General:
1/√2 = Normalization factor
Aₙₒzzₗₑ = Cross-sectional area of directional release (m²)
ω = Angular perturbation frequency
ω = Coupling efficiency (0.0001-0.01)
Ω = Triple-phase QCD perturbation efficiency (dimensionless)
ψ = Weak-force coupling efficiency (dimensionless, ~0.1-0.9)
Ψₘ = Mana-BEC field density (quanta/m³)
Ψₘ² = BEC coherence squared for stability
C_cₒₕₑₛᵢₒₙ = Fluid channel cohesion coefficient (unitless)
Ψₘⁿ = Mana-BEC coherence for n simultaneous filaments
Δ = Barrier energy gap
ΔE = Energy for transduction
δQCD = QCD perturbation strength (MeV/fm) (dimensionless, 0.01–10)
Δℓ_q = Quark orbital displacement amplitude (fm) / Change in quark orbital
Δℓ_q² = Squared change in quark orbital angular momentum (ħ²)
Δℓ_q₍ᵥₑ𝒸ₜₒᵣ₎ = Directional change in quark orbital angular momentum (ℏ units)
∂ℓ_q/∂t = Rate of change of quark orbital deformation (s⁻¹)
ℏ = Reduced Planck's constant
P_cₒₙ𝒹ₑₙₛₑ = Internal condensation pressure (Pa)
P_cₒₙ𝒹ₑₙₛₑ² = Squared internal condensation pressure (Pa²)
P_wₐₜ = Internal water pressure generated (Pa)
Sₐdₕₑₛᵢₒₙ = Weak-force surface bonding coefficient (N/m²) (0.1–5.0)
Swₑₐₖₑₙ = Structural cohesion suppression factor (0.1–1.0)
S_fₗₒ𝓌 = Structural consistency of fluid pathing (0.0–1.0)
Q = Total elemental yield
Qₑₙₜₛᵧₙ = Entanglement synchronization quality (0-1 dimensionless)
Qₑₙₜₛᵧₙ² = Squared entanglement sync quality
R_gᵣₒwₜₕ = Crystalline reconstruction rate multiplier (× natural growth rate)
μ = Radial impulse transmission efficiency (0–1) / Mana-BEC coupling coefficient
τ = Perturbation duration (s) + Characteristic decay or relaxation time
τ_network = Duration of hydroduct stabilization (s)
τ₉ = Tau-9 genetic expression factor in microtubule neurons (scaled 0–1)
Nzₒₙₑ = Active earth nuclei count in the zone (dimensionless, ~10²⁴)
N = Number
N = Number of faces in the geometric barrier (Hexagon vs Triangle Stability)
Nₐᵢᵣ = Number of air nuclei entangled (10²³–10²⁵ nuclei)
λ = Quartic self-coupling constant/ Lateral kinetic energy transfer efficiency (dimensionless)
κ = Shock impulse coefficient (dimensionless) / Vertical compression efficiency (0–1)
θ = Angle between force vector and velocity gradient/ Impulse transduction efficiency
θₗ = Launch angle (radians)
Γᵣ = Radiative decay rate (zero ⇒ no decay)
Γ = Neural entrainment efficiency (0.1–1.0 dimensionless)
Γᵢₛₒ = Isomeric transition emission rate
γ = Scaling constant (dimensionless)
β = Impulse efficiency coefficient (0–1) / Spell efficiency constant
β⁺ᵣₐₜₑ = Micro-singularity β⁺ decay rate (decays/s)
β⁻𝚛ₐₜₑ = Coordinated beta-minus decay rate (decays/s)
α = Coupling constant (dimensionless)
φ = Activation factor (dimensionless)
ζ = Efficiency constant (dimensionless) / Surge amplification factor (0.2–0.7)
η = Efficiency coefficient (dimensionless)
η² = Squared neural field synchronization efficiency (unitless)
M = Mass density of medium (kg/m³)
ΔP = Pressure differential created (Pa)
dV = Differential volume element (m³)
dx = Differential length element along σ (m)
