http://popups.lib.uliege.be/1373-5411/index.php?id=2388 Publications of Auteurs Bernard M. Diaz fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3444 A novel approach to a proof of the Riemann Hypothesis (that all the zeros of the Zeta function lie on the line x = 1/2) is presented. It is based on the universal nilpotent computational rewrite system (NUCRS), derived in the World Scientific book Zero to lnfinity, from a single nilpotent Dirac operator (Rowlands, 2007), establishing an entirely novel semantic computational foundation simultaneously for both mathematics and quantum physics. Tangible evidence is that the Zeta function is known to represent a quantum system and that the criterion of nilpotence corresponds to (a) Pauli exclusion with unique fermion states spin 1/2 and (b) an infinite rewrite alphabet that also corresponds to the infinite roots of -1, of which the nilpotent generalization of Dirac' s famous quantum mechanical equation is the universal computational order code. Thu, 19 Sep 2024 12:00:50 +0200 Thu, 19 Sep 2024 12:01:02 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3444 http://popups.lib.uliege.be/1373-5411/index.php?id=2586 We present D, a synbol that can be used in the universal alphabet that provides a computational path to the nilpotent Dirac equation (Diaz & Rowlands, 2004) and which results in a tractable computer representation of the infinite square roots of -1. We outline how the representation is derived, the properties of the representation, and how the form can be used. Think of D as an infinite table of 1's in any representation e.g. binary or hexadecimal. Any specified column Di of the table has the property that when multiplied with a row Di, the result is a representation of -1. Di multiplied with Dj anticommutes as - (Dj*Di) and produces Dk in a way identical to Hamilton's quaternion i, j, and k. With an infinite and uniquely identifiable set of such triad forms D can be considered both a symbol and because of this behaviour, an alphabet. Thu, 29 Aug 2024 14:33:43 +0200 Thu, 29 Aug 2024 14:33:49 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2586 http://popups.lib.uliege.be/1373-5411/index.php?id=2386 Using a rewrite approach we introduce a computational path to a nilpotent form of the Dirac equation. The system is novel in allowing new symbols to be added to the initial alphabet and starts with just one symbol, representing 'nothing', and two fundamental rules: create, a process which adds news symbols, and conserve, a process which examines the effect of any new symbol on those that currently exist. With each step a new sub-alphabet of an infinite universal alphabet is created. The implementation may be iterative, where a sequence of algebraic properties is required of the emerging subalphabets. The path proceeds from nothing through conjugation, complexification, and dimensionalisation to a steady (nilpotent) state in which no fundamentally new symbol is needed. Many simple ways of implementing the computational path exist. Wed, 07 Aug 2024 15:48:48 +0200 Wed, 07 Aug 2024 15:49:48 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2386