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No iframe · no decorative random dataInteractive
Interactive
visual laboratory
Change parameters and watch the declared equations respond. Each module states whether it is canonical SSZ, a standard reference calculation, an asymptotic diagnostic, or a conceptual reconstruction.
φ
Conceptual reconstruction
φ-segmentation geometry
Rebuilt from the archived SEGMENTED_SPACETIME/Slider.html, with no CodePen or iframe. This is an explanatory geometry of exponential radial levels—not a derivation of the canonical metric.
rn = r₀eλn
The golden-ratio step is λ=lnφ≈0.4812. Moving away from it is a deliberate conceptual comparison.
Canonical field mapping
How Ξ changes clocks and radial rulers
The same normalized radius drives Ξ, D=1/(1+Ξ), and s=1/D. Concentric circles are coordinate spheres; the gold radial intervals show the corresponding proper radial scale of the diagonal ansatz.
Ξ—
D—
s=1/D—
regime—
P0 dependency explorer
Interior and Global Structure Explorer
Move from the asymptotic region toward the areal centre while keeping three logically separate questions visible: finite static coefficients at the horizon, curvature of the present diagonal continuation near the centre, and the still-open global causal completion.
Logarithmic control: 10⁻⁴ to 10² rs
Ξ—
D=dτ/dt—
A=D²—
grr=D⁻²—
radial |dr/(c dt)|—
proper radial distance from 10⁻⁴rₛ—
P0 R asymptotic—
P0 K asymptotic—
| Display | Source level | What it establishes | What it does not establish |
|---|---|---|---|
| Ξ, D, A, grr, light slope | Canonical static metric definition | Local coefficients in the declared chart | Global event-horizon structure or completeness |
| R~3/(2r²), K~9/(4r⁴) | P0 centre asymptotics | Present areal-centre divergence | Exact invariants at every plotted radius |
| Proper radial integral | Constant-t slice of diagonal ansatz | Slice distance in this chart | Affine completeness of every causal geodesic |
Two non-equivalent classifications
Two-Level Regime Map
Analytic branch routing answers “which formula is evaluated?” Physical description answers “which interpretation is useful?” The two rows are synchronized but are not synonyms.
Analytic formula
strong analytic branchderivative-matched C² bridgeweak analytic branch
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Physical description
formal interiorhorizon neighbourhoodcompact fieldtransitionweak fieldasymptotic
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P0 branch audit
C² continuity microscope
Zoom into either join and inspect Ξ, dΞ/dx and d²Ξ/dx² on both sides. This makes the six Hermite endpoint conditions visible rather than merely asserting “smoothness”. The displayed Δ values compare finite numerical probes immediately to either side; exact endpoint identities are tested separately.
probe ΔΞ—
probe ΔΞ′—
probe ΔΞ″—
status—
SSZ-METRIC_COMPLETE · canonical pure metric
Metric, inverse and local-frame explorer
This reconstruction follows the repository’s primary chain \(\Xi\rightarrow D,s\rightarrow g_{\mu\nu}\), rather than plotting two detached coefficients. Compare the diagonal static form with the repository’s non-diagonal flow form; inspect algebraic identities, signature, determinant and local radial null slopes at the same event.
Ξ / regime—
D · s—
gtt/c²—
grr—
gtr/c—
signature—
det(g)/(c²r⁴sin²θ)—
radial dr/(c dt)—
Diagonal form
\[\frac{g_{\mu\nu}}{\{c^2,1,r^2,r^2\sin^2\theta\}}=\operatorname{diag}(-D^2,s^2,1,1),\quad Ds=1\]
The exact repository identity gives \(\det g=-c^2r^4\sin^2\theta\) away from spherical-coordinate axes.
Flow form
\[ds^2=-c^2(1-\beta^2)dt^2+2\beta c\,dt\,dr+dr^2+r^2d\Omega^2\]
This is a coordinate representation provided by the repository. A nonzero cross term is not an additional force or a rotating solution.
P0 boundary
At \(r\to0^+\), the diagonal coefficients tend to finite values \(D^2\to1/4\) and \(s^2\to4\), but \(R\sim3/(2r^2)\) and \(K\sim9/(4r^4)\). Component finiteness, determinant identities and Lorentzian signature do not establish a regular areal centre.
