NovaBeam OS AURA(TM) Produces Five Erdős-Straus Quartic Specializations Formally Machine-Checked in Lean
Bay Area, California – October 6, 2026 –
IMPORTANT: This announcement does not claim that the Erdős-Straus conjecture has been solved. The verified results concern five explicit parameterized families inside the known Type-I/Rosati framework.
Tyrone M. Sanders, founder of House Of The QR Code(TM), announced that five explicit quartic polynomial specializations identified through NovaBeam OS AURA(TM) ConjectureCore have completed formal machine verification in Lean 4 / Mathlib.
The frozen Lean project defines each polynomial family over the natural numbers, proves the exact Type-I certificate 20B(k)D(k)=N(k)(B(k)+5)+1, establishes positivity of the required polynomial quantities, and derives the corresponding three-term unit-fraction decomposition for every natural-number value of k represented by the theorem statements.
On October 3, 2026, the project completed a successful `lake build` using Lean 4.34.1 and Mathlib v4.34.1. The terminal reported `Build completed successfully (765 jobs).` A subsequent source search returned no `sorry` or `admit` placeholders in the main proof file. The exact verified source snapshot has been preserved with a SHA-256 integrity hash.
What the result means
The formal check strengthens the correctness record for the five displayed families: the result is not based only on finite numerical testing or an AI-generated derivation. Lean checks the formal theorem statements and proofs against its kernel for all natural k in the encoded families.
What the result does not mean
- It is not a proof of the full Erdős-Straus conjecture for every integer n >= 2.
- It is not a claim that the Type-I/Rosati parametrization is new.
- It is not a formal proof of historical novelty. Whether the exact five quartic coefficient families were previously published remains under expert literature review.
Research workflow
The project progressed through NovaBeam OS AURA(TM) symbolic discovery, exact candidate filtering, prior-art/equivalence audits, independent Python and BigInt verification, and finally Lean formalization. The current public status separates mathematical correctness from historical priority.
About the research
Tyrone M. Sanders is the founder of House Of The QR Code(TM) and research lead for NovaBeam OS AURA(TM) ConjectureCore. The AURA research pipeline was used to generate, filter, classify, and audit the candidate polynomial families before formal verification.
Media Contact
Company Name: House Of The QR Code™
Contact Person: Tyrone M. Sanders
Email: Send Email
Country: United States
Website: https://novabeamosauraprojects.netlify.app/
 Produces Five Erdős-Straus Quartic Specializations Formally Machine-Checked in Lean){kind=link}