Math typo-corrected 2nd draft

The role of the Ricci coefficients is subtle. I corrected a few more
math typos from late last night in the clarity of the morning.

Paul Zielinski has been trying to separate out the real intrinsic
geometry from the appearance of coordinate transformations. He has
failed to get anywhere specific for three or more years because he is
not familiar with the Cartan tetrad way of doing Einstein's gravity
theory. The problem becomes simple in the tetrad formalism below. The
"gauge potential" is is what Zielinski has been looking for, but he
could not find it using old-fashioned tensor methods. It requires the
Cartan tetrad technique introduced in the 1920s after Einstein did his
1915 work. Einstein, apparently was never really happy with tetrads
(Einstein-Cartan letters) and got into a three-year tiff with
Schrodinger about them in early thirties?

Bu = Lp^2Bu^aPa

from locally gauging T4 is the "intrinsic geometry" where the Cartan
tetrad is

eu^a = (Kronecker Delta)u^a + Bu^a

When Bu = 0, i.e. when the Goldstone Phase = 0 in a spacetime region,
then all the GCTs are simply different descriptions of globally flat
Minkowski space-time seen from the POVs of arbitrary arrays of LNIF
observers firing their rocket engines in empty deep space. The
connection field is derived simply from the tetrads eu^a. Under GCTs,
eu^a is a first rank GCT tensor in the u LNIF base space index, where a
is the LIF tangent fiber space index. That is, for the Jacobian Matrix
of the GCT

eu’^a = Xu'^ueu^a

Where the Levi-Civita connection field for parallel transport is

{LC}^wvu = ea^we^av,u + e^waA^abue^bv

A^abu is the spin connection that couples to the Lie algebra of the
Lorentz symmetry group O(1,3) of the LIF tangent fiber. O(1,3) is not
locally gauged here in 1916 GR only T4 is locally gauged to give the Bu
gauge potential equivalent to geometrodynamic curvature under the proper
map. A^abc are globally constant "phases" canonically conjugate to the
Sab space-time rotation Lie algebra generators of O(1,3). When O(1,3) is
locally gauged then the spin connection coefficients A^abc are arbitrary
functions in which the torsion tensor field of Gennady Shipov is the
compensating field. Of course, A^abu is an arbitrary variable function
in spacetime because

A^abu(x) = eu^c(x)A^abc

and the variable spacetime dependence is in the tetrad eu^c(x). Locally
gauging O(1,3) in addition to T4 is beyond 1916 GR. I am going further
than Frank Wilczek here suggesting that Einstein's general relativity GR
in the form of the exotic vacuum field equation

Guv + /\zpfguv = 0

where the dark zero point energy (matter) energy density

(c^4/8piG)/\zpf = (String Tension)(DeSitter Curvature)

plays a major role on the small-scale where the constant large-scale
DeSitter Curvature /\zpf generalizes to a local scalar field.

Bu = Lp^2Bu^aPa/h = Lp^2(Macro-Quantum Vacuum World Hologram
GoldstonePhase),u

Bu^a is dimensionless, where

Bu^aPa/h = (Macro-Quantum Vacuum World Hologram Goldstone Phase),u

eu^a = (Kronecker Delta)u^a + Bu^a = flat trivial piece + curved
intrinsic piece

guv(LNIF) = nuv(Minkowski) + (1/2)[Bu,v + Bv,u] is dimensionless
Einstein metric tensor for LNIFs

Lp^2 = hG/c^3 = quantum of area of World Hologram

eu^a = Cartan tetrad (dimensionless)

Bu = gauge potential compensating field from locally gauging the
translation group T4 (dimension of length)

{Pa} = "Mom-energy" Lie algebra of T4

The Ricci rotation coefficients (spin-connection) Au^ab are not
independent dynamical fields in this torsion-free plain vanilla
1916Einstein GR emergence theory.

The covariant derivative on spinors is

Psi;u = Psi,u + Au^abSabPsi

{Sab} is Lie algebra of Lorentz group O(1,3), which, when locally
gauged, gives Gennady Shipov's torsion field theory that Akimov in
Moscow says has practical WMD potential. Shipov is currently in Bangkok.