This page aggregates reproducible numerical checks of WILL predictions. Each item links to a runnable notebook and, where available, an interactive lab with a clear falsifiability clause.
🧪 Interactive Labs
1) Galactic Dynamics Lab — SPARC rotation curves
Headline metric: median RMSE ≈ 20 km/s over ~175 galaxies.
Try it: Open the Galactic Dynamics toolFalsification Clause
If, with fixed data-selection rules on the SPARC dataset, the median RMSE exceeds 50 km/s for ≥ 25% of the sample, the prediction is considered falsified.
2) Cosmology Lab — All cosmology out of one scale and one dynamic input
Headline metric: \(\Omega_\Lambda = 2/3\), \(\Omega_m = 1/3\) (no free parameters).
Try it: Open the Cosmology toolFalsification Clause
If, for a fixed \(H_0\), the predicted values for \(\{\Omega_\Lambda, \Omega_m, t_0\}\) systematically fall outside consolidated observational bounds, the prediction is considered falsified.
3) Lab — Relativistic Time Offset (Geometric Projections)
Primary calculation: the daily relativistic time offset between a surface observer and an orbiting body. Secondary check: Classical energy consistency. Object-agnostic: applies to any circular orbit.
Presets:
Δt per day (μs)
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Geometric Energy (ΔE)
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Normalized Physical Energy
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Energy Ratio
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Show Calculation Breakdown
1) Define projections
Gravitational projection at the surface \(A\): \( \kappa_A^2 = \dfrac{2GM}{R_A c^2} \).
Gravitational projection at the orbit \(B\) (radius \( r \)): \( \kappa_B^2 = \dfrac{2GM}{r c^2} \).
Kinematic projection for a circular orbit at \(B\): from \( v^2 = GM/r \) we get \( \beta_B^2 = \dfrac{v^2}{c^2} = \dfrac{GM}{r c^2} \). On the surface we take \( \beta_A^2 = 0 \).
2) Combine into \(Q^2\) and \(Q_t\)
\( Q^2 = \kappa^2 + \beta^2 \). Thus \( Q_A^2 = \kappa_A^2 + \beta_A^2 \) and \( Q_B^2 = \kappa_B^2 + \beta_B^2 \).
The time-axis complement is \( Q_t = \sqrt{1 - Q^2} \).
3) Time offset (core result)
Daily clock difference in microseconds per day: \( \Delta t_{B\to A}[\mu s/\text{day}] = (1 - \frac{Q_{tA}}{Q_{tB}})\times 86400\times 10^6 \).
4) Classical energy consistency
Fix the potential zero at the surface \(R_A\). For a circular orbit at radius \( r \):
Potential \( E_p = \big(-\dfrac{GMm}{r}\big) - \big(-\dfrac{GMm}{R_A}\big) \).
Kinetic \( E_k = \tfrac{1}{2} m v^2 \) with \( v^2 = GM/r \).
Total \( E_{tot} = E_p + E_k \). Normalize by \( mc^2 \) to get \( E_{tot}/(mc^2) \).
Geometric energy (mass-independent):
\( \Delta E_{A\to B} = \tfrac{1}{2}\big[(\kappa_A^2-\kappa_B^2) + (\beta_B^2-\beta_A^2)\big] \).
Consistency statement for the closed surface–orbit subsystem:
\( \dfrac{E_{tot}/(mc^2)}{\Delta E_{A\to B}} = 1 \).
📄 Reproducible Notebooks
D) Absolute Scale Cosmology
Cosmological scale metric predictions, tests, and demonstrations
Notebook