Static-clock comparison
Two clocks at different radii
Coordinate time is shared by the diagram; each static clock accumulates its own proper time dτ=D(r)dt. This animation distinguishes a comparison of clocks from a claim that photons locally slow down.
D inner—
D outer—
dτi/dτo—
redshift z—
Static redshift teaching model
Spectral-line shift explorer
Choose an emitted wavelength and two static radii. The line moves according to 1+z=D(ro)/D(re). Doppler motion, plasma and radiative transfer are deliberately not hidden inside the result.
z—
observed λ—
Coordinate diagnostic
Radial null-path integration
For ds²=0 and dΩ=0, dr/dt=±cD²(r). The animation integrates the coordinate slope while reiterating that every local freely falling observer measures light at c.
coordinate travel time—
flat reference—
Weak-field reference
Light-deflection geometry
This module visualises the leading PPN expression α=(1+γ)rs/b with γ=1. It is an intentionally scaled diagram; screen curvature is not a ray-traced strong-field prediction.
α = 2rs/b = —
For b≫rs, increasing b reduces the leading deflection. Near the compact object, the weak-field approximation is not sufficient.
Metric-derived diagnostic
Null and timelike orbit diagnostics
For the declared static spherical ansatz, the circular-null diagnostic is \(A(r)/r^2\) with \(A=D^2\). The same shared metric engine now derives the critical-impact proxy and searches the circular-timelike \(L^2\) curve for a stationary minimum; none of these radii is hard-coded.
SSZ null stationary point—
critical impact proxy—
timelike L² minimum—
Schwarzschild referencerph=1.5 rₛ
A bridge-localised stationary point may be sensitive to the matching prescription. Accessibility, stability, a complete rotating geometry and radiative transfer are still required before calling a feature an observed photon ring, ISCO or shadow.
Gaia-derived repository catalogue
Interactive SSZ Starmaps explorer
A faithful static-browser adaptation of the repository’s coordinate, filtering and comparison workflow. It uses 3,000 real catalogue stars with ICRS position, parallax distance, magnitude, colour, temperature and proper motion. The legacy constant Ξ/D columns are deliberately ignored because they conflict with the current P0 piecewise model.
catalogueloading…
visible—
projection—
selectionclick a star
Drag to rotate or pan; wheel/pinch to zoom; arrow keys rotate the focused canvas. The SSZ comparison belongs to radial metric diagnostics, not to an invented deformation of measured sky angles.
galactic-year · source-level consistency audit
Solar Galactic Year: measurements, dynamics and clock rate
Follow the full inference chain instead of collapsing unlike quantities into one “orbit model”. The directly constrained angular motion, an adopted circular speed, the equivalent enclosed mass, the inadequate Sgr A* point-mass countermodel and the SSZ weak-field clock factor answer different questions.
Illustrative drawing controls
The ×10 default makes the vertical oscillation visible; the state table retains the physical value.
kinematic period 2πR₀/Θ₀—
angular period from μ—
μ-derived total transverse speed—
equivalent enclosed mass—
Sgr A* point-mass period—
weak-field Ξ / D—
SSZ clock increment per orbit—
declared legacy period230 Myr
Initialising local WebGL renderer…
Accessible 2D fallback and print view
| Time | Phase | R | z | Speed | Ξ | D | Accumulated clock difference | Evidence role |
|---|---|---|---|---|---|---|---|---|
| Initialising… | ||||||||
Two observational routes
\[T_{\rm kin}=\frac{2\pi R_0}{\Theta_0},\qquad T_\mu=\frac{2\pi}{|\mu_l|}\]
The first route combines radius and adopted circular speed. The second reads the reflex angular motion of Sgr A*. They need not be identical because Θ₀, Solar peculiar motion and the angular observable are distinct inputs.
Dynamical consistency
\[M(<R_0)=\frac{\Theta_0^2R_0}{G},\qquad T_{\rm BH}=2\pi\sqrt{\frac{R_0^3}{GM_{\rm BH}}}\]
The equivalent enclosed mass encodes the extended Galactic potential. Sgr A* alone predicts about 1.49 km/s and a period of many billions of years, so it is a counterexample—not a Solar-orbit model.
