A(r)
D²(r), the positive lapse-like metric function in the diagonal ansatz. A→1/4 at the formal centre.
Definitions before conclusionsGlossary,
Glossary,
symbols and FAQ
Search the vocabulary of SSZ, geometry, observables, testing and scientific status.
Aa
Symbol index
Ξ(r)
Dimensionless segment-density field. Its operative form depends on the declared radial regime.
D(r)
Dimensionless time factor 1/(1+Ξ), relating dτ to dt for static observers.
φ
Golden ratio (1+√5)/2≈1.6180339887 used in the canonical strong branch.
r_s
Schwarzschild length scale 2GM/c².
R, K
Ricci scalar and Kretschmann scalar. In the current diagonal centre limit they diverge as r⁻² and r⁻⁴.
γ, β — overloaded symbols
In PPN, γ and β are weak-field parameters and the declared completion uses γPPN=βPPN=1. In the pure metric’s flow module, \(\gamma_{\rm flow}=1+\Xi=D^{-1}\) and \(\beta_{\rm flow}=\sqrt{1-\gamma_{\rm flow}^{-2}}\). These meanings must never be mixed.
z
Redshift convention defined by \(1+z=\nu_e/\nu_o\). The identity z=1/D−1=Ξ applies only to a static emitter compared with a static observer at infinity.
A(r), B(r)
Temporal and radial coefficients \(A=D^2\) and \(B=D^{-2}\). Their product is one in the current diagonal ansatz.
Determinant
For the diagonal spherical form, \(\det g=-c^2D^2s^2r^4\sin^2\theta=-c^2r^4\sin^2\theta\). This exact cancellation tests algebraic coupling; it does not prove a regular centre.
Flow form
The non-diagonal repository form with \(g_{tr}=\beta c\). The cross term belongs to a chosen coordinate representation and is not, by itself, rotation, frame dragging or material flow.
Inverse metric
The tensor \(g^{\mu\nu}\) satisfying \(g_{\mu\alpha}g^{\alpha\nu}=\delta_\mu^{\ \nu}\). Passing this identity validates construction and inversion—not observational truth.
x
Normalised areal radius \(x=r/r_s\). Branch derivatives must state whether they are taken with respect to x or physical radius r.
Glossary
Areal radius
The radius defined by a symmetry sphere’s area 4πr². Its zero is geometrically significant.
Canonical
The currently selected source or definition within the project hierarchy. A later P0 correction can supersede an older file labelled canonical.
Coordinate singularity
A chart failure removable by changing coordinates, unlike an invariant curvature divergence.
C² bridge
The quintic Hermite transition that matches Ξ, its first derivative and its second derivative at x=1.8 and x=2.2. Smooth joining does not derive a physical phase transition.
Captured run
A dated execution with environment, command and outcome. The 1,296-pass record is a historical twelve-repository subset. The complete catalogue contains 9,300 records and 5,294 unique repository/test definitions across 28 test-bearing repositories.
Test outcome
One assertion outcome under a named runner and environment. It is not interchangeable with a script, parameterisation, phase, log, report file or independent physical experiment.
Empirical preference
A comparison whose data, uncertainties, nuisance parameters, flexibility and selection protocol are specified. Lower residuals in one pipeline remain conditional evidence until independently reproduced.
Empirical compatibility
Data do not reject a model within a defined analysis. It is weaker than unique confirmation.
Event horizon
A global causal boundary, definable only from the full spacetime—not merely a zero or finite value of one local coefficient.
Effective source
The stress tensor obtained by inserting the metric into a GR-style Einstein tensor. It diagnoses the geometry but is not a derived fundamental SSZ matter theory.
vfall
The complementary fall scale vfall = c√(r/rs) = c2/vesc. Its product with vesc is exactly c2. It is not a locally measured material 3-velocity and is distinct from the metric proxy c√(1−D2).
Falsifiability
The existence of observations or mathematical results that could rule out a model.
Geodesic completeness
Whether all inextendible geodesics have complete affine/proper parameter ranges. Finite coefficients do not prove it.
Local orthonormal frame
A tetrad in which an observer reports physical components. It separates local measurements from chart-dependent quantities such as dr/dt.
Legacy
Historical material retained for development history but not used as current scientific authority.
Model lock
A frozen formula/parameter/method specification used to make downstream results reproducible.
Observable class
The physical type of measurement—static clock, null path, timelike orbit, wave or dataset fit—which determines the required forward model.
Paired sign test
A test of how often one method wins within matched pairs. It does not measure effect size or correct automatically for selection, flexibility or correlation.
P0 scope clarification
A highest-priority scientific clarification. Here it separates the repeatedly tested finite horizon factor from the unresolved construction of a physical global interior.
PPN
Parameterized post-Newtonian formalism for systematic weak-field comparisons.
Proper time
The invariant time measured by a clock along a timelike worldline.
Regular centre
An areal centre with appropriate local geometry and finite curvature invariants—not merely finite metric components.
Regime boundary
A declared formula-domain join, observable approximation boundary or physical transition. These three meanings are distinct and must be labelled.
Residual
A defined difference between data and model output. A small residual supports only that pipeline until uncertainty, covariance and alternative models are included.
Software validation
Evidence that code satisfies specified tests. It is not direct evidence that nature selects the model.
Strong field
A regime where weak-field expansions are insufficient and full metric/geodesic dynamics matter.
Frequently asked questions
Is SSZ a complete theory of gravity?
No. It is a concrete effective research programme with geometry, calculations and tests, but lacks a completed fundamental action, global interior and several dynamical sectors.
Can SSZ resolve the black-hole singularity question?
Tests repeatedly verify that the declared horizon time factor remains finite. The present diagonal extrapolation has divergent curvature at the areal centre, so that expression alone is not the completed interior. A different SSZ inner solution, matching construction or boundary geometry may still resolve the centre question; deriving and testing such a completion remains open research.
Does local light slow down?
No local observer measures a vacuum light speed other than c. Coordinate speeds can change with coordinates and metric coefficients.
Why use φ?
φ is structurally selected in the current branch. A deeper dynamical derivation of why nature should select it remains an open foundational question.
What would falsify SSZ?
Locked strong-field forward predictions that fail sufficiently precise data, weak-field regressions, or a mathematical inconsistency in any proposed dynamical completion.
Why are there multiple test totals?
Different reports count functions, parameterised cases, custom phases, repositories or historical result artefacts. A valid total must state its scope and command.
Do all supplied tests pass?
No single captured command has yet executed the entire current corpus as one run. A historical twelve-repository subset records 1,296 passed and zero failed. The complete inventory contains 9,300 records, 5,294 unique repository/test definitions and 9,216 repository/file/test identities across 28 test-bearing repositories. Repository-specific reruns remain separately visible, including 184/184 qubit and 54/54 Lagrange tests.
How do the earlier finite results relate to the centre calculation?
The finite horizon values and C² transition tests remain valid within their domains. The centre asymptotics evaluate a different locus and the present diagonal extrapolation. Future supplementary work can construct and test whether another SSZ interior completes the geometry.
Can a passing fit prove SSZ?
No. Model flexibility, data selection, nuisance parameters, covariance and alternative models must be assessed independently.