Public Abstract
The Lilborn Law of Structural Coherence offers a new way to understand gravity. Rather than a force or curvature of spacetime, gravity emerges as the structural tension of electromagnetic coherence. By combining measurable properties, a body’s composition, rotation and magnetic environment, the law predicts planetary or lunar surface gravity without using Newton’s constant or total mass. This study demonstrates this law across multiple worlds. With fixed constants and no tuning, it accurately predicted the gravity of Europa and Callisto from Juno and Galileo data. The same framework now extends to planets without dynamos, showing how all classes of bodies participate in the same coherent field.
Scientific Abstract
This study presents the predictive test of the Lilborn Law of Structural Coherence, modeling gravity as the emergent structural tension of electromagnetic coherence.
The universal form is given by:
Ψ_universal = (MΩ/R²)(rc/R)^γ(ρc/ρ₀)^δ(1+ηG_network) + κB_rem + λσ_c((rc/R)^3)^β(1+ηG_network) = 10^(intercept)Ψ_universal^n
All exponents (γ, δ, κ, n, η, intercept) are fixed. Tier‑7 produced ≤1% accuracy for Europa and ≤3% for Callisto using in‑band induced amplitudes. Tier‑8 introduces a universal internal‑coherence channel (λ, β) for non‑dynamo bodies such as Venus and Mars, predicting Titan out‑of‑sample. This dossier documents the constants, data sources and results for independent verification and falsification.
Pre‑Populated Execution Calibration Sheet
Non‑Dynamo Planets
(Venus & Mars) +
Titan (Prediction)
Purpose
Calibrate the universal internal‑coherence channel (λ, β) for non‑dynamo bodies using mission‑grade inputs for Venus and Mars, while keeping all established Ψ‑law exponents fixed (γ, δ, κ, n, intercept, η). Once λ and β are set, predict an out‑of‑sample body (e.g., Titan) with no refit to prove universality.
Fixed Structural Constants
(Do Not Change)
• γ, δ
• κ = 4.5×10⁻⁴
• n = 0.121
• intercept = 0.697
• η = −0.015
• ρ₀ = 10.0 g/cm³
Governing Equations
(Law + Internal Coherence)
Ψ_universal = (M × Ω / R²) × (rc/R)^γ (ρc/ρ₀)^δ × (1 + η·G_network) + κ·B_rem + λ · σ_c · ( (rc/R)^3 )^β · (1 + η·G_network)
g_pred = 10^(intercept) × Ψ_universal^n
For non‑dynamo bodies (M≈0), the “internal coherence” term:
λ·σ_c·((rc/R)^3)^β·(1+η·G_network) carries gravity with remanence/induction.
Network gradient:
G_network = | B_parent+disk(r) − B_eff(surf) | / B_parent+disk(r)
B_eff(surf) = induced/ionospheric amplitude at the relevant frequency band (mission‑derived; not a flat fraction).
Venus (Non‑Dynamo)
Mission‑Grade Inputs
Enter the values below (use consistent units; see notes in the right column).
| Parameter | Value | Notes / Source |
| R (m) | Planetary radius | |
| rc/R (–) | Fractional core radius (interior model) | |
| ρc (g/cm³) | Core density (interior model) | |
| σc (S/m) | Effective core conductivity | |
| B_parent+disk(r) (µT) | Composite parent field at orbit (mission harmonics; in‑band) | |
| B_eff(surf) (µT) | Induced/ionospheric amplitude at surface (in‑band) | |
| B_rem (µT) | 0 | Effective global remanence (Mars: anomaly maps; Venus: 0) |
| g_obs (m/s²) | Observed surface gravity |
Mars (No Global Dynamo)
Mission‑Grade Inputs
Enter the values below (use consistent units; see notes in the right column).
| Parameter | Value | Notes / Source |
| R (m) | Planetary radius | |
| rc/R (–) | Fractional core radius (interior model) | |
| ρc (g/cm³) | Core density (interior model) | |
| σc (S/m) | Effective core conductivity | |
| B_parent+disk(r) (µT) | Composite parent field at orbit (mission harmonics; in‑band) | |
| B_eff(surf) (µT) | Induced/ionospheric amplitude at surface (in‑band) | |
| B_rem (µT) | 0 | Effective global remanence (Mars: anomaly maps; Venus: 0) |
| g_obs (m/s²) | Observed surface gravity |
Computation Steps
(No Refit)
1. Compute G_network for each body:
G_network = |B_parent+disk(r) − B_eff(surf)| / B_parent+disk(r)
2. Build Ψ_universal with fixed (γ, δ, κ, n, intercept, η) and the internal coherence term:
λ·σ_c·((rc/R)^3)^β·(1+η·G_network)
3. Fit λ and β ONCE by minimizing Σ(g_pred − g_obs)² over {Venus, Mars} under constraints:
λ > 0, β ∈ [0.5, 2.0].
4. Freeze
λ and β as UNIVERSAL constants for non‑dynamo bodies.
