First-Run Test Plan
Simulation Inputs & Tolerances
Idle — awaiting run
Tips: start with small kp, kd. Increase slowly after damping appears. Keep ε values realistic.
Equations
Master System & Control Law
Linearized Einstein equation
\[ \square\,\bar{h}_{\mu\nu} = -16\pi G\,S_{\mu\nu},\quad S_{\mu\nu}=\langle \hat T_{\mu\nu}\rangle + T_{\mu\nu}^{\text{class}} + F^{\text{CST}}_{\mu\nu} \] Quantum single-mode Lindblad
\[ \dot{\hat\rho} = -\frac{i}{\hbar}\left[\hbar\omega\big(1+\gamma\,\Phi[h]\big)a^\dagger a,\hat\rho\right] + \kappa \mathcal D[a]\hat\rho + \gamma_\phi \mathcal D[a^\dagger a]\hat\rho + \mathcal L_{\text{CST}} \]
\[ \square\,\bar{h}_{\mu\nu} = -16\pi G\,S_{\mu\nu},\quad S_{\mu\nu}=\langle \hat T_{\mu\nu}\rangle + T_{\mu\nu}^{\text{class}} + F^{\text{CST}}_{\mu\nu} \] Quantum single-mode Lindblad
\[ \dot{\hat\rho} = -\frac{i}{\hbar}\left[\hbar\omega\big(1+\gamma\,\Phi[h]\big)a^\dagger a,\hat\rho\right] + \kappa \mathcal D[a]\hat\rho + \gamma_\phi \mathcal D[a^\dagger a]\hat\rho + \mathcal L_{\text{CST}} \]
CST feedback (PD)
\[ F^{\text{CST}}_{\mu\nu} = -k_p\,\Delta h_{\mu\nu} - k_d\,\Delta \dot h_{\mu\nu},\quad \Delta h_{\mu\nu} = h_{\mu\nu} - h^{\text{target}}_{\mu\nu}(t_{\text{CST}}) \]
Renormalized vacuum
\[ T_{\mu\nu}^{(\text{vac})} = \langle 0|\hat T_{\mu\nu}|0\rangle - \langle 0|\hat T_{\mu\nu}|0\rangle_{\text{flat}} \]
\[ F^{\text{CST}}_{\mu\nu} = -k_p\,\Delta h_{\mu\nu} - k_d\,\Delta \dot h_{\mu\nu},\quad \Delta h_{\mu\nu} = h_{\mu\nu} - h^{\text{target}}_{\mu\nu}(t_{\text{CST}}) \]
Renormalized vacuum
\[ T_{\mu\nu}^{(\text{vac})} = \langle 0|\hat T_{\mu\nu}|0\rangle - \langle 0|\hat T_{\mu\nu}|0\rangle_{\text{flat}} \]
Fix Lorenz gauge & monitor constraints
Avoid hidden energy injection
Tune controller gradually
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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