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"

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 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. 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 Xu'^u

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^abu 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 are arbitrary
functions in which the torsion tensor field of Gennady Shipov is the
compensating field. This is beyond 1916 GR.

I am going further than Frank here suggesting that Einstein's general
relativity GR in the form of the exotic vacuum field equation

Guv + /\zpfguv = 0

where the dark energy (matter) energy density is

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

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

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

guv(LNIF) = nuv(Minkowski) + (1/2)[Bu,v + Bv,u] dimensionless

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 1916
Einstein 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.

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"

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 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. 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 Xu'^u

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^abu 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 are arbitrary
functions in which the torsion tensor field of Gennady Shipov is the
compensating field. This is beyond 1916 GR.

I am going further than Frank here suggesting that Einstein's general
relativity GR in the form of the exotic vacuum field equation

Guv + /\zpfguv = 0

where the dark energy (matter) energy density is

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

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

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

guv(LNIF) = nuv(Minkowski) + (1/2)[Bu,v + Bv,u] dimensionless

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 1916
Einstein 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.