First-Run Test Plan
Simulation Inputs & Tolerances
Idle — awaiting run
All values are pre-filled with a consistent first run. After everything is green you can tweak them.
Equations + CST Timing Layer
Master System, Control Law & Cosmic-Time Corrections
Einstein–CST master equation (linearized)
\[ \Box\,\bar{h}_{\mu\nu} = -16\pi G\, \Big[ S_{\mu\nu}^{\text{local}} + S_{\mu\nu}^{\text{CST}} \!\left( \gamma_{\text{SR}}, \Gamma_{\text{GR}}, \Delta t_{\text{sid}}, t_{\text{light}}, \mathbf{n}(\alpha,\delta) \right) \Big] \] with \[ S_{\mu\nu}^{\text{local}}=\langle \hat T_{\mu\nu}\rangle + T_{\mu\nu}^{\text{class}}, \qquad S_{\mu\nu}^{\text{CST}} = F^{\text{CST}}_{\mu\nu} + T_{\mu\nu}^{(\text{vac})}. \] Quantum single-mode Lindblad (toy)
\[ \dot{\hat\rho} = -\frac{i}{\hbar} \Big[ \hbar\omega\big(1+\gamma\,\Phi[h]\big)a^\dagger a,\hat\rho \Big] + \kappa \mathcal D[a]\hat\rho + \gamma_\phi \mathcal D[a^\dagger a]\hat\rho + \mathcal L_{\text{CST}}[\gamma_{\text{SR}},\Gamma_{\text{GR}},t_{\text{light}}]. \]
\[ \Box\,\bar{h}_{\mu\nu} = -16\pi G\, \Big[ S_{\mu\nu}^{\text{local}} + S_{\mu\nu}^{\text{CST}} \!\left( \gamma_{\text{SR}}, \Gamma_{\text{GR}}, \Delta t_{\text{sid}}, t_{\text{light}}, \mathbf{n}(\alpha,\delta) \right) \Big] \] with \[ S_{\mu\nu}^{\text{local}}=\langle \hat T_{\mu\nu}\rangle + T_{\mu\nu}^{\text{class}}, \qquad S_{\mu\nu}^{\text{CST}} = F^{\text{CST}}_{\mu\nu} + T_{\mu\nu}^{(\text{vac})}. \] Quantum single-mode Lindblad (toy)
\[ \dot{\hat\rho} = -\frac{i}{\hbar} \Big[ \hbar\omega\big(1+\gamma\,\Phi[h]\big)a^\dagger a,\hat\rho \Big] + \kappa \mathcal D[a]\hat\rho + \gamma_\phi \mathcal D[a^\dagger a]\hat\rho + \mathcal L_{\text{CST}}[\gamma_{\text{SR}},\Gamma_{\text{GR}},t_{\text{light}}]. \]
CST feedback (PD control on geometry)
\[ F^{\text{CST}}_{\mu\nu} = -k_p\,\Delta h_{\mu\nu} - k_d\,\Delta \dot h_{\mu\nu}, \qquad \Delta h_{\mu\nu} = h_{\mu\nu} - h^{\text{target}}_{\mu\nu}(t_{\text{CST}}). \]
Renormalized vacuum piece
\[ T_{\mu\nu}^{(\text{vac})} = \langle 0|\hat T_{\mu\nu}|0\rangle - \langle 0|\hat T_{\mu\nu}|0\rangle_{\text{flat}}. \] CST timing & sky layer (cosmic clock)
Special relativity: \[ \gamma_{\text{SR}}(v) = \frac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}, \qquad t'_{\text{SR}} = t_{\text{CST}}\sqrt{1-\dfrac{v^2}{c^2}}. \] Gravity well: \[ \Gamma_{\text{GR}}(r) = \sqrt{1-\dfrac{2GM}{r c^2}}, \qquad t'_{\text{GR}} = t_{\text{CST}}\sqrt{1-\dfrac{2GM}{r c^2}}. \] Sidereal drift: \[ \Delta t_{\text{sid}} = N_{\text{days}}\big(T_{\odot} - T_{\star}\big), \quad T_{\odot}\approx24\text{ h},\ T_{\star}\approx23^{\text h}56^{\text m}4.1^{\text s}. \] Sky direction: \[ \mathbf{n}(\alpha,\delta) = \big(\cos\delta\cos\alpha,\ \cos\delta\sin\alpha,\ \sin\delta\big). \] Light-time: \[ t_{\text{light}} = \frac{d}{c} \;\approx\;d_{\text{ly}}\ \text{years}. \]
\[ F^{\text{CST}}_{\mu\nu} = -k_p\,\Delta h_{\mu\nu} - k_d\,\Delta \dot h_{\mu\nu}, \qquad \Delta h_{\mu\nu} = h_{\mu\nu} - h^{\text{target}}_{\mu\nu}(t_{\text{CST}}). \]
Renormalized vacuum piece
\[ T_{\mu\nu}^{(\text{vac})} = \langle 0|\hat T_{\mu\nu}|0\rangle - \langle 0|\hat T_{\mu\nu}|0\rangle_{\text{flat}}. \] CST timing & sky layer (cosmic clock)
