Datasets:
RANDMEDIATION
/
PhysicsBabel

Dataset card Data Studio Files
xet
 Community
1
size
int64
2
8
keys
stringlengths
10
106
symbols
stringlengths
3
29
domains
stringclasses
62 values
pi
stringlengths
3
46
equation
stringlengths
10
59
name
stringclasses
19 values
n_const
int64
0
4
n_domains
int64
1
6
max_exp
int64
1
34
exp_l1
int64
2
134
complexity
float64
0
113
score
float64
-104.8
10
plausible
bool
2 classes
exponents
stringlengths
27
177
5
bfield,energy,mass,resistance,time
m·t·E·R·B
em,mechanics
m²·t⁻³·E⁻¹·R·B⁻²
E = k₀ · m²·t⁻³·R·B⁻²
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-3", "energy": "-1", "resistance": "1", "bfield": "-2"}
5
conductivity,energy,mass,resistance,time
m·t·E·R·σ
em,mechanics
m·t⁻²·E⁻¹·R⁻²·σ⁻²
m = k₀ · t²·E·R²·σ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "energy": "-1", "resistance": "-2", "conductivity": "-2"}
5
energy,mass,resistance,resistivity,time
m·t·E·R·ρ_e
em,mechanics
m·t⁻²·E⁻¹·R⁻²·ρ_e²
m = k₀ · t²·E·R²·ρ_e⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "energy": "-1", "resistance": "-2", "resistivity": "2"}
5
bfield,capacitance,energy,mass,time
m·t·E·C_e·B
em,mechanics
m²·t⁻²·E⁻¹·C_e⁻¹·B⁻²
E = k₀ · m²·t⁻²·C_e⁻¹·B⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "time": "-2", "energy": "-1", "capacitance": "-1", "bfield": "-2"}
5
capacitance,energy,mass,permittivity,time
m·t·E·C_e·ε
em,mechanics
m·t⁻²·E⁻¹·C_e²·ε⁻²
m = k₀ · t²·E·C_e⁻²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "energy": "-1", "capacitance": "2", "permittivity": "-2"}
5
capacitance,energy,mass,permeability,time
m·t·E·C_e·μ₀
em,mechanics
m·t²·E⁻¹·C_e⁻²·μ₀⁻²
m = k₀ · t⁻²·E·C_e²·μ₀²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "energy": "-1", "capacitance": "-2", "permeability": "-2"}
5
capacitance,conductivity,energy,mass,time
m·t·E·C_e·σ
em,mechanics
m·t⁻⁴·E⁻¹·C_e²·σ⁻²
m = k₀ · t⁴·E·C_e⁻²·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "energy": "-1", "capacitance": "2", "conductivity": "-2"}
5
capacitance,energy,mass,resistivity,time
m·t·E·C_e·ρ_e
em,mechanics
m·t⁻⁴·E⁻¹·C_e²·ρ_e²
m = k₀ · t⁴·E·C_e⁻²·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "energy": "-1", "capacitance": "2", "resistivity": "2"}
5
bfield,energy,inductance,mass,time
m·t·E·L_e·B
em,mechanics
m²·t⁻⁴·E⁻¹·L_e·B⁻²
E = k₀ · m²·t⁻⁴·L_e·B⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "time": "-4", "energy": "-1", "inductance": "1", "bfield": "-2"}
5
energy,inductance,mass,permittivity,time
m·t·E·L_e·ε
em,mechanics
m·t²·E⁻¹·L_e⁻²·ε⁻²
m = k₀ · t⁻²·E·L_e²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "energy": "-1", "inductance": "-2", "permittivity": "-2"}
5
energy,inductance,mass,permeability,time
m·t·E·L_e·μ₀
em,mechanics
m·t⁻²·E⁻¹·L_e²·μ₀⁻²
m = k₀ · t²·E·L_e⁻²·μ₀²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "energy": "-1", "inductance": "2", "permeability": "-2"}
5
efield,energy,mag_flux,mass,time
m·t·E·E_f·Φ
em,mechanics
m·t⁻⁴·E⁻¹·E_f⁻²·Φ²
m = k₀ · t⁴·E·E_f²·Φ⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "energy": "-1", "efield": "-2", "mag_flux": "2"}
5
efield,energy,mass,permittivity,time
