Vijay Shankar Sharma
One symbol, one meaning. If BFUT derives a counterpart of an established quantity, the standard symbol is kept and the _vss suffix is added. BFUT-only quantities such as ρ_s, R₀, A, B, C, D have no suffix. ρ_s = 7.3 × 10⁻²⁷ kg m⁻³.
| Symbol | Definition | Expression / value |
|---|---|---|
| ρₛ | BFUT-constrained/adopted paper value 7.3 × 10⁻²⁷ kg m⁻³ | |
| A, B, C, D | A=1/2; B=0.56308; C=−1/3; D=1 | |
| R₀ | 1.27348220802151 | |
| ℓ_model | rₚ/R₀ | |
| m_eff | ħ_vss/(c_vss·ℓ_model) | |
| ħ_vss | mₚ·c_vss·rₚ/(πR₀) | |
| α_vss | α_vss = e²/(4πε₀·ħ_vss·c) = e²R₀/(4ε₀mₚc²rₚ) = 1/137.037 (measured 1/137.036, 0.00048%) | |
| αₛ_vss | αₛ_vss = B·R₀⁴/(8πA) = 0.11785 | |
| sin²θ_W_vss | sin²θ_W_vss = 1 − (m_W_vss/m_Z_vss)² = 0.23257 | |
| m_W_vss, m_Z_vss | m_Z_vss = π⁴mₚ = 91.396 GeV/c²; m_W_vss = 256M = (256/3)mₚ = 80.066 GeV/c² | |
| m_H_vss | λ_H_vss = 2AR₀/π² = 0.12903; v_vss = 6E_unit/α_vss; m_H_vss = v_vss√(2λ_H_vss) = 124.75 GeV/c² | |
| λₛ | Cosmological/substrate quartic; distinct from λ_H_vss | |
| κₛ | 1/c_vss² | |
| μₛ | √(3Gρₛ/c_vss²) | |
| Lₛ | 1/μₛ | |
| aₛ | c_vss²μₛ/3 | |
| R_d, R_eff | Defined from ρₛ and rotation | |
| E_unit | mₚ·c_vss²/π | |
| (Vgap/Vq) | (2√3−π)/(4π/3) | |
| K_s | ρₛ c_vss² | |
| u_vac | ρₛ c_vss² | |
| c_vss | Mechanical substrate form: c_vss = √(K_s/ρₛ). Independent electromagnetic-condensation calculation with standard α: c_vss = √[e²R₀/(4ε₀mₚrₚα)] = 2.99791740 × 10⁸ m/s (0.000239% below standard c). Independent calculation with BFUT-derived α_vss: c_vss = √[e²R₀/(4ε₀mₚrₚα_vss)] = 2.99792458 × 10⁸ m/s (exact match to standard c). | |
| h_vss, Lmin | h_vss=2πħ_vss; Lmin=ħ_vss/2 | |
| κ_vss, λC_vss, λdB_vss, E_n_vss | Preserve standard symbols when provenance is unambiguous | |
| ℓ_P_vss, m_P_vss, t_P_vss | Expressions derived using ħ_vss | |
| Amodel | 1/2 | |
| P_restore, ρmax, J_entrain | BFUT expressions defined in P26 | |
| m_Shankar | m_Shankar c² = 2.60E_unit = 776.5 MeV; BFUT-specific symbol, no _vss suffix | |
| m_BFUT | m_BFUT c² = 4.70E_unit = 1403.7 MeV; BFUT-specific symbol, no _vss suffix | |
| mₚ | External physical anchor | |
| rₚ | External SI length anchor | |
| ħ | External validation value | |
| α | External validation value | |
| c | External reference value | |
| G | External physical constant | |
| mₑ | External comparison value | |
| sin²θW | External comparison value | |
| ρₛ | 7.3 × 10⁻²⁷ kg m⁻³ | |
| mₚ | 1.67262192369 × 10⁻²⁷ kg | |
| rₚ | 0.8414 × 10⁻¹⁵ m | |
| c / c_vss | Standard: c = 2.99792458 × 10⁸ m/s. BFUT with standard α: c_vss = √[e²R₀/(4ε₀mₚrₚα)] = 2.99791740 × 10⁸ m/s (0.000239% below standard c). BFUT with α_vss: c_vss = √[e²R₀/(4ε₀mₚrₚα_vss)] = 2.99792458 × 10⁸ m/s (exact match to standard c). Mechanical form: c_vss = √(K_s/ρₛ). | |
| G | 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² | |
