Lattice and loop under one roof

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jal
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Two approaches under one roof?
Would it be too much to say that the following paper has made it possible for the double tetra to be imbeded into the cube?
http://arxiv.org/abs/0803.4483
Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology
Authors: William Nelson, Mairi Sakellariadou (King's College London)
(Submitted on 31 Mar 2008)
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Could someone explain "twists".
 
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The following paper should also be included “under one roof.”
http://xxx.lanl.gov/abs/0801.0861
Quantum Graphity: a model of emergent locality
Authors: Tomasz Konopka, Fotini Markopoulou, Simone Severini
(Submitted on 6 Jan 2008)
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly connected and the physics is invariant under the full symmetric group acting on the vertices. We present evidence that the model also has a low-energy phase in which the graph describing the system breaks permutation symmetry and appears to be ordered, low-dimensional and local. Consideration of the free energy associated with the dominant terms in the dynamics shows that this low-energy state is thermodynamically stable under local perturbations. The model can also give rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. We also reformulate the model in graph-theoretic terms and compare its dynamics to some common graph processes.
 
I would assume that the pros are aware of the following paper and how to use the info to put everything “under one roof”.
http://arxiv.org/abs/nucl-th/0611050
Nucleon electromagnetic form factors
Authors: J. Arrington, C.D. Roberts, J.M. Zanotti
(Submitted on 14 Nov 2006)