The Scale Dimension: Framework and First Predictions

Abstract

The scale dimension is a fifth dimension of spacetime along which position isscale: depth along it is the resolution at which four-dimensional physicsdescribes an object, and motion along it is the running of the couplings. Theframework is three postulates: that scale is a fifth dimension, that itsconversion to elapsed time is logarithmic, and that the phase of the resultinggeometry is a sixth. It is realized in a linear-dilaton throat of finite length,capped at one end and terminating at the other on the boundary that carriesfour-dimensional physics. The construction takes two numerical inputs: the dimensionless productkL = 34.5754, set by the measured vacuum energy density, and a fivebrane countN = 57 posited in advance. From those follow afundamental scale of 2347.4 GeV, independent of the count entirely, and aHagedorn temperature of 49.485 GeV. With the tip mass parameter set equalto the dark-energy scale and a per-component reading of a sourced amplitude, alight scalar follows at 7.545e-18 eV. Its field oscillatesat 1.824 mHz and its observable metric line sits at twice that, 3.649 mHz, withan amplitude scaling with an uncomputed dark-matter fraction. The line isinaccessible to a laser interferometer, which cancels a perturbation common toboth light paths. The vacuum admits no thin-wall winding decay channel, and the geometrycontributes zero tilt to the primordial spectrum at both orders computed. Every result is sourced or recomputable from the two inputs by the accompanyingverification script. The paper states what would end it: a dark-energy sectormeasured to evolve, an inverted neutrino mass ordering determined by oscillationexperiments, and a galactic center black hole spin determined above 0.75.