[2502.20642] A proof of the Collatz conjecture
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Music is always downstream from what’s happening in society at large. It may take some time, but popular contemporary music will always end of reflecting the general zeitgeist.Some data scientists (professional and otherwise) have noticed something about pop songs on the Billboard Top 100. Through careful analysis of a variety of metrics, this music has
Mathematics (like programming) is often called an art form. This makes mathematics the art of argument, not in the sense that anything is debatable, but in the sense that the beauty of a proof lies in its method. Analogously, a painting is not necessarily beautiful only for what it depicts or the medium used, but
type StringBool = “true”|”false”; interface AnyNumber { prev?: any, isZero: StringBool }; interface PositiveNumber { prev: any, isZero: “false” }; type IsZero = TNumber[“isZero”]; type Next = { prev: TNumber, isZero: “false” }; type Prev = TNumber[“prev”]; type Add = { “true”: T2, “false”: Next }[IsZero]; // Computes T1 * T2 type Mult = MultAcc;
I introduced Plonk in a series of 12 videos here. That was almost a year and half ago! So I’m back with more :) In this new series of videos I will explain how proof composition and recursion work with different schemes. Spoiler: we’ll talk about Sangria, Nova, PCD, IVC, BCTV14 and Halo (and perhaps
Free, anonymous, distributed, and secure proof of existence for any digital document.Drop your document here, or click to select it from your computer.Max. 1MBReferenceThis will be included in the certificate email for future reference.How does it work?Free Blockchain Proof is like a free anonymous notary, where you can create a proof of the existance of
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Godel showed that it is impossible to formally prove the consistency of a system of arithmetic WITHIN that system of arithmetic.Given a static system that is clearly true.However, I claim a self-modifying system can extend itself to “look down” on the initial system of arithmetic.I'm not sure how to show this yet. My intuition is…