Reconstruction Consistency
   Lean verified that the informational encoding is preserved after reconstruction:

   Info(Rec(D(s))) = Info(s)

   in the tested finite CNVS model.

2. Root Reconstruction
   The root element preserves its information after reconstruction.

3. Non-Uniform Fragmentation
   Lean verified that two fragments of the same decomposition may carry different informational sizes:

   Info(1) ≠ Info(2)

4. Fragment Membership
   Lean verified that the fragments 1 and 2 belong to the decomposition of the root element.

Important Technical Observation:

This is NOT a tautological proof.

The test uses:

* explicit finite structured elements;
* explicit information values;
* explicit fragment membership;
* explicit non-uniform information sizes;
* explicit reconstruction behavior.

Interpretation:

The successful Lean 4 verification confirms that CNVS reconstruction consistency and non-uniform fragmentation can be encoded coherently in Lean 4.

The model supports the CNVS claim that fragmentation may be non-uniform while reconstruction preserves the intended informational structure.

Status:
RECONSTRUCTION CONSISTENCY TEST PASSED — ZERO ERRORS.
