An open research program investigating the Riemann Hypothesis through rigorous mathematical analysis, spectral methods, positivity criteria, and reproducible computational verification.
ACTIVE RESEARCH — NO PROOF CLAIMED.
The Riemann Hypothesis remains an open problem. This repository is a research program, not a claim of a solution.
Governing rule: No gap closed, no proof claim.
Results are classified as CONJECTURAL, DERIVED, NUMERICALLY_SUPPORTED, VERIFIED, PROVED, REFUTED, or BLOCKED.
- Completed zeta function and equivalent formulations of RH.
- Weil explicit-formula quadratic form and positivity.
- Spectral/operator formulations and the Hilbert-Polya direction.
- Finite-dimensional approximations and the finite-to-infinite limit problem.
- Reproducible numerical experiments for discovery and falsification.
- Independent verification and adversarial attempts to break proposed arguments.
A mathematically attractive construction is not a theorem. Numerical agreement is not a proof. A proof is not complete until every dependency and limiting argument is explicit.
Investigate whether a rigorously controlled finite spectral/positivity construction can be connected to the full Weil object in a limit that preserves the required positivity and identifies the resulting spectrum with the non-trivial zeros of the Riemann zeta function.
This is an open research question, not an asserted result.
PUBLIC EXPERIMENTAL RESEARCH REPOSITORY — NO RH PROOF CLAIMED
This repository is intentionally open for:
- reproducible experiments;
- mathematical derivations and lemma audits;
- adversarial attempts to find counterexamples or proof gaps;
- independent verification of computational and analytic results;
- discussion of alternative routes to the Riemann Hypothesis.
The project distinguishes external theorems, repository-derived results, numerical evidence, verified results, and complete proofs. See RESEARCH_INTEGRITY.md, CONTRIBUTING.md, and RESEARCH_STATUS.md.
Important: finite numerical verification, spectral matching, finite-dimensional positivity, or an operator construction is not by itself a proof of the Riemann Hypothesis.
The repository now includes a dedicated review layer:
- Formal Proof Guidelines — exact proof-boundary and function-space requirements.
- Reproducibility Suite — computational reproducibility and independent-recomputation requirements.
- Adversarial Counterexample Challenges — explicit attempts to falsify the finite-to-global, coverage, sector, spectral, and numerical claims.
These documents are deliberately designed to make the program easier to audit and harder to overclaim.
The 2026-09-20 public-release audit is recorded in research-log/2026-09-20-public-release-audit.md.
Current active research branch: main.