We determine the asymptotics of the independence number of the random $d$-regular graph for all $d \ge d_0$. It is highly concentrated, with constant-order fluctuations around $nα_* - c_*\log n$ for explicit constants $α_*(d)$ and $c_*(d)$. Our pro...
We present a dynamical theory of statistical convergence in which the law of large numbers arises from outcome-outcome feedback rather than assumed independence. Defining the convergence field and its derivative, we show that empirical frequencies ev...
Libia Lobo Sardesai (née Lobo; born 25 May 1924) is an Indian independence activist and lawyer. Along with Vaman Sardesai, whom she later married, she
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence and identica...
A formal proof of the independence of the continuum hypothesis (⭐ 142)
I am not Scottish but love the country and the people. I understand some of reasons as to why Scotland voted no on the last referendum but now those reasons don't really matter (Brexit and all that). ...
We prove that among 1 and the odd zeta values $ζ(3)$, $ζ(5)$, \ldots, $ζ(s)$, at least $ 0.21 \sqrt{s}/\sqrt{\log s}$ are linearly independent over the rationals, for any sufficiently large odd integer $s$. This is the first asymptotic improvement...
Open-source financial independence dashboard (⭐ 53)
The classic theorem of Gallai and Milgram (1960) asserts that for every graph G, the vertex set of G can be partitioned into at most α(G) vertex-disjoint paths, where α(G) is the maximum size of an independent set in G. The proof of Gallai--Milgram...
On July 4, 2026, America will celebrate the most important milestone in our country’s history—250 years of American Independence.
We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-lik...
Thoughts on resolution independence (⭐ 145)
You don't have a clue what's best and neither do I We're not qualified or knowledgeable enough to make an informed decision on which course of action would prove best in the long term I'm not ...
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Python code of Hilbert-Schmidt Independence Criterion (⭐ 91)
If anyone has queries regarding Indy please fire away....
America’s 250th anniversary arrives at a time of deep political divisions and, in some quarters, heightened anxiety over whether representative government in the world’s oldest democracy can be …
SwiftShader is a high-performance CPU-based implementation of the Vulkan graphics API. Its goal is to provide hardware independence for advanced 3D graphics. (⭐ 2447)
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YNAB Financial Independence (FIRE) Calculator (⭐ 96)