A FORMAL PROOF OF THE KEPLER CONJECTURE
- T. Hales, Mark Adams, R. Zumkeller
- MathematicsForum of Mathematics, Pi
- 9 January 2015
This paper constitutes the official published account of the now completed Flyspeck project and describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants.
Algorithmic randomness, reverse mathematics, and the dominated convergence theorem
- J. Avigad, Edward T. Dean, Jason M. Rute
- MathematicsAnnals of Pure and Applied Logic
- 3 June 2011
Van Lambalgen's Theorem for uniformly relative Schnorr and computable randomness
- Kenshi Miyabe, Jason M. Rute
- Mathematics
- 25 September 2012
We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van…
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
- J. Avigad, Jason M. Rute
- MathematicsErgodic Theory and Dynamical Systems
- 19 March 2012
Abstract Let $ \mathbb{B} $ be a $p$-uniformly convex Banach space, with $p\geq 2$. Let $T$ be a linear operator on $ \mathbb{B} $, and let ${A}_{n} x$ denote the ergodic average $(1/ n){\mathop{\sum…
Topics in algorithmic randomness and computable analysis
- Jason M. Rute
- Mathematics, Computer Science
- 2013
This dissertation develops connections between algorithmic randomness and computable analysis. In the first part, it is shown that computable randomness can be defined robustly on all computable…
Proof Artifact Co-training for Theorem Proving with Language Models
- Jesse Michael Han, Jason M. Rute, Yuhuai Wu, Edward W. Ayers, Stanislas Polu
- Computer ScienceInternational Conference on Learning…
- 11 February 2021
PACT is proposed, a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective and applied to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date.
Computable randomness and betting for computable probability spaces
- Jason M. Rute
- Mathematics, Computer ScienceMathematical Logic Quarterly
- 25 March 2012
The paper contains a new type of randomness—endomorphism randomness)—which the author hopes will shed light on the open question of whether Kolmogorov‐Loveland randomness is equivalent to Martin‐Löf randomness.
Algorithmic randomness for Doob's martingale convergence theorem in continuous time
- B. Kjos-Hanssen, Paul Kim Long V. Nguyen, Jason M. Rute
- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 1 November 2014
Doob's martingale convergence theorem for computable continuous time martingales on Brownian motion is studied, showing that a point is Doob random if its tail is computably random in a certain sense.
A metastable dominated convergence theorem
- J. Avigad, Edward T. Dean, Jason M. Rute
- MathematicsJournal of Logic and Analysis
- 2012
A slight strengthening of Tao's theorem is proved, and it is shown that when the first bound is given by a continuous functional, the bound in the conclusion can be computed by a recursion along the tree of unsecured sequences.
On the computability of graphons
- N. Ackerman, J. Avigad, Cameron E. Freer, Daniel M. Roy, Jason M. Rute
- Mathematics, Computer SciencearXiv.org
- 31 January 2018
This work establishes basic computable equivalences, and shows that $L^1$ representations contain fundamentally more computable information than the other representations, but that $0'$ suffices to move between computable such representations.
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