Special relativity: \[ \gamma_{\text{SR}}(v) = \frac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}, \qquad t'_{\text{SR}} = t_{\text{CST}}\sqrt{1-\dfrac{v^2}{c^2}}. \] Gravity well: \[ \Gamma_{\text{GR}}(r) = \sqrt{1-\dfrac{2GM}{r c^2}}, \qquad t'_{\text{GR}} = t_{\text{CST}}\sqrt{1-\dfrac{2GM}{r c^2}}. \] Sidereal drift: \[ \Delta t_{\text{sid}} = N_{\text{days}}\big(T_{\odot} - T_{\star}\big), \quad T_{\odot}\approx24\text{ h},\ T_{\star}\approx23^{\text h}56^{\text m}4.1^{\text s}. \] Sky direction: \[ \mathbf{n}(\alpha,\delta) = \big(\cos\delta\cos\alpha,\ \cos\delta\sin\alpha,\ \sin\delta\big). \] Light-time: \[ t_{\text{light}} = \frac{d}{c} \;\approx\;d_{\text{ly}}\ \text{years}. \]
Relativistic energy & rockets (link to 0.99c)
\[ E_{\text{tot}} = \gamma_{\text{SR}}(v)\,m c^2, \qquad K(v) = \big(\gamma_{\text{SR}}(v)-1\big)m c^2. \] At \(v = 0.99\,c\), \(\gamma_{\text{SR}}\approx 7\), so \(K\approx 6 m c^2\). In a future CST–guided rocket, this dashboard would track how close you can safely push the ship toward \(0.99c\) while keeping the Einstein side self-consistent.
\[ E_{\text{tot}} = \gamma_{\text{SR}}(v)\,m c^2, \qquad K(v) = \big(\gamma_{\text{SR}}(v)-1\big)m c^2. \] At \(v = 0.99\,c\), \(\gamma_{\text{SR}}\approx 7\), so \(K\approx 6 m c^2\). In a future CST–guided rocket, this dashboard would track how close you can safely push the ship toward \(0.99c\) while keeping the Einstein side self-consistent.
Residuals are driven below tolerance so all checks go green
SR/GR timing feeds into \(S_{\mu\nu}^{\text{CST}}\) for realistic clocks
Panels glow / animate when the system is “live”
Run Log
Residuals vs. Time (Convergence)
Self-consistency: —
Stability: —
Physicality: —
Field Plots
hμν Snapshots & Spectral Content
Snapshot: pre-control
Snapshot: post-control
Spectrum: pre
Spectrum: post
Energy
Input Power vs. Curvature Change (Efficiency)
Efficiency: —
Total power: —
Validation
Observable Checks (Pass/Fail)
| Test | Target | Measured | Status |
|---|---|---|---|
| Solar-system orbits (fractional err/orbit) | < 1e-8 | — | — |
| Cosmology (recover Friedmann in homogeneous limit) | match | — | — |
| Lab EM cavity (Δf vs synthetic h) | linear | — | — |
Checkoff
Six Categories — Status
Geometry
Specify \(g_{\mu\nu}(x,t;\theta)\)
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Specify \(g_{\mu\nu}(x,t;\theta)\)
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Source
Closed forms for \(T_{\mu\nu}^{\text{matter}},T_{\mu\nu}^{\text{EM}},T_{\mu\nu}^{\text{plasma}},T_{\mu\nu}^{\text{vac}}\)
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Closed forms for \(T_{\mu\nu}^{\text{matter}},T_{\mu\nu}^{\text{EM}},T_{\mu\nu}^{\text{plasma}},T_{\mu\nu}^{\text{vac}}\)
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Boundaries
Initial & asymptotic conditions
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Initial & asymptotic conditions
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Computation
Tensor integrator / solver
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Tensor integrator / solver
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Feedback
CST law \(F_{\mu\nu}=K_{\mu\nu}\Delta h_{\mu\nu}+D_{\mu\nu}\Delta\dot h_{\mu\nu}\)
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CST law \(F_{\mu\nu}=K_{\mu\nu}\Delta h_{\mu\nu}+D_{\mu\nu}\Delta\dot h_{\mu\nu}\)
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Validation
Observable tests
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Observable tests
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