| A | 0.500000 | |
| B | 0.56308 | |
| C | -0.333333 | |
| D | 1.000000 | |
| ρₛ | 7.3 × 10⁻²⁷ kg m⁻³ | |
| ψ_vss or ψ_vss(r,t) | ψ_vss(r,t) = −(GM/r) exp(−r/Reff)·R(τc,∂t)·N(Σᵢ) | |
| δψ_vss | δψ_vss = ψ_vss − ψ_vssvac | |
| ψ_vssvac | Vacuum equilibrium configuration of ψ_vss | |
| λₛ | Fixed by the selected field normalization | |
| κₛ | κₛ = 1/c² | |
| μₛ | μₛ² = 3Gρₛ/c² = (4.03358955 × 10⁻²⁷ m⁻¹)² | |
| τc | Local carrier response-time parameter | |
| Lrlx | Lrlx = cτc | |
| μₛ | μₛ = √(3Gρₛ/c²) = 4.03358955 × 10⁻²⁷ m⁻¹ | |
| Lₛ | Lₛ = 1/μₛ = 2.47918135 × 10²⁶ m ≈ 26.205 Gly | |
| aₛ | aₛ = c²μₛ/3 = c√(Gρₛ/3) = 1.20840317 × 10⁻¹⁰ m s⁻² | |
| ξ | ξ(t) = τc|Ṡ_GR/SGR(t)| | |
| ξorg | >> Lrlx | |
| R_d | = (3M/8πρₛ)¹ᐟ³ | |
| R_eff | = Rd·(1 + vrot²/c²)¹ᐟ³ | |
| DME | v²(R) = vb²(R)[1 + aₛR/vb²(R)]¹ᐟ²; Mextra(<R) = Mb(R){[1 + aₛR²/(GMb(R))]¹ᐟ² − 1} | |
| F1-cov | gμν∇μ∇ν(δψ_vss) − μₛ²δψ_vss = κₛ∇²ψ_vssmatter | |
| Sobs(t) | = SGR(t) + δScarrier(t) | |
| δScarrier(t) | Basic form: ≈ −∫ exp(−(t−t′)/τc)·[dSGR/dt′]dt′. Extended form: = Amem·Θ(t−t0) + Atr·exp(−(t−t0)/τc)·Θ(t−t0) | |
| ρ∇ | = αg|∇ψ_vss|² | |
| E(n) | = −J·pairs(s) + λcond·Σ(s)² + (n−3)² + αgeom·(n−k) + Dₛ·cos(3φ) | |
| Dₛ | = 1.5 [demonstrative]. Must be positive. | |
| φ | 3+e: φ=π/3→cos(3φ)=−1 (min). 4+0: cos=+1. | |
| E_unit | = mₚ·c²/π = 298.661 MeV | |
| (Vgap/Vq) | = (2√3 − π)/(4π/3) = 0.0770 | |
| α_vss | = 1/137.036 [measured]. BFUT: α_vss = e²/(4πε₀ħ_vssc), ħ_vss = mₚcrₚ/(πR₀) → 1/137.037 (0.00048%) | |
| αₛ_vss | BFUT: αₛ_vss = B·R₀⁴/(8πA) = 0.11785 | |
| sin²θ_W / sin²θ_W_vss | BFUT: sin²θ_W_vss = 1 − (m_W_vss/m_Z_vss)² = 0.23257. | |
| m_W_vss, m_Z_vss | m_Z_vss = π⁴mₚ = 91.396 GeV/c²; m_W_vss = 256M = (256/3)mₚ = 80.066 GeV/c² | |
| m_H_vss | λ_H_vss = 2AR₀/π² = 0.12903; v_vss = 6E_unit/α_vss = 245.565 GeV; m_H_vss = 124.75 GeV/c² | |
| λₛ | Fixed by the selected field normalization | |
| m*_vss | m_e_vss/α_vss = 1.2483430 × 10⁻²⁸ kg | |
| rₑ_vss | α_vss·ħ_vss/(m_e_vss·c) = 2.8178873 × 10⁻¹⁵ m | |
| a₀ / a₀_vss | a₀_vss = ħ_vss/(m_e_vss·c·α_vss) = 52,916.71 fm. Measured a₀: 52,917.8 fm (0.002%) | |
| Kphys | 197.33 MeV·fm | |
| T5 | = αT·T·|Ψ|² | |
| Ψ | Field variable used in the P19 thermal treatment | |
| η | η = √(1 − v²/c²) = 1/γ | |
| tsub | tsub = ∫η dt | |
| K_s | Ks = ρₛc² = 6.5635567 × 10⁻¹⁰ Pa | |
| u_vac | uvac = ρₛc² = 6.5635567 × 10⁻¹⁰ J m⁻³ | |
| vspatial | vspatial² + vinternal² = c² | |
| vinternal | vinternal² = c² − vspatial² | |
| dτ/dt | = η = √(1−v²/c²) kinematic; √(1−2GM/rc²) gravitational | |
| cs | η = cs/c₀; cs < c₀ in compressed/deformed substrate regions | |
| c₀ | η = cs/c₀; c₀ is the undisturbed-vacuum value, numerically equal to c | |
| ηmin | ηmin > 0; finite floor set by BFUT Paper 26 restoring pressure and coherence threshold | |
| ψ(x,t) | Phase exp(−iEt/ℏ) accumulates through substrate reorganisation; Schrödinger equation derived in P19A | |