ρ = Local material / mana density (kg/m³)
ρₘ = Mana spectral density
ν = Detection frequency bandwidth (Hz)
χ = Slipstream generation efficiency (dimensionless)
σ = Surface area of slash (m²) / Tectonic stress coupling coefficient (0.1-10 MPa⁻¹)
Dictionary (Alphabetical):
Aₗᵢₘb = Limb surface area (m²)
Aᵣᵢₙg = Area affected by the ripple (m²)
Aᵇᵘᵇᵇˡᵉ = Effective surface area of the mana-formed bubble (m²)
Aₒᵤₜₚᵤₜ = Total projected flood output area (m²)
B𝚌ₒₙ𝚏ᵢₙₑ = Magnetic confinement field strength (Tesla)
C𝚠ₑₐₖ = Electroweak coupling efficiency (dimensionless)
Cᵥₑᵢₗ = Veil reinforcement coefficient (dimensionless)
Cₚₗₒw = Water synthesis rate (mol/s)
Cₙₑᵤ – Cognitive sharpness coefficient (spells per thought unit)
Eₙ_𝚍ₑ𝚌ₐy = Neutron decay energy released per neutron (MeV)
E_e⁻ = Electron energy from decay (MeV)
Eₐₙₙᵢₕ = Energy per positron-electron annihilation event (MeV)
Eᵢ₉ₙᵢₜₑ = Total ignition energy output
E𝒻ᵢᵣₑbₐₗₗ = Total radiative energy of the fireball
E𝒻ₗₐₘₑₛₕₐᵣd = Radiative-piercing energy of the Flame Shard
E𝒸ᵢₙ𝒹ₑᵣ = Total energy output of the cinder sphere
Eₛₕᵢₘₘₑᵣ = Thermal energy increase within mage's zone
Eₛₜₑₚ = Energy output sustaining plasma trail
E𝓏ₒᵣ = Energy per physical strike
Eₐᵣᵣₒ𝓌ₛ = Combined energy output of all fire arrows
E𝒷ₗₐₛₜ = Total energy of the expanding blast wave
E𝒻ₗₐᵣₑ = Combined thermal energy of all flares
Eₛₕᵤ𝒻𝒻ₗₑ = Total propulsion energy of movement
Eₚᵣₒₚ = Upward propulsion energy
Eₛₙᵢₚₑ = Energy of directed thermal beam
Eₘᵢᵣₐgₑ = Thermal energy supporting mirage illusion
Eₚyᵣₒ = Energy input for active fire modulation
Eₛₚᵢᵣₑ = Energy output of flame pillar
E𝒻ₗᵢgₕₜ = Total sustained flight energy
fᵣₑₛₒₙₐₙcₑ = Subsurface resonance coupling factor (0–1)
fₖᵢₙ = Fraction of energy converted to kinetic energy (0–1)
fₜₕₑᵣₘ = Fraction of energy converted to thermal plasma energy (0–1)
f_wₐᵥₑ = Frequency of mana-BEC wave modulation (Hz)
Fₘₐₙₐ = Mana-amplified force output (N)
g = Self-interaction strength of the BEC
gₑₘ = Electroweak coupling constant
gₘ = Modified gluon (gₘ) coupling strength (mana-chromodynamic factor)
G𝚠ₑₐₖ_ₗₑₙₛ = Gravito-weak lens strength (dimensionless)
ħ = Reduced Planck's constant
Iₛₒₗₑ = Weak-force impulse from soles (N·s)
Iₘ = Neuromuscular impulse (kg·m/s)
i = Imaginary unit
L = Total Lagrangian density
L_int = Additional interaction Lagrangian
Lₛᵧₙ = Neural synaptic latency (ms) between mana command and muscular reaction
kₛ = Shield rigidity constant
kTₘ = Thermal energy scale of the mage
kₚₕₒₜₒ = Photosynthesis conversion coefficient (mol O₂/quanta)
kₚₕₒₜₒ = Photochemical recombination rate constant (m³/mol·s)
k_ν = Neutrino steering efficiency (dimensionless)
Mdₑbᵣᵢₛ = Total mass of accelerated debris (kg)
κ·𝓜 = Magical conductivity (unique to Kael's spellform, tying mana density to optical properties)
κⁿ = Systemic coherence raised to the nth degree (n = number of active subsystems)
Mcₒₗᵤₘₙ = Mass of compressed column (kg)
Mₒ_bⱼ = Mass of the launched object (kg)
Mₚᵣₒⱼ = Mass of projectile (kg)
ṁₙₛ = Neutron star current rate (neutrons/s)