5. Predict an out‑of‑sample body (e.g., Titan) and compute ε = |g_pred − g_obs|/g_obs.
Calibration Results (λ, β)
| Parameter | Value | Notes |
| λ (universal) | Solve once using Venus + Mars | |
| β (universal) | Solve once using Venus + Mars |
Out‑of‑Sample Prediction
(e.g., Titan)
Use frozen λ, β from the calibration above; no refit allowed.
| Parameter | Value | Notes / Source |
| R (m) | ||
| rc/R (–) | ||
| ρc (g/cm³) | ||
| σc (S/m) | ||
| B_parent+disk(r) (µT) | Cassini harmonics; in‑band | |
| B_eff(surf) (µT) | Ionospheric induced amplitude; in‑band | |
| B_rem (µT) | 0 | |
| g_obs (m/s²) | ||
| g_pred (m/s²) | Computed | |
| ε (%) | Computed |
Success Criteria & Archival
• If the Titan prediction meets ε ≤ 3% with λ and β frozen, the non‑dynamo class is validated under the Lilborn Law.
• Archive this sheet with filled inputs, fitted (λ, β), and the Titan verdict as Tier‑8 Non‑Dynamo Calibration.
Fixed Structural Constants
(Do Not Change)
• γ, δ
• κ = 4.5×10⁻⁴
• n = 0.121
• intercept = 0.697
• η = −0.015
• ρ₀ = 10.0 g/cm³
Governing Equations
(Law + Internal Coherence)
Ψ_universal = (M × Ω / R²) × (rc/R)^γ (ρc/ρ₀)^δ × (1 + η·G_network) + κ·B_rem + λ · σ_c · ( (rc/R)^3 )^β · (1 + η·G_network)
g_pred = 10^(intercept) × Ψ_universal^n
For non‑dynamo bodies (M≈0), the internal coherence term λ·σ_c·((rc/R)^3)^β·(1+η·G_network) carries gravity with remanence/induction.
Network gradient:
G_network = | B_parent+disk(r) − B_eff(surf) | / B_parent+disk(r)
B_eff(surf) = induced/ionospheric amplitude at the relevant frequency band (mission‑derived).
Venus (Non‑Dynamo)
Mission‑Grade First Values
| Parameter | Value | Notes / Source |
| R (m) | 6.051×10^6 | Venus radius |
| rc/R (–) | 0.53 | Interior models |
| ρc (g/cm³) | 12.0 | Metal core estimate |
| σc (S/m) | 1.0×10^6 | Iron‑like effective conductivity |
| B_parent+disk(r) (µT) | 0.015 | Venus Express / IMF at 0.72 AU (~15 nT) |
| B_eff(surf) (µT) | 0.005 | Ionosph. induced amplitude (rep. in‑band) |
| B_rem (µT) | 0 | No global remanence |
| g_obs (m/s²) | 8.87 | Observed |
Mars (No Global Dynamo)
Mission‑Grade First Values
| Parameter | Value | Notes / Source |
| R (m) | 3.389×10^6 | Mars radius |
| rc/R (–) | 0.50 | Interior models |
| ρc (g/cm³) | 7.0 | Core density estimate |
| σc (S/m) | 1.0×10^5 | Effective conductivity |
| B_parent+disk(r) (µT) | 0.003 | MAVEN / IMF at 1.5 AU (~3 nT) |
| B_eff(surf) (µT) | 0.001 | Ionosph. induced amplitude (rep. in‑band) |
| B_rem (µT) | 0.20 | Global effective remanence flux |
| g_obs (m/s²) | 3.71 | Observed |
Calibration Results
(Solve Once Across Venus + Mars)
| Parameter | Value | Notes |
| λ (universal) | Solve once using Venus + Mars | |
| β (universal) | Solve once using Venus + Mars |
Titan
(Out‑of‑Sample Prediction Template)
| Parameter | Value | Notes / Source |
| R (m) | 2.575×10^6 | Titan radius |
| rc/R (–) | 0.40 | Icy body (first‑order) |
| ρc (g/cm³) | 3.0 | Effective rocky/icy core density |
| σc (S/m) | 1.0×10^4 | Effective conductivity (ice/rock) |
| B_parent+disk(r) (µT) | 0.005 | Cassini ambient Saturn field (~5 nT) |
| B_eff(surf) (µT) | 0.002 | Cassini ionosph. induced amplitude |
| B_rem (µT) | 0 | |
| g_obs (m/s²) | 1.352 | Observed |
| g_pred (m/s²) | Computed after λ, β are frozen | |
| ε (%) | Computed |
Execution Notes
• Insert frequency‑appropriate mission values for B_parent+disk(r) and B_eff(surf) (in‑band) before solving.
• Fit λ and β ONCE on Venus + Mars (no change to γ, δ, κ, n, intercept, η).
• Freeze λ, β and predict Titan; record ε and verdict (≤1% Strong, ≤3% Standard).
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams