Direct proof
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A proof of the Ohsawa–Takegoshi theorem with sharp estimates Open
We give a proof of the Ohsawa-Takegoshi extension theorem with sharp estimates. The proof is based on ideas of Blocki to use variations of domains to simplify his proof of the Suita conjecture, and also uses positivity properties of direct…
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Pros and cons of consensus algorithm proof of stake. Difference in the network safety in proof of work and proof of stake Open
The consensus algorithm is a mechanism that allows you to protect the network against attacks.The work of the algorithm is to provide rules that act on the network members.Proof of Work is one of the consensus algorithms based on the calcu…
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Avicenna’s Proof for God’s Existence: the Proof from Ontological Considerations Open
This paper argues that there is only one proof for God’s existence in Avicenna, and only one way for establishing the proof within his metaphysical system. This metaphysical proof is essentially derived from a priori notions, among which t…
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Proof of the renormalizability of the gradient flow Open
We give an alternative perturbative proof of the renormalizability of the\nsystem defined by the gradient flow and the fermion flow in vector-like gauge\ntheories.\n
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Mathematical proof: from mathematics to school mathematics Open
Proof plays a central role in developing, establishing and communicating mathematical knowledge. Nevertheless, it is not such a central element in school mathematics. This article discusses some issues involving mathematical proof in schoo…
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A Direct Proof of the Equivalence between Brouwer's Fan Theorem and König's Lemma with a Uniqueness Hypothesis Open
From results of Ishihara it is known that the weak (that is, binary) form of König’s lemma (WKL) implies Brouwer’s fan theorem (Fan). Moreover, Berger and Ishihara [MLQ 2005] have shown that a weakened form WKL! of WKL, where as an additio…
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Finding Good Proofs for Description Logic Entailments using Recursive Quality Measures Open
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
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KdV is well-posed in $H^{-1}$ Open
We prove global well-posedness of the Korteweg--de Vries equation for initial data in the space $H^{-1}(R)$. This is sharp in the class of $H^{s}(R)$ spaces. Even local well-posedness was previously unknown for $s
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Note on Pontryagin maximum principle with running state constraints and smooth dynamics -- Proof based on the Ekeland variational principle Open
In this note our aim is to give a proof of the Pontryagin maximum principle for a general optimal control problem with running state constraints and smooth dynamics. Our proof is based on the classical Ekeland variational principle. The ma…
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First-Order Interpolation and Interpolating Proof Systems Open
It is known that one can extract Craig interpolants from so-called local proofs. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. However, standard complete proof systems, such as supe…
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The fundamental theorem of homological projective duality via variation of GIT stability Open
We reprove Kuznetsov's "fundamental theorem of homological projective duality" using LG models and variation of GIT stability. This extends the validity of the theorem from smooth varieties to nice subcategories of smooth quotient stacks, …
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THE LOGICS OF DOUBLE PROOF IN PROOF OF CONCEPT: A DESIGN THEORY-BASED MODEL OF EXPERIMENTATION IN THE UNKNOWN Open
The literature on design distinguishes between exploration-based experimentation and validation-based experimentation. This typology relies on an assumption that exploration and validation cannot and should not be performed simultaneously …
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Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness Open
We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essential…
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Impediments to mathematical creativity: Fixation and flexibility in proof validation Open
Mathematical techniques in proof writing can be narrowed down to specific proof styles. Simply put, proofs can be direct or indirect- the latter using the Law of the Excluded Middle from logic as well as the axiom of Choice, to prove exist…
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Yet Another Proof of the Entropy Power Inequality Open
Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or Rényi entropies. The proof is based on a sim…
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A new proof of Jacquet-Rallis's fundamental lemma Open
We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on a previous result of W. Zhang on the compatibility of …
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Detailed Proof of Classical Gagliardo–Nirenberg Interpolation Inequality with Historical Remarks Open
A carefully written Nirenberg's proof of the famous Gagliardo–Nirenberg interpolation inequality for intermediate derivatives in \mathbb R^n seems, surprisingly, to be missing in literature. In our paper, we shall first introduce this fund…
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Multi-focused Proofs with Different Polarity Assignments Open
In this work, we will reason on how a given focused proof, where atoms are assigned with some polarity, can be transformed into another focused proof, where the polarity assignment to atoms is changed. This will allow, in principle, transf…
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An elementary and constructive proof of Grothendieck's generic freeness lemma Open
We present a new and direct proof of Grothendieck's generic freeness lemma in its general form. Unlike the previously published proofs, it does not proceed in a series of reduction steps and is fully constructive, not using the axiom of ch…
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A direct proof of Stahl's theorem for a generic class of algebraic functions Open
Under the assumption that Stahl's $S$-compact set exists we give a short proof of the limiting distribution of the zeros of Padé polynomials and the convergence in capacity of diagonal Padé approximants for a generic class of algebraic fun…
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Tree-Like Proof Systems for Finitely-Many Valued Non-deterministic Consequence Relations Open
The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valu…
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Sources of Students’ Difficulties with Proof By Contradiction Open
The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is “more difficult” for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this c…
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A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane Open
We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives h…
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Coalition-proof stable networks Open
We propose the notion of coalition-proof stability for predicting the networks that could emerge when group deviations are allowed. A network is coalition-proof stable if there exists no coalition which has a credible group deviation. A co…
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A one-line proof for complementary symmetry Open
textabstractComplementary symmetry was derived before under particular theories, and used to test those. Progressively general results were published. This paper proves the condition in full generality, providing a one-line proof, and shed…
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An elementary proof of walk dimension being greater than two for Brownian motion on Sierpi\'{n}ski carpets Open
We give an elementary self-contained proof of the fact that the walk dimension of the Brownian motion on an \emph{arbitrary} generalized Sierpinski carpet is greater than two, no complete proof of which had been available in the literature…
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Dinv and Area Open
We give a new combinatorial proof of the well known result that the dinv of an $(m,n)$-Dyck path is equal to the area of its sweep map image. The first proof of this remarkable identity for co-prime $(m,n)$ is due to Loehr and Warrington. …
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Axiomatic Thinking, Identity of Proofs and the Quest for an Intensional Proof-Theoretic Semantics Open
Starting from Hilbert’s Axiomatic Thinking , the problem of identity of proofs and its significance is discussed in an elementary proof-theoretic setting. Identifying two proofs, one of which is obtained from the other one by removing redu…
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Simplest Kochen-Specker Set Open
Kochen-Specker (KS) sets are fundamental in physics. Every time nature produces bipartite correlations attaining the nonsignaling limit, or two parties always win a nonlocal game impossible to always win classically, it is because the part…
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Twenty-Two New Approximate Proof Labeling Schemes Open
Introduced by Korman, Kutten, and Peleg (Distributed Computing 2005), a proof labeling scheme (PLS) is a system dedicated to verifying that a given configuration graph satisfies a certain property. It is composed of a centralized prover, w…