Mₜₒₜₐₗ = Total mass involved (kg)
M₍wₐₜₑᵣ₎ = Mass of water in the pulse (kg)
m = Effective mass of mana bosons
m² = Mass-term coefficient (field inertia)
M₁→₂ = Transition matrix element between states 1 and 2
|M₁→₂|² = Probability density of transition
N₂ₙₑ = Zone nuclei count (entangled, 10²³-10²⁵ nuclei)
Nc = Ground contact nuclei count (entangled)
Nₛ = Strip nuclei count (entangled)
Nₜₐᵣgₑₜ = Effective nuclei count in the entrapment region (~10²¹–10²³)
Ncₒₗᵤₘₙ = Nuclei count in column (10²²–10²⁴ nuclei)
Nₒ_bⱼ = Number of nuclei in the object
Nₐᵣₑₐ = Number of nuclei in targeted area
Nₚᵣₒⱼ = Number of nuclei in projectile
Nₐₜₒₘₛ = Number of atoms affected (dimensionless count)
n_aᵢᵣ = Number density of air molecules (m⁻³)
n₀ = Base refractive index of water (1.33)
N₍wₐₜₑᵣ₎ = Number of water nuclei coherently involved (∼10²³–10²⁵)
Nₘᵤ = Effective mana-reactive myonuclei per region
Pₜ = Local crustal pressure (Pa)
Pₘᵢ𝒸ᵣₒ_ₛᵢₙg = Directional kinetic pulse power (J)
Pₐₜₘ = Atmospheric pressure (Pa)
Pₕₐ𝓌ₖᵢₙg = Hawking radiation pressure (Pa)
P𝚌ᵤₛₕᵢₒₙ = Downward plasma cushion pressure (Pa)
P𝒻ₗₒw = Internal pressure of formed water channel (Pa)
Pᵢₙₜₑʳₙₐₗ = Internal pressure exerted by the sealed fluid (Pa)
Re(𝒱_verbal) = Real part of the vocal modulation potential
R_Bₑ꜀ = Mana-BEC reactor output rate (quanta/s)
Rᴮᴱᶜ = Condensate coherence radius (m)
R_cₒₘₚ = Compression ratio of condensed water
Rₛwᵢₜcₕ = Responsiveness of internal mana state switching (Hz or events/sec)
Sᵣₑ = Spell recast stability factor (0.5-2.0)
Sᵣₑ𝒻ₒᵣₘ = Bond reformation stability factor (dimensionless)
Sₙₑᵤᵣₐₗ = Neural signal fidelity (0.5–2.0 dimensionless)
Sₛₕₑₐₜₕ = Torque sheath coherence (dimensionless)
Sₛₚᵢₙ = Nuclei spin alignment factor (dimensionless)
Sₐₗᵢgₙ = Lattice alignment factor (0–1)
Scₒₕ = Coherence factor for quark spin alignment (0–1)
Sₐₗᵢ𝓰ₙ = Quark spin alignment factor (0–1)
Sₛᵤʳ𝒻ₐ𝒸ₑ = Active water surface area under manipulation (m²)
S𝒸ₒₙdₑₙₛₑ = Compression stability factor (0.1–1.5)
Scₒₕₑₛᵢₒₙ = Surface cohesion factor (0.2–1.0), governs tension retention
Sₑₓ = Entropy of execution: degree of randomness or complexity in movement/spellcasting (higher = less efficient)
Sʰₑₗᵢ𝚌ₐₗ = Helical quark orbital stability factor (0–1)
V_ext(𝐫) = External potential landscape
vₙ = Wave propagation velocity (m/s)
V_zₒₙₑ = Volume of manipulated terrain (m³)
Vₛᵤᵦₛᵤᵣfₐcₑ = Scanned subsurface volume (m³)
Vdₑbᵣᵢₛ = Average debris ejection velocity (m/s)
vₑⱼₑcₜ = Ejection velocity of the pillar (m/s)
Vwₐᵥₑ = Velocity of the moving destabilization wave (m/s)
Vₗₐᵤₙ𝚌ₕ = Final launch velocity (m/s)
V_rₑ = Reactor volume (m³)
Vᵣᵢₙg = Volume of torque field ring (m³)
V𝒹ₒ𝓌ₙ = Downward air velocity (m/s)
vₗₐₜ = Lateral velocity along spiral (m/s)
Vₗₐₜₜᵢ𝒸ₑ = Volume of mana-BEC lattice (m³)
Vᵢₙⱼₑ𝚌ₜ = Volume of air injected/saturated (m³)
Vₛₕₑₐₜₕ = Sheath volume (m³)
Vᵦₒdᵧ = Body velocity (m/s)
Vwₐₖₑ = Volume of low-pressure wake region (m³)
Vₛₚᵢᵣₐₗ = Volume of mana-BEC spiral (m³)
Vfᵢₑₗd = Volume of affected field (m³)
Vcₒₙₑ = Volume of shock cone (m³)
Vsₚₕₑᵣₑ = Spherical volume of effect (m³)
Vₑ𝒻𝒻 = Effective volume of influence (m³)
Vₛᵧₙₜₕ = Effective synthesis volume (m³)
V_dₑₙₛᵢfᵧ = Volume affected by densification (m³)
vₚᵤₗₛₑ = Resulting velocity of the water pulse (m/s)
Vₐᵣₑₐ = Volume of effect zone (m³)
v_wₐₖₑ = Wave propagation speed (m/s)
V𝚌ₒₕₑₛᵢₒₙ = Cohesive volume under weak-force resonance (m³)
Wₑₘᵢₜ = W-boson emission rate (s⁻¹)
W𝚌ₐₛ𝚌ₐ𝚍ₑ = W-boson cascade intensity (dimensionless)
𝒲ₗₐcc = Wind-energy flux of Lacerate
Dictionary (Special Characters):
ψ(𝐫,t) = Mana wavefunction (BEC order parameter)
𝓥ₙ = Chiral flux vortices, stabilized via:
𝓥ₙ = ∫∂Ω (𝑔ₘ 𝒜𝜇 − 𝑖κ𝐹𝜇𝜈)𝑑𝑥𝜇 ∧ 𝑑𝑥𝜈
ℬ = BEC coherence operator (scales with caster's Tau-9 receptor density)
𝒟 = Current shield deformation metric
𝒟ₒ = Optimal deformation threshold
𝒟, 𝒟ₒ, kₛ = As defined above
|Alive⟩ = Undeformed (intact) shield state
|Vegetable⟩ = Fully collapsed (failed) shield state
|𝑛⟩⟨𝑛| = Pentagonal face eigenstates (n=1-4 for cube)
|ψ|² = Local mana density
𝒮 = Shield stability parameter
ℳ_cast = Casting efficiency metric
⟨ϕ|ψₙ⟩ = Overlap of mana field with nuclear state n
ψᵥ = Vortex-mode wavefunction
∫ … dE = Integration over energy spectrum
∫|ψᵥ|² dA = Total vortex energy over area A
|Ψ⟩ = Superposed shield-state vector
Ψₛₕᵢₑₗₜ = Shield wavefunction
δQCDw = QCD wavefront perturbation strength (MeV/fm²)
δQCDᵣₑₛ = Resonant QCD perturbation amplitude (dimensionless)
δQCDᵣₐ𝒹 = Radial QCD perturbation amplitude (dimensionless)
δQCDfᵢₗₐₘₑₙₜ = Filament-based QCD perturbation strength
δQCDvₑᵣₜᵢcₐₗ = QCD perturbation strength in vertical axis
δQCDₛᵤₛₜₐᵢₙ = Sustained QCD perturbation magnitude
δQCDdᵢf𝒻ᵤₛₑ = Diffuse QCD Color Charge perturbation magnitude
δQCDrₑₛ = Residual QCD perturbation magnitude (dimensionless)
δQCD𝚜ₚᵢₙ = Quark spin perturbation magnitude (dimensionless)
δQCDᶜₒₘₚ = QCD perturbation factor for volumetric compression
δQCDᵇᵘᵇᵇˡᵉ = Degree of QCD perturbation shaping spherical boundary layers
δQCDₛₜᵣₑₐₘ = QCD perturbation along streaming vector (unitless, 0–1)
Δγ = Lorentz shear gradient (mana-enhanced velocity differential)
ΔE₆ = Bond energy modulation capacity (eV/nucleus)
ΔEₓ = Energy released per nuclear relaxation (~keV–MeV)
ΔEₚ = Energy per plasma-phase decay event
ΔEₗ = Energy density of the plasma filament
ΔE_c = Energy release associated with carbon isotope nucleation
ΔE_v = Energy increase per vibrational excitation
ΔEₚₗₐₛₘₐ = Energy release per plasma filament unit
ΔE_b = Energy per nuclear decay contributing to blast
ΔEₗ = Energy per linear plasma filament
ΔEₚ = Energy per plasma microburst
ΔEₖ = Kinetic energy augmentation per stride
ΔE_d = Decay energy per unit thrust
ΔEₗₒₙg = Energy across extended channel
Δnᵣ = Change in refractive index
ΔEₖ = Additional kinetic transfer
ΔEᵣ = Reaction energy per cubic meter
ΔEₜ = Total decay-to-thrust conversion
ΔPₑᵣₙₒᵤₗᵢ = Bernoulli pressure differential (Pa)
ΔQₛᵣᵉ = Strange quark resonance delta (energy shift in QCD springs)
Δtᵣ = Neural reaction time (ms) from stimulus to decision
ΔEₘ = Mana energy cost of maintaining this state (MeV)
∂/∂t = Time derivative
∂ₘϕ = Partial derivative of ϕ w.r.t. coordinate xᵐ
∂κ / ∂Ψₘ = Change in coherence as a function of mana density (adaptability)
∇² = Laplacian operator (spatial curvature)
∇ × [M₀⊗SU(2)ₘ] = Curl of mana-Wₘ boson interaction field
∇v(x) = Velocity gradient along the slash path (s⁻¹)
∇×(vₐᵢᵣ) = Curl of air velocity field (turbulent rotation)
∇μᵢ(x) = Friction coefficient gradient over surface
∇Θ(x) = Angular precision gradient
∇Tₐᵢᵣ = Temperature gradient in the ignition zone
∇ρₚₗₐₛₘₐ = Gradient of plasma density in the fireball core
∇vₚₗₐₛₘₐ = Velocity gradient along the shard's axis
∇ρ_c(x) = Density gradient of superheated carbon plasma
∇T_z = Temperature gradient across mage's zone
∇F_g = Gradient in ground friction forces
∇P_r = Radial pressure gradient in blast zone
∇Fₕ = Vertical force differential (hover vector)
∇Φᶠ = Gradient of flame potential field
∇T = Temperature variation vector
∇T = Temperature gradient variation
∇aₗ = Limb acceleration differential
∇ρₐ = Ambient air density gradient
∇𝒻ᵥ = Jet vector adjustment gradient
∇Φₘ = Spatial gradient of mana potential across regions (V/mₐₙₐ)
ε_dᵣₐg = Drag coefficient reduction (0–1 dimensionless)
εᵣₑ𝒸ₒᵢₗ = Recoil energy loss fraction (0–1)
εₜᵤᵣb = Turbulence suppression efficiency (0–1)
εₗₒₛₛ = Reaction energy loss factor (0–1, dimensionless)
εₛₜₐbₗₑ = Enemy balance factor (0–1)
ζₑff = Total efficiency of full-body mana resonance (dimensionless 0–1)
η_ᵣₑ𝒸𝓎𝒸ₗₑ = Momentum recycling efficiency (0–1 dimensionless)
η𝚌ₕₐₙₙₑₗ = Electroweak coupling efficiency (0–1)
η𝚍ₑg = Degeneration efficiency (0–1 dimensionless)
ωᵥₒᵣₜₑₓ = Vortex angular velocity factor (rad/s)
ωᵣₑₗ = Relative angular velocity at lattice edge (rad/s)
τ_fₒᵣₘ = Formation time constant (seconds)
τʰₒₗ𝒹 = Temporal stability of containment (s), inversely proportional to decay rate of cohesion field
τ_lock = Duration of metastable hydroduct locking phase (s)
τ_stabilize = Duration of lattice-wide hydroduct stabilization (s)
ι = Flowfield propagation efficiency (dimensionless, 0–1)
τₘᵢᵣᵣₒʳ = Tau-9 receptor mirror activation rate (unitless, 0–1)
θ = Entrainment coefficient for sealed hydro-volumes (0.01–0.3)
θₙ = Phase angles recursively defined by:
θₙ₊₁ = arcsin(ℏωₙ / 2‖𝓥ₙ‖)
Γᵥᵢb = Vibrational mode excitation rate
Γₒₓ = Rate of oxidation reactions along footpath
Γ_β = Rate of β decay events
Γₛ = Spire formation decay chain rate
β⁻_ν_ₛₜₑₑᵣ = β⁻ decay neutrino thrust vectoring factor (dimensionless)
β·∇P = Pressure gradient term (from rapid vaporization in confined space)
α·ΔT = Thermal modulation term (accounts for Leidenfrost-effect steam layers)
Φᵥₐ𝒸 = Vacuum energy density (J/m³)
ϕ = Scalar mana field (Largan Density)
ϕ = Complex conjugate of ϕ* (Largan Density)
(ϕ*ϕ)² = Four-point interaction term
ξ = Coupling constant for swirl effect (dimensionless)
ξₚ = Caster's plasma coherence factor
σᵦ⁻ = Cross-section for β⁻ decay events
∑∇Tᵢ = Sum of temperature gradients in flare spots
∑∇vᵢ = Sum of velocity gradients per arrow