https://github.com/bwesterb/ks

https://github.com/bwesterb/ks

kochen-specker latex math

Last synced: 2 months ago
JSON representation

• Host: GitHub
• URL: https://github.com/bwesterb/ks
• Owner: bwesterb
• Created: 2014-05-28T15:00:55.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2023-07-04T09:00:08.000Z (over 1 year ago)
• Last Synced: 2023-07-04T10:06:56.681Z (over 1 year ago)
• Topics: kochen-specker, latex, math
• Language: Makefile
• Homepage: kochen-specker.info
• Size: 6.94 MB
• Stars: 4
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
A Kochen-Specker System has at least 22 vertices

================================================

* Bas Westerbaan ([email protected])

* Sander Uijlen ([email protected])

Abstract

--------

At the heart of the Conway-Kochen Free Will theorem and Kochen and

Specker's argument against non-contextual hidden variable theories

is the existence of a Kochen-Specker (KS) system: a set of points

on the sphere that has no {0, 1}-coloring such that at most one of

two orthogonal points are colored 1 and of three pairwise orthogonal

points exactly one is colored 1. In public lectures, Conway

encouraged the search for small KS systems. At the time of writing,

the smallest known KS system has 31 vectors.  Arends, Ouaknine and

Wampler have shown that a KS system has at least 18 vectors, by

reducing the problem to the existence of graphs with a topological

embeddability and non-colorability property. The bottleneck in their

search proved to be the sheer number of graphs on more than 17

vertices and deciding embeddability.  Continuing their effort, we

prove a restriction on the class of graphs we need to consider and

develop a more practical decision procedure for embeddability to

improve the lower bound to 22. In 2022, Li, Bright, and Ganesh improved

the lower bound to 23, then shortly after to 24 in 2023 using a SAT solver + 

Computer Algebra System approach to dramatically reduce the search space.

This repository

---------------

This repository contains the

 * LaTeX sourcecode of the preprint (under `/paper`);

 * LaTeX sourcecode for the slides used at QPL2014 (under `/qpl2014`);

 * Data generated by some of the computations (under `/graphs`);

 * source code used for the computation (under `/code`,

   in particular `/code/comp.py`) and

 * source code of the website kochen-specker.info (under `/site`).

    * First, in `/code`, run `python generateSite.py`.

    * Then, in  `/site`, run `jekyll build`.

    * Find the site in `/site/_site`.