| γ | γ = 1/√(1 − v²/c²) | |
| tcoord | Reference coordinate time in an undisturbed substrate region | |
| vgrav | vgrav² = c²(2GM/rc²)f(r,Rd) | |
| f(r,Rd) | f(r,Rd) = 1 inside the active domain and 0 outside the domain boundary | |
| ηN | Empirical parameter constrained by Lunar Laser Ranging | |
| c_vss | Using standard measured α: c_vss = √[e²R₀/(4ε₀mₚrₚα)] = 2.99791740 × 10⁸ m/s (0.000239% below standard c). Using BFUT-derived α_vss: c_vss = √[e²R₀/(4ε₀mₚrₚα_vss)] = 2.99792458 × 10⁸ m/s (exact match to standard c). | |
| U(t) | U(t) = exp(−iHt/ħ_vss) = exp(−iHπR₀t/(mₚ·c·rₚ)) | |
| tmin | tmin = θ·mₚ·c·rₚ/(R₀·π·Hmax) | |
| C(θA,θB) | C(θA,θB) = −cos(θA − θB) | |
| CHSH | S ≤ 2 (classical); S ≤ 2√2 (quantum, Tsirelson bound) | |
| P_restore | Prestore = (ρₛ/4)(ρ − ρₛ) | |
| ρmax | ρmax ~ ρₛ·c²/(G·rs²). Finite by substrate physics. | |
| J_entrain | ∝ ∇(ρ − ρₛ) | |
| h_vss | h_vss = 2πħ_vss = m_eff c_vss 2πℓ_model (action of one condensation circulation) | |
| Lmin | Lmin = ħ_vss/2 = (1/2)·m_eff c·ℓ_model | |
| κ_vss (tunnelling form) | κ_vss = πR₀√(2m(V−E))/(mₚ·c_vss·rₚ) | |
| λC_vss | λC_vss = mₚ·rₚ/(π·R₀·m) = ħ_vss/(mc). Universal: all particles 0.00048% agreement. | |
| λdB_vss | λdB_vss = mₚ·c·rₚ/(π·R₀·p) = ħ_vss/p | |
| E_n_vss (HO form) | E_n_vss = (n+1/2)·mₚ·c_vss·rₚ·ω/(π·R₀) = (n+1/2)ħ_vssω | |
| ℓ_P_vss | ℓ_P = √(mₚ·rₚ·G/(π·R₀·c_vss²)) = 1.6163×10⁻³⁵ m (0.0002%) | |
| m_P_vss | mP = √(mₚ·c_vss²·rₚ/(π·R₀·G)) = 2.1764×10⁻⁸ kg (0.0002%) | |
| t_P_vss | tP = √(mₚ·rₚ·G/(π·R₀·c_vss⁴)) = 5.3912×10⁻⁴⁴ s (0.0002%) | |
| u_vac | uvac = ρₛc² = 6.5635567 × 10⁻¹⁰ J m⁻³ | |
| ℓ_model | ℓmodel = rₚ/R₀ = 6.607×10⁻¹⁶ m | |
| R₀ | R₀ = 1.27348. Derived from observed rₚ, mₚ, c, ħ: R₀ = rₚ·mₚ·c/(π·ħ). Also the minimum of the P16 free-energy functional with derived coefficients. Approximate closed form: 4/π = 1.27324 (0.02%). | |
| Amodel | Amodel = 1/2 exactly. Proved: A = ħ_vss²/(2m_eff), in model units = 1/2 by definition m_eff = ħ_vss/(c·ℓ_model). Exact, not approximate. | |
| uCMB | = 4.17 × 10⁻¹⁴ J/m³ (measured by COBE) | |
| σSB | = 5.670 × 10⁻⁸ W/m²/K⁴ | |
| jL | ≈ 2.6 × 10⁻³³ W/m³ (measured from galaxy surveys) | |
| TCMB | T = (uCMB · c / 4σSB)¹ᐟ⁴ = 2.725 K | |
| σT | = 6.6524 × 10⁻²⁹ m²; σT = (8π/3)(e²/mₑ c²)² | |
| ΓT | = ne · σT · c | |
| λmfp | = 1/(ne · σT) | |
| Ddiff | = c/(3 ne σT) = λmfp · c/3 | |
| P(k) | P(k) = I(k)/D(k) in statistical steady state | |
| I(k) | From shell-like and ripple-like structure generation | |
| D(k) | D(k) = k² · Ddiff (diffusion damping) | |
| TI | TI = Trot / 13.8 Gyr; TI > 1 implies rotational period exceeds standard cosmic age | |
| Trot | Trot = 2πR/vrot; measured in Gyr | |
| y | y = ∫(kB Te / mₑ c²) ne σT dl; dimensionless | |
| Te | ~ 10 keV ≈ 10⁸ K for massive clusters | |
