Relation to General Relativity

Status: CANONICAL

SSZ as GR Extension, Not Replacement

A useful way to read SSZ is:

GR provides a geometric description (curvature) that works extremely well
SSZ keeps the successful GR structure in weak fields — identically
SSZ adds one extra operational layer — a segment density field Ξ — whose primary observational footprint is modified time dilation, saturating in strong fields

SSZ is not "anti-GR." It is closer to "GR + structured strong-field correction," with an explicit cap that avoids runaway divergences.

In the weak field (r/r_s > 2.2), SSZ and GR are identical to observational precision:

Observable	GR	SSZ	Difference
GPS time correction	45.85 μs/day	45.85 μs/day	< 1 ns/day
Pound-Rebka Δν/ν	2.46×10⁻¹⁵	2.46×10⁻¹⁵	< 0.01%
Mercury perihelion	42.98"/century	42.98"/century	0.00%
Eddington lensing	1.75"	1.75"	0.00%
Cassini Shapiro γ	1.000021	1.000021	0.00%
S2 star redshift	0.00018	0.00018	< 0.01%

SSZ is designed to pass every existing weak-field test exactly.

SSZ deviates from GR only in the strong field (r/r_s < ~10):

Property	GR	SSZ	Interpretation
Time dilation D	0	0.555	Finite vs infinite
Redshift z	∞	0.802	Bounded vs divergent
Proper time τ	0	> 0	Observable vs frozen
Singularity	YES	NO	SSZ resolves it
Energy conditions	Violated	Satisfied	SSZ is regular

Object	z_GR	z_SSZ	Excess
PSR J0030+0451 (r/r_s=3.06)	0.219	0.328	+50%
PSR J0740+6620 (r/r_s=2.23)	0.346	0.413	+19%
PSR J0348+0432 (r/r_s=2.10)	0.380	0.457	+20%

Systematic prediction: NS redshift +13% higher than GR — testable with NICER.

SSZ and GR agree at mass-independent comparison radii. The numerical value depends on the declared Xi form:

r*/r_s = 1.594811,  D* = 0.610710  for Xi_A(x)=1-exp(-phi/x)
r*/r_s = 1.386562,  D* = 0.528007  for Xi_B(x)=1-exp(-phi*x)

These intersection points are:

They are not hard regime boundaries. The operative blend remains fixed at 1.8 <= r/r_s <= 2.2.

Parameter	GR	SSZ	Measurement
β	1	1 (exact)	—
γ	1	1 (exact)	Cassini: 1.000021 ± 0.000023

SSZ is PPN-identical to GR. All Solar System tests are passed by construction.

Aspect	GR	SSZ
Core object	Metric tensor g_μν	g_μν + Ξ(r)
Singularities	Present at r_s	Absent (D > 0 everywhere)
Information paradox	Problematic	Avoided (finite D)
Falsifiability	Weak-field confirmed	Explicit strong-field predictions
Free parameters	0	0
Strong-field behavior	Divergent	Saturating

SSZ = GR in the weak field + bounded segment density in the strong field, with zero free parameters and explicit falsification targets.