**Authors:** Terrence J. McMahon

An ‘interaction constant’ with the irrational number phi is discovered, unifying Nature’s principal constants with gravity. This constant reveals an elegant symmetry permitting the universe to have change, while conserving principal parameter ratios. New relationships for principal constants are shown. Magnetic permeability and electric permittivity of free space, set by convention last century are found to have new values. This allows an exact value for the Planck constant, and a precise value for the elementary charge e to be obtained. Errors in current Planck units are discussed. A reevaluation of dimensional analysis introduces new dimensional units for G, ε, µ, gravity, the Coulomb constant and electric force. The fine-structure constant is found to have dimensions Hz. Pi and phi are found to have dimensions in some configurations. Energy variation causes most principal constants to run, while still adhering to this scale invariant, overall symmetry. Electromagnetic and gravitational forces also run, with gravity dominating at high energies as expected. Wavelength red-shifting occurs via dilation of space-time, attenuated by running of gravity and energy. Structural symmetry requires a new cosmic model where the universe has a constant form. Discussion of a toroidal cosmology introduces candidates for the Hubble and cosmological constants, and a mass-density parameter. These are found to have identical values to most recent Planck data. Standard Model anomalies become redundant. This study confirms and extends general relativity.

**Comments:** 23 Pages. Note: This updates and extends 1701.0524, however both works contain sufficient differences to be separate articles. However, where there is conflict between the two papers, this research is to be preferred.

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[v1] 2018-03-21 03:12:43

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