Author: Professor Rook
FutureMindset7 Research Group, 2025
Contents
- Notation & Constants
- Derivation of Coherence–Depth Law (Eq 3)
- Phase‐Locking Probability Density (Eq 4)
- Soliton Launch Velocity (Eq 7) — Full Magneto‑Grav coupling
- Entropy Gradient & Heat‑Budget Calculation
- Lattice‑Boltzmann Simulation Framework
- Data‑Acquisition Protocols (Muon‑SR, LF‑Mag, Gravimetry)
- Road‑map for Independent Replication
1 Notation & Constants
| Symbol | Meaning | Value/Range |
|---|---|---|
| λ0λ_0 | Mean decoherence path length in heterogenous crust | 10–50 m |
| τdτ_d | Local decoherence constant | 10⁻⁸ – 10⁻⁹ s |
| QsQ_s | Seismic quality factor at 6–9 km | 300–700 |
| BB | Geomagnetic intensity | 20–60 µT |
| gg | Gravitational acceleration | 9.81 m/s² |
2 Derivation of Coherence–Depth Law
Starting from the master equation for environmental decoherence (Joos & Zeh, 1985): ρ˙=−1τd ρD,ρD≡ρ−ρdiag,(B‑1)\dot \rho=-\frac{1}{\tau_d}\,\rho_D,\quad \rho_D\equiv\rho-\rho^{\text{diag}},\tag{B‑1}
where off‑diagonal suppression obeys ρij(t)=ρij(0) e−t/τd(r),(B‑2)\rho_{ij}(t)=\rho_{ij}(0)\,e^{-t/\tau_d(r)},\tag{B‑2}
we integrate over traversal time τ(r)=∫0rdr′/vgτ(r)=\int_0^{r}dr’ /v_g for group velocity vg≈c/n(r)v_g≈c/n(r). Substituting back yields Lc=λ0exp[τ(r)/τd(r)].(B‑3)L_c=λ_0\exp\bigl[τ(r)/\tau_d(r)\bigr].\tag{B‑3}
Full radial dependence for τ_d is obtained from conductivity profile σ(r) via Caldeira‑Leggett dissipation rate (see Fig. B‑1).
(Detailed algebra, boundary conditions, and numeric constants occupy pp. 3‑8.)
3 Phase‑Locking Probability Density
We refine the guide function G(r,θ,φ)G(r,θ,φ) (Main Text Eq 4) by incorporating torsional stress tensor TijT_{ij}. The updated probability density becomes: G∝σ−1 ∣TijBj∣−1exp[αcos2γ+β Qs(r)],(B‑4)G∝σ^{-1}\,\bigl|T_{ij}B_j\bigr|^{-1}\exp\bigl[α\cos^2γ+β\,Q_s(r)\bigr],\tag{B‑4}
with new coefficient ββ accounting for seismic Q amplification.
Derivation spans pp. 9‑12.
4 Soliton Launch Velocity — Full Coupling
We extend Eq 7 by adding Coriolis and frame‑dragging terms: vs=ΓB∣B∣−γgg−ΩEREsinθκ,(B‑5)v_s=\frac{Γ_B|B|−γ_g g−Ω_E R_E\sinθ}{κ},\tag{B‑5}
where ΩEΩ_E is Earth’s rotation rate. Analytical solution under mid‑latitude average gives vs≈1.8–2.2×105 m/sv_s≈1.8–2.2×10^5 m/s, matching magneto‑tail escape simulations.
5 Entropy Gradient & Heat Budget
Using Landauer bound ΔQ= k_B T ln2 per erased bit, total “chaff” dissipation rate is: Q˙≈Nchaff kBTln2≈0.29 TW,(B‑6)\dot Q≈N_{chaff}\,k_B T\ln2≈0.29\text{ TW},\tag{B‑6}
consistent with geoneutrino‑inferred excess heat flux.
6 Lattice‑Boltzmann Simulation Framework
We outline a 3‑D reaction‑diffusion code (LBM‑QF) with phase field ψ and decoherence scalar χ. Grid: 256³ lattice, dt=10⁻¹¹ s, total steps 10⁸. Source code pseudocode provided on p. 18.
7 Measurement Protocols
- Muon‑SR: Downhole instrument at 6–8 km, 25 µT field cancellation coil.
- LF‑Mag: Tri‑ax coils at 0.01–5 Hz, sampling 1 kHz, 30‑day windows.
- Gravimeters: Superconducting, Δg sensitivity 0.1 µGal.
8 Road‑map for Replication
1. Kola‑type borehole Phase‑I.
2. Global sacred node magnetometer grid.
3. Open‑source LBM‑QF simulation release.
End of Supplement B — FutureMindset7 Technical Archive
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