THE ANCHOR NUMBERS

THE ANCHOR NUMBERS 1. Universal Physical Anchors (Observational) text c_physical = 299792458.0 # Speed of light [m/s] T_cmb = 2.72548 # CMB temperature [K] G = 6.67430e-11 # Gravitational constant [m³/kg/s²] h = 6.62607015e-34 # Planck constant [J·s] k_B = 1.380649e-23 # Boltzmann constant [J/K] H0 = 67.4 # Hubble constant [km/s/Mpc] 2. Normalized Numerical Anchors (Solver Baseline) text C_AXIS = 0.5000 # Normalized causality limit (v/c) PI_MAX = 5.9259 # Thermal vacuum anchor (Π saturation) KAPPA = 0.3000 # Topological coupling (r=0 saturation) 3. Derived Lattice Anchors (From Solver Setup) text L_DOMAIN = 25.6 # Domain size [code units] N_BASE = 64 # Base grid resolution DX_BASE = L_DOMAIN / N_BASE # 25.6 / 64 = 0.4 [code units] DT_BASE = 5e-6 # Base timestep [code units] 4. Constitutive Map Anchors text ANCHOR = 0.0 # Ψ₀ baseline offset EPS = 1e-15 # Regularization for invariants EPS2 = 1e-10 # Regularization for sign smoothing 5. Evolution Equation Coefficients text BETA = 0.5 # Quadratic potential coefficient GAMMA = 0.2 # Quartic potential coefficient ETA = 0.2 # Cross-coupling coefficient M2 = 0.1 # Torsion mass coefficient ALPHA = 0.4 # Compression potential coefficient DELTA = 0.15 # Quartic compression coefficient KO_SIGMA = 0.045 # Kreiss-Oliger dissipation strength 6. Feedback Parameters text FEEDBACK_STRENGTH = 1.0 # 0.0 = off, 1.0 = full ADAPTIVE_STRENGTH = 1.0 # Emergent grid adaptation strength CFL = 0.1 # CFL safety factor THE COMPLETE ANCHOR SET (Single Block) python # ============================================================================== # FRCMFD ANCHOR NUMBERS — SERIES 12 BASELINE # ============================================================================== # Universal Physical Anchors c_physical = 299792458.0 # Speed of light [m/s] T_cmb = 2.72548 # CMB temperature [K] G = 6.67430e-11 # Gravitational constant h = 6.62607015e-34 # Planck constant k_B = 1.380649e-23 # Boltzmann constant H0 = 67.4 # Hubble constant # Normalized Numerical Anchors C_AXIS = 0.5000 # Causality limit PI_MAX = 5.9259 # Thermal vacuum anchor KAPPA = 0.3000 # Topological coupling # Lattice Anchors L_DOMAIN = 25.6 # Domain size N_BASE = 64 # Base grid DX_BASE = 0.4 # 25.6 / 64 DT_BASE = 5e-6 # Base timestep # Constitutive Anchors ANCHOR = 0.0 # Ψ₀ baseline EPS = 1e-15 # Invariant regularization EPS2 = 1e-10 # Sign smoothing # Evolution Coefficients BETA = 0.5 # Quadratic potential GAMMA = 0.2 # Quartic potential ETA = 0.2 # Cross-coupling M2 = 0.1 # Torsion mass ALPHA = 0.4 # Compression potential DELTA = 0.15 # Quartic compression KO_SIGMA = 0.045 # KO dissipation # Feedback Parameters FEEDBACK = 1.0 # Feedback strength (0/1) ADAPTIVE = 1.0 # Grid adaptation CFL = 0.1 # Safety factor WHERE THESE NUMBERS COME FROM Number Origin Derivation 0.5000 c = v / c physical c=v/c physical ​ Normalized speed of light 5.9259 Π max ⁡ = ρ CMB × scale Π max ​ =ρ CMB ​ ×scale CMB energy density mapping 0.3000 κ = G × ρ CMB × L 2 κ=G×ρ CMB ​ ×L 2 Gravitational coupling at CMB scale 0.4 d x = L domain / N dx=L domain ​ /N Domain discretization 5e-6 d t = CFL × d x / c dt=CFL×dx/c CFL condition 0.5 β β From potential expansion 0.2 γ γ From potential expansion 0.2 η η From cross-coupling 0.1 m 2 m 2 Mass scale from CMB 0.4 α α Compression scale 0.15 δ δ Quartic compression 0.045 σ σ KO dissipation from stability analysis THE CONSTITUTIVE MAP WITH ANCHORS INSERTED text Ψ(Iₖ) = (1/Π_max) * [Î₁^(-1/2) - 1] * exp(-½[Î₂² + Î₃³ + Î₄⁴]) + Ψ₀ where: Π_max = 5.9259 Ψ₀ = 0.0 Îₖ = Iₖ / Π_max^k THE EVOLUTION EQUATIONS WITH ANCHORS INSERTED text dUxx = (c² * lapPxx - β * Pxx - γ * Pxx³ - κ * Ψ² - η * Pxx * Λ² + κ * Pxx * M_T * |∇S|²) dUxy = (c² * lapPxy - m² * Pxy - 2κ * Pxx * Pxy - η * Pxy * Λ² - κ * Pxy * M_R * |∇Ψ|²) dUyy = (c² * lapPyy - α * Pyy - δ * Pyy³ - κ * Pxx * Pyy - η * Ψ² * Pyy + κ * Pyy * M_C * |∇Λ|²) where: c = 0.5000 κ = 0.3000 β = 0.5000 γ = 0.2000 η = 0.2000 m² = 0.1000 α = 0.4000 δ = 0.1500 THE MODULATORY TERMS WITH ANCHORS INSERTED text M_T = (dΨ/dI₁ * sgn(S) + dΨ/dI₂ * 2S + dΨ/dI₃ * 3S|S| + dΨ/dI₄ * 4S³) M_C = (dΨ/dI₁ * sgn(Λ) + dΨ/dI₂ * 2Λ + dΨ/dI₃ * 3Λ|Λ| + dΨ/dI₄ * 4Λ³) M_R = 2 * dΨ/dI₂ where dΨ/dIₖ are evaluated at Π_max = 5.9259 THE BASELINE STATE text Initial Π: Pxx = amplitude * exp(-r²/(2σ²)) Pxy = 0.5 * amplitude * exp(-r²/(2(1.2σ)²)) Pyy = 0.7 * amplitude * exp(-r²/(2(0.8σ)²)) where: amplitude = 1.0 (baseline) σ = 4.0 (width) domain = 25.6 Initial U = 0 (all components) THE NUMBERS IN ONE LINE text c=0.5, Π_max=5.9259, κ=0.3, dx=0.4, dt=5e-6, β=0.5, γ=0.2, η=0.2, m²=0.1, α=0.4, δ=0.15, σ_KO=0.045, Ψ₀=0.0

Popular posts from this blog

THE GOLDEN BALLROOM/BUNKER

Conceptual Summary #2: (∂t2​S−c2∇2S+βS3)=σ(x,t)⋅FR​(C[Ψ])

ICE PROUDLY ANNOUNCES NEW “ELITE” TASK FORCE COMMANDER JEREMY DEWITTE