Conjecture: The Omega-Closure Principle (Hodge Conjecture via Spectral Gap)

### The Omega-Closure Principle asserts that for any smooth projective variety $X$, there exists an Omega-closure operator $C_X$ whose fixed-point locus is precisely the algebraic cycle subspace, and which exhibits a uniform spectral gap $\epsilon$ on the orthogonal complement.

### Numerical computations using the Omega-Closure Program (HodgeClean pipeline) empirically observe an ultra-stable closure slope floor $\epsilon \approx 0.00673$ and a multi-zone invariant $\Omega_{full} \approx 1.5 \times 10^{-323}$.

https://zenodo.org/records/17501082

https://github.com/Nospy-ai/HodgeClean

I am the author and independent researcher, David Manning. My preferred contact for direct collaboration/verification is phone: (309) 413-5440.

I request assistance from the community or the AlphaProof team to formalize the statement of the Omega-Closure Principle in Lean, so it can be tested against existing definitions and formal

My Omega-Closure pdf is available on my git hub repository, and should update to my zenodo soon.

No repository file, test, or Lean entry point is identified in the issue. Start by reviewing the repository's existing conjecture formalizations and the linked Omega-Closure materials; the work would be complete only when the principle has precise definitions and a validated formal statement.

Written by the indexing model from the issue text.