Defined geometry
A scalar segment-density field Ξ(r), a time factor D(r), a diagonal metric ansatz, explicit weak/strong branches, and an operational C² blend.
✓ P0-corrected scientific scope · August 2026
Segmented
Segmented
Spacetime
An inspectable public research portal for SSZ: geometry, observables, source code, test evidence, falsification criteria, conflicts, papers, and the unresolved interior problem.
Ξ
Scientific classification
What SSZ is — and what it is not
SSZ is a scientifically serious, mathematically concrete and falsifiable strong-field research programme. It is not yet a complete or empirically confirmed fundamental theory of gravity.
Computable observables
Clock rates, redshift proxies, PPN limits, trajectories, lensing pipelines, and strong-field model comparisons are implemented in public code.
Next foundations
The tested static geometry provides a concrete base. A complete action, a globally specified interior, a non-perturbative rotating solution and a derived gravitational-wave theory are the next major research layers.
Horizon result and interior scope: finite horizon time dilation is the strongest secure theoretical result and is repeatedly reproduced by the test corpus. If the same diagonal expression is extrapolated to the areal centre, A(r)→1/4 while R(r)~3/(2r²) and K(r)~9/(4r⁴). This diagnoses that particular continuation; a different SSZ inner solution or boundary completion remains an open possibility.
Self-hosted scientific animation
See the equations change
Seven responsive visual modules connect parameters to geometry: conceptual φ levels, canonical radial scaling, weak-field lensing, null effective potential, an observational ICRS catalogue, Sagnac rotation and the P0 curvature divergence.
Canonical mappings
Move through r/rs and watch Ξ, D and s change together, with the active strong, transition or weak branch shown explicitly.
Paths and rotation
Change a lensing impact parameter, inspect the metric-derived null potential, and follow counter-propagating signals on a rotating loop.
Scientific boundaries
Every animation is labelled as canonical, reference, asymptotic or conceptual so that explanatory graphics never silently become evidence.
Counts are generated from the current local corpus. They are inventory counts, not claims of independent scientific confirmation.
Interactive metric explorer
Ξ and D across radial regimes
The plot uses the P0 decay branch below 1.8 rs, a derivative-matched quintic Hermite C² bridge from 1.8 to 2.2 rs, and Ξ=rs/(2r) outside. The blue Schwarzschild curve is a reference, not an interpolation target.
Ξ(r)—
D(r)—
z proxy—
Branch—
Strong branch
Ξstrong(r)=1−exp(−φrs/r)
Operative for r/rs<1.8. It gives Ξ(rs)≈0.801711847.
C² blend
Ξ(r)=H5(t)
Values, slopes, and curvatures are matched at both endpoints. The original dashboard’s simplified cubic smoothstep has been corrected.
Weak branch
Ξweak(r)=rs/(2r)
Operative for r/rs>2.2 and asymptotically flat.
Live calculators
From mass scale to static clock factors
Every output below is computed in the browser from the declared public formulas. No decorative or random values are used.
Mass and Schwarzschild scale
rs = 2GM/c² = —
The mass sets the length scale. The normalized SSZ curves depend on x=r/rs.
Static SSZ quantities
Ξ—
D—
z=1/D−1—
Comparison point—
Strong-field comparisons
ISCO: —
Shadow: —
Why no invented number? Photon sphere, ISCO and shadow values depend on the exact metric branch and geodesic derivation. The portal displays only values with an explicit provenance chain.
Theory map
From definition to confrontation with nature
Ξ(r)
field definition
field definition
D(r), metric
geometry
geometry
Observables
clocks, paths, orbits
clocks, paths, orbits
Data tests
uncertainty and falsification
uncertainty and falsification
Understand
Begin with segmentation, proper time, coordinate time, local light speed, and the difference between a model field and a physical mechanism.
Theory from A to Z →Formula reference →
Inspect
Trace a claim through formula, implementation, input, test, result, and commit-level repository evidence.
Test and provenance dashboard →Challenge
Read what observations could reject SSZ and which calculations remain too incomplete for a decisive comparison.
Falsification and limitations →Papers and claim history →
Current state
Secure results, model results, and open questions
Finite horizon factor
For the declared branch, Ξ(r_s)≈0.801711847 and D(r_s)≈0.555027709. This is directly calculable.
Weak-field machinery
PPN β=γ=1 paths reproduce the corresponding standard weak-field formulas. This establishes compatibility of that implementation scope.
Interior and dynamics
A globally regular inner solution, complete action, field equations, stability analysis, and rotating completion remain research tasks.
Source discipline
How conflicting sources are handled
Priority order
- Current P0 corrections
- Explicit canonical / single-source documents
- Model and branch locks
- Current reproducible tests
- Current repository documentation
- Legacy papers and audits
Non-negotiable distinction
Software PASS means the implementation met its assertions. Data compatibility means a model was not rejected within a stated analysis. Empirical confirmation requires independent measurement, uncertainty control, and model comparison.