The Dinitz-Garg-Goemans theorem (1999) is a solution to the Single-Source Unsplittable Flow (SSUF) problem. Goemans formulated then a conjecture about the costs.
💡 The generally formulated Dinitz-Garg-Goemans conjecture has been falsified by a very specific, highly theoretical counterexample, which was even generated by an AI system after a few prompts. The conjecture is falsified by exploiting a loophole in the semantically somewhat too general formulation of the conjecture.
📡 It is not entirely clear how the AI generated the example. A mathematical proof or counterproof always requires all boundary conditions that can be verified. The counterexample itself seems to fit and is being heavily promoted on social media, even though hardly anyone understands, let alone needs, the mathematical conjecture and the associated theorem. It is simply intended to demonstrate what AI systems are supposedly capable of. Mathematical formalisms that could be directly verified by mathematicians are completely lacking. A peer review, which would also examine the conditions under which it was generated, is still pending.
🪖 The formal mathematical proof:
I have taken the trouble to present a formal mathematical research theorem that falsifies the Dinitz-Garg-Goemans conjecture. The fully presented falsification can be verified by mathematicians through peer review. This allows the immediate development of applications in industry, business, and computer science, such as the rapid detection of vulnerabilities during the validation of network topologies.
By the way: Generally speaking, purely static systems with rigid constraints are doomed to failure, as reflected, for example, in the inflexible chip technology of recent decades.
⛑️ Saving the conjecture:
Furthermore, I formulated a minimal extension of the DGG conjecture without breaking the base statement. I added a minimal, dynamic time component to the conjecture’s constraints, elevating the conjecture to a previously missing real-world dimension. The conjecture, extended by the time component and applicable to real-world scenarios, could be formally verified mathematically. Applications include logistics, warehouse logistics and data transport on a system-on-a-chip.
The paper was published on Zenodo: The Formal Mathematical Falsification of the Dinitz-Garg-Goemans Cost Conjecture
cheers
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