| Φ | ΔT/T = 2∫(∂Φ/∂η)dη where η is conformal time | |
| AISW | AISW = 1 is the Λ-CDM expectation; observed 4-10 in stacked analyses | |
| ηISW | Distinct from Lorentz factor η used in P22; context distinguishes usage | |
| S₈ | S₈ = σ₈ × (Ωm/0.3)⁰·⁵; not a direct observable | |
| σ₈ | Planck reference: 0.832 ± 0.013 | |
| Ωm | Ωm = ρm/ρcrit; standard measured value ~0.315 | |
| [Li-7] | Spite plateau: 1.6 × 10⁻¹⁰; BBN prediction: 5.6 × 10⁻¹⁰ | |
| kdest | From spallation cross-sections; measured in laboratory | |
| Rprod | From cosmic-ray spallation and stellar processes | |
| CI | CI = CI₀ × S; scalar; CIfloor = 1.0 | |
| CI₀ | CI₀ = C × I × D (multiplicative); human average calibrated at 100 | |
| S | 0 < S ≤ 1; modifies effective CI without changing CI₀ | |
| C | Sensory bandwidth, environmental interaction, social communication, manipulation, internal sensing | |
| ICI | Structural connectivity, dynamic coordination, hierarchical processing; nonlinear amplifier. | |
| DCI | Autonomy, memory depth, adaptive flexibility; nonlinear. | |
| rPearson | r = 0.675 achieved in N-body simulation after gravitational sorting; 84% of survivors receding | |
| G | 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻² | |
| c / c_vss | Standard: c = 2.99792458 × 10⁸ m/s. BFUT, standard α: c_vss = √[e²R₀/(4ε₀mₚrₚα)] = 2.99791740 × 10⁸ m/s (0.000239% below standard c). BFUT, α_vss: c_vss = √[e²R₀/(4ε₀mₚrₚα_vss)] = 2.99792458 × 10⁸ m/s (exact match to standard c). Mechanical form: c_vss = √(K_s/ρₛ). | |
| ħ / ħ_vss | 1.054572 × 10⁻³⁴ J·s. BFUT: mₚ·c·rₚ/(π·R₀) = 1.054577×10⁻³⁴ J·s. Agreement: 0.00048%. Inverted: R₀ = rₚ·mₚ·c/(π·ħ) = 1.27349. | |
| mₚ | 938.272 MeV/c² | |
| mₑ / m_e_vss | 0.510999 MeV/c². BFUT: mₚ/(6π⁵) = 0.511009 MeV (0.002%); E_unit/(6π⁴) = 0.511009 MeV (0.002%). | |
| rₚ | 0.8414 fm [CODATA 2018]. BFUT: R₀·ℓmodel = rₚ by construction. | |
| λemit | Wavelength at emission | |
| λobs | λobs = λemit(1+z) | |
| νemit | Frequency at emission | |
| νobs | νobs/νemit = √[(1+β)/(1−β)] for approach | |
| β | β = v/c | |
| m_ν | Small non-zero rest mass in the BFUT substrate-ripple description | |
| ΔEimbalance | m_ν ~ ΔEimbalance/c² | |
| Keff(ω) | Keff(ω) = K′(ω) + iK″(ω) | |
| K′(ω) | Real part of Keff(ω) | |
| K″(ω) | Imaginary part of Keff(ω) | |
| αatt | E(x) = E₀e^(−2αatt x) | |
| Latt(ω) | Latt(ω) ≈ (c/ω)[K′(ω)/K″(ω)] | |
| udef | E = udef·Acs·Δx | |
| Acs | Cross-sectional area of a directed disturbance | |
| Δx | Longitudinal extent of a directed coherent disturbance | |
| εatt | dE/dx = −(εatt/Δx)E | |
| dV | dV = Acs·dx | |
| τrelax | Relaxation timescale of the internal substrate mode | |
| ΔK | Stiffness change associated with internal relaxation | |
| q(x,t) | Wave-amplitude function used for the KdV soliton illustration | |
| κGW | Empirical attenuation parameter constrained by GW propagation observations |