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A proof of the Kepler conjecture
 Math. Intelligencer
, 1994
"... This section describes the structure of the proof of ..."
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Cited by 112 (11 self)
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This section describes the structure of the proof of
The Flyspeck Project
"... Abstract. This article gives an introduction to a longterm project called Flyspeck, whose purpose is to give a formal verification of the ..."
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Cited by 15 (2 self)
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Abstract. This article gives an introduction to a longterm project called Flyspeck, whose purpose is to give a formal verification of the
Proving bounds for real linear programs in isabelle/HOL (Extended Abstract)
 THEOREM PROVING IN HIGHER ORDER LOGICS (TPHOLS 2005), VOLUME 3603 OF LECT. NOTES IN COMP. SCI
, 2005
"... The Flyspeck project [3] has as its goal the complete formalization of Hales’ proof [2] of the Kepler conjecture. The formalization has to be carried out within a mechanical theorem prover. For our work described in this paper, we have chosen the generic proof assistant Isabelle, tailored to Higher ..."
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Cited by 8 (0 self)
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The Flyspeck project [3] has as its goal the complete formalization of Hales’ proof [2] of the Kepler conjecture. The formalization has to be carried out within a mechanical theorem prover. For our work described in this paper, we have chosen the generic proof assistant Isabelle, tailored to HigherOrder Logic (HOL) [4]. In the following, we will refer to this environment as Isabelle/HOL. An important step in Hales ’ proof is the maximization of about 10 5 real linear programs. The size of these linear programs (LPs) varies, the largest among them consist of about 2000 inequalities in about 200 variables. The considered LPs have the important property that there exist a priori bounds on the range of the variables. The situation is further simplified by our attitude towards the linear programs: we only want to know wether the objective function of a given LP is bounded from above by a given constant K. Under these assumptions, Hales describes [1] a method for obtaining an arbitrarily precise upper bound for the maximum value of the objective function of an LP. This method still works nicely in the context of mechanical theorem
Can padic integrals be computed
"... This article gives an introduction to arithmetic motivic integration in the context of padic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives. 1 ..."
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Cited by 7 (2 self)
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This article gives an introduction to arithmetic motivic integration in the context of padic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives. 1
A proof of the dodecahedral conjecture
, 1998
"... This article gives a proof of Fejes Tóth’s Dodecahedral conjecture: the volume of a Voronoi polyhedron in a threedimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius. 1 ..."
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Cited by 5 (2 self)
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This article gives a proof of Fejes Tóth’s Dodecahedral conjecture: the volume of a Voronoi polyhedron in a threedimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius. 1
exact linear arithmetic decision procedure
, 2009
"... using floatingpoint computations to help an ..."