10 papers
Diophantine Quadruples and Cayley's Hyperdeterminant
Philip Gibbs
A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Such Diophantine se…
A Generalised Stern-Brocot Tree from Regular Diophantine Quadruples
Philip Gibbs
Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which ca…
Some Rational Diophantine Sextuples
Philip Gibbs
A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six su…
A White Hole Model of the Big Bang
Philip Gibbs
A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole w…
String Partons and Multiple Quantisation
Phil E. Gibbs
I consider an algebraic construction of creation and annihilation operators for superstring and p-brane parton models. The result can be interpreted as a realisation of multiple qu…
Is the Universe Uniquely Determined by Invariance Under Quantisation?
Phil E. Gibbs
In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is…