Separate SSZ clock layer
\[\Xi=\frac{r_s}{2R_0},\quad D=(1+\Xi)^{-1},\quad \Delta T=T_{\rm kin}(D^{-1}-1)\]
The portal reports the weak-field proper-time increment in years per orbit. It does not multiply a point-mass trajectory into agreement with Galactic data.
| Quantity | Repository source | Role | Portal treatment |
|---|---|---|---|
| R₀ = 8.122 ± 0.031 kpc | GRAVITY Collaboration (2019) | Geometric distance scale | Slider and propagated uncertainty |
| Θ₀ = 240 ± 8 km/s | Reid et al. (2014) capture | Adopted circular speed | Kinematic period and enclosed mass |
| |μl| = 6.411 mas yr⁻¹ | Reid & Brunthaler (2020) capture | Reflex angular motion | Independent angular-period route |
| MBH = 4.3×10⁶ M☉ | Repository constant | Central black-hole mass | Deliberately inadequate point-mass countercheck |
| e = 0.07; z-period = 70 Myr | Repository illustration parameters | Drawing only | Not presented as a fitted Galactic orbit |
Resolved audit finding: the generated JSON’s 1.492 km/s follows from applying \(v=\sqrt{GM/R}\) to Sgr A* alone; the README’s 247.8 km/s and 230 Myr use a Galactic-scale orbit. They are not competing SSZ predictions. The interactive comparison makes that category error visible and links to the source repository.
chord-partition · 103-test captured suite
Chord-partition eigenmodes and φ convergence
Explore the repository’s parametric curve \(C(t;p,k,R)=(R\cos pt,R\sin kt)\). Integer winding pairs close exactly; consecutive Fibonacci pairs make \(k/p\) approach φ. The geometry visualises the tested construction without claiming that the curve derives spacetime microphysics.
k/p—
|k/p−φ|—
gcd / lcm—
repository eigenmode n—
Curve
\[C(t;p,k,R)=\bigl(R\cos(pt),R\sin(kt)\bigr)\]
Mode index
\[n=\frac{\operatorname{lcm}(p,k)}{\gcd(p,k)}\]
Evidence boundary
The suite tests closure, derivatives, perimeter scaling, numerical stability and φ convergence. Those mathematical tests do not establish a physical segmentation mechanism.
Source: chord-partition repository. The current all-tests capture records 103 passing outcomes for this repository.
ssz-schumann · cavity model
Schumann mode and common-shift explorer
Calculate the repository’s baseline Earth–ionosphere cavity modes and apply a uniform relative frequency shift. A common shift across modes is a test signature; it is not uniquely attributable to SSZ until ionospheric height, conductivity, solar and geomagnetic effects are modelled.
mode 1 baseline—
mode 1 shifted—
relative shift all modes—
raw data statusexternal download
Baseline
\[f_n=\eta\frac{c}{2\pi R}\sqrt{n(n+1)}\]
Common-shift hypothesis
\[\frac{\Delta f_n}{f_n}\approx-\delta_{\rm seg}(t)\quad\text{for every }n\]
Evidence boundary
Synthetic recovery tests validate the pipeline’s ability to recover an injected common signal. Real-data preference additionally needs the licensed external datasets and environmental covariates.
Source: ssz-schumann repository. Raw measurements are not embedded in this portal; the source repository documents their external provenance.
Standard rotating-loop reference
Counter-propagating signals on a rotating loop
The detector moves while two signals traverse opposite directions. Their reunion times differ. The leading standard expression is Δt≈4AΩ/c²; the animation uses scaled units for visibility.
Δt = — s
P0 asymptotic diagnostic
Approaching the areal centre
On logarithmic axes, the canonical diagonal continuation has R∼3/(2r²) and K∼9/(4r⁴). The steeper K line exposes why finite A→1/4 does not imply central regularity.
Interpretation: these are stated leading asymptotics, not a numerical solution at r=0. Both invariants diverge as the radius tends to zero.