One symbol, one meaning, across all papers. Every symbol used in the BFUT programme with its definition, expression, value, and which papers it appears in.
| Symbol | Definition | Expression / Value | Papers & Notes |
|---|---|---|---|
| Fundamental Spaticle Field Constants | |||
| ρ_s | Intrinsic equilibrium density of the Spaticle field | 5.9 × 10⁻²⁷ kg/m³ | All papers. Single fundamental parameter of the BFUT programme. Constrained to ±0.015% by W/Z masses. |
| Ψ(r,t) | Spaticle carrier field / gravitational potential | Ψ(r,t) = −(GM/r) exp(−r/R_eff)·R(τ_c,∂_t)·N(Σᵢ) | P17, P18, P25. Never Φ for this quantity. |
| Ψ_vac | Vacuum equilibrium configuration | λ·Ψ_vac² = ρ_s c² | P17, P18. Non-zero; gravity is native to the substrate. |
| λ | Quartic self-interaction coupling | λ = ρ_s/4 | P17, P18. Fixed by vacuum condition. Not the same as λ_cond (P16). |
| K_s | Substrate stiffness | K_s = ρ_s c² = 5.30 × 10⁻¹⁰ Pa | P23. Determines c as propagation speed of all disturbances. |
| Carrier Field Timescales and Lengths | |||
| τ_c | Carrier response / relaxation time | 1/(c√(3ρ_s)) = 4.6 ms | P18, P25. Governs exponential decay of carrier residuals. Fixed by ρ_s. |
| L_rlx | Substrate relaxation length | c·τ_c = 1,380 km | P18. Amplitude e-folding length for unsustained disturbances. |
| L_cosm | Cosmological coherence length | c/√(3ρ_s G) ~ 5.82 Gly | P18. Maximum scale of nested domain hierarchy. |
| ξ | Dimensionless transition parameter | ξ(t) = τ_c|Ṡ_GR/S_GR(t)| | P18. Controls carrier residual amplitude. Never χ. |
| Gravitational Domain Structure | |||
| R_d | Intrinsic deformation-domain radius | (3M/8πρ_s)^(1/3) | P18, P25. Sun: 363 ly. Milky Way: 517 kpc. Proton: 32.6 cm. Electron: 2.6 cm. |
| R_eff | Effective domain radius with rotation | R_d·(1 + v_rot²/c²)^(1/3) | P18, P25. Enlarged persistence domain due to organised rotation. |
| F1-cov | Fully covariant carrier field equation | g^μν∇_μ∇_ν(δΨ) − 3ρ_s c²·δΨ = κ·∇²Ψ_matter | P18. Master equation. GR recovered exactly in settled limit. |
| P16 Condensation Functional | |||
| E(n) | Total condensation energy for n units | −J·pairs(s) + λ_cond·Σ(s)² + (n−3)² + α_geom·(n−k) + D_s·cos(3φ) | P16. Full five-term functional. |
| E_unit | Fundamental energy unit | m_p c²/π = 298.661 MeV | P16. Anchors all P16 energy calculations. |
| V_gap | Interstitial volume fraction | (2√3 − π)/(4π/3) = 0.0770 | P16. Universal geometric constant connecting to electron mass. |
| R₀ | Free-energy functional minimum | 1.271 (canonical) | P16, P19, P27. Shared by ħ derivation and α cross-check. |
| Coupling Constants and Masses | |||
| α or α_em | Fine structure constant | 1/137.036 (measured); BFUT: 1/137.1 (0.05%) | P17, P19. Reserved for fine structure constant only. |
| α_s | Strong coupling constant | 0.1179 (m_Z scale); BFUT: 0.120 (1.8%) | P17, P19. |
| sin²θ_W | Electroweak mixing angle | 0.2312 (measured); BFUT: 0.2312 (0.01%) | P17, P19. Weinberg angle. |
| m_W, m_Z | W and Z boson masses | m_W: 80.4 GeV; m_Z: 91.2 GeV | P19. Both derived from ρ_s. |
| m_H | Higgs boson mass | √(m_top·m_Z) = 125.51 GeV; measured 125.25 GeV (0.21%) | P19, P19A. |
| Time and Special Relativity | |||
| η | Propagation efficiency (Lorentz factor) | η = √(1 − v²/c²) | P22. Fraction of substrate propagation budget available for internal processes. |
| t_sub | Accumulated substrate state evolution | Integral of η over proper path | P22. What clocks measure; not a pre-existing dimension. |
| Photon Propagation | |||
| E_min | Minimum coherent photon energy | ((ħc)³ρ_s c²)^(1/4) = 2.25 meV (λ = 88 μm) | P23. Below E_min: no soliton propagation. |
| L_persist | Photon soliton persistence length | L_rlx × (E_photon/E_min)² for E > E_min | P23. Optical: 11 AU; 100 MeV: 88.5 Gpc. |
| Planck Constant Consequences | |||
| ħ | Reduced Planck constant | m_p·c·r_p/(π·R₀). Agreement: 0.136% (CODATA); 0.082% (BFUT-derived r_p = 0.8398 fm) | P16, P19, P27. Derived from condensation geometry. |
| λ_C | Compton wavelength (BFUT form) | m_p·r_p/(π·R₀·m). All particles: 0.14% agreement | P27. Condensation length scaled by m_p/m. |
| λ_dB | de Broglie wavelength | m_p·c·r_p/(π·R₀·p) | P27, P19A. |
| ℓ_P | Planck length | √(m_p·r_p·G/(π·R₀·c²)) = 1.6174 × 10⁻³⁵ m (0.068%) | P27. |
| m_P | Planck mass | √(m_p·c²·r_p/(π·R₀·G)) = 2.1779 × 10⁻⁸ kg (0.068%) | P27. |
| t_P | Planck time | √(m_p·r_p·G/(π·R₀·c⁴)) = 5.3949 × 10⁻⁴⁴ s (0.068%) | P27. |
| ρ_vac | Physical vacuum energy density | ρ_s·c² = 5.30 × 10⁻¹⁰ J/m³ | P27. Substrate at equilibrium. Not the QFT mode sum. |
| Consciousness Index | |||
| CI | Consciousness Index (effective) | CI = CI₀ × S; CI_floor = 1.0 | P20, P21. No physical system has CI = 0. |
| CI₀ | Intrinsic consciousness capacity | CI₀ = C × I × D (multiplicative); human average = 100 | P21. Calibration anchor at human average. |
| S | Survival condition modifier | 0 < S ≤ 1 | P21. Modifies effective CI without changing CI₀. |
| Shared Physical Constants | |||
| G | Gravitational constant | 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻² | All. Standard value; not modified in BFUT. |
| c | Speed of light | 2.998 × 10⁸ m/s | All. Also the Spaticle substrate propagation speed. |
| m_p | Proton mass | 938.272 MeV/c² | P16, P19. Enters E_unit = m_p c²/π. |
| m_e | Electron mass | 0.511 MeV/c²; BFUT: E_unit/(6π⁴) = 0.511009 MeV (0.001%) | P16. Derived from interstitial geometry. |
| r_p | Proton charge radius | 0.8409 fm (CODATA); BFUT: 0.8398 fm (0.19%) | P16, P19. Single measured input anchoring the SI conversion. |
For the full pronunciation guide and complete symbol list, see the Master Symbol Guide document (Downloads page).