m·t·E·E_f·ε
em,mechanics
m³·t⁻⁶·E⁻¹·E_f⁻⁴·ε⁻²
E = k₀ · m³·t⁻⁶·E_f⁻⁴·ε⁻²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "time": "-6", "energy": "-1", "efield": "-4", "permittivity": "-2"}
5
efield,energy,mass,permeability,time
m·t·E·E_f·μ₀
em,mechanics
m·t⁻⁶·E·E_f⁻⁴·μ₀²
m = k₀ · t⁶·E⁻¹·E_f⁴·μ₀⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "time": "-6", "energy": "1", "efield": "-4", "permeability": "2"}
5
conductivity,efield,energy,mass,time
m·t·E·E_f·σ
em,mechanics
m³·t⁻⁸·E⁻¹·E_f⁻⁴·σ⁻²
E = k₀ · m³·t⁻⁸·E_f⁻⁴·σ⁻²
null
0
2
8
18
16.2
-6.7
false
{"mass": "3", "time": "-8", "energy": "-1", "efield": "-4", "conductivity": "-2"}
5
efield,energy,mass,resistivity,time
m·t·E·E_f·ρ_e
em,mechanics
m³·t⁻⁸·E⁻¹·E_f⁻⁴·ρ_e²
E = k₀ · m³·t⁻⁸·E_f⁻⁴·ρ_e²
null
0
2
8
18
16.2
-6.7
false
{"mass": "3", "time": "-8", "energy": "-1", "efield": "-4", "resistivity": "2"}
5
efield,elem_charge,energy,mass,time
m·t·E·E_f·e
constants,em,mechanics
m·t⁻²·E·E_f⁻²·e⁻²
m = k₀ · t²·E⁻¹·E_f²·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "time": "-2", "energy": "1", "efield": "-2", "elem_charge": "-2"}
5
bfield,energy,mag_flux,mass,time
m·t·E·B·Φ
em,mechanics
m·t⁻²·E⁻¹·B⁻¹·Φ
m = k₀ · t²·E·B·Φ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "energy": "-1", "bfield": "-1", "mag_flux": "1"}
5
bfield,energy,mass,permittivity,time
m·t·E·B·ε
em,mechanics
m⁵·t⁻⁶·E⁻³·B⁻⁴·ε⁻²
ε = k₀ · m⁵ᐟ²·t⁻³·E⁻³ᐟ²·B⁻²
null
0
2
6
20
16.6
-7.1
false
{"mass": "5", "time": "-6", "energy": "-3", "bfield": "-4", "permittivity": "-2"}
5
bfield,energy,mass,permeability,time
m·t·E·B·μ₀
em,mechanics
m³·t⁻⁶·E⁻¹·B⁻⁴·μ₀²
E = k₀ · m³·t⁻⁶·B⁻⁴·μ₀²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "time": "-6", "energy": "-1", "bfield": "-4", "permeability": "2"}
5
bfield,conductivity,energy,mass,time
m·t·E·B·σ
em,mechanics
m⁵·t⁻⁸·E⁻³·B⁻⁴·σ⁻²
σ = k₀ · m⁵ᐟ²·t⁻⁴·E⁻³ᐟ²·B⁻²
null
0
2
8
22
19
-9.5
false
{"mass": "5", "time": "-8", "energy": "-3", "bfield": "-4", "conductivity": "-2"}
5
bfield,energy,mass,resistivity,time
m·t·E·B·ρ_e
em,mechanics
m⁵·t⁻⁸·E⁻³·B⁻⁴·ρ_e²
ρ_e = k₀ · m⁻⁵ᐟ²·t⁴·E³ᐟ²·B²
null
0
2
8
22
19
-9.5
false
{"mass": "5", "time": "-8", "energy": "-3", "bfield": "-4", "resistivity": "2"}
5
energy,mag_flux,mass,permittivity,time
m·t·E·Φ·ε
em,mechanics
m·t²·E·Φ⁻⁴·ε⁻²
m = k₀ · t⁻²·E⁻¹·Φ⁴·ε²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "2", "energy": "1", "mag_flux": "-4", "permittivity": "-2"}
5
energy,mag_flux,mass,permeability,time
m·t·E·Φ·μ₀
em,mechanics
m·t⁻²·E⁻³·Φ⁴·μ₀⁻²
m = k₀ · t²·E³·Φ⁻⁴·μ₀²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "-2", "energy": "-3", "mag_flux": "4", "permeability": "-2"}
5
elem_charge,energy,mass,permittivity,time
m·t·E·ε·e
constants,em,mechanics
m·t⁻²·E⁻³·ε⁻²·e⁴
m = k₀ · t²·E³·ε²·e⁻⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "1", "time": "-2", "energy": "-3", "permittivity": "-2", "elem_charge": "4"}
5
conductivity,energy,mass,permeability,time
m·t·E·μ₀·σ
em,mechanics
m·t⁻¹·E⁻¹·μ₀⁻¹·σ⁻¹
m = k₀ · t·E·μ₀·σ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "energy": "-1", "permeability": "-1", "conductivity": "-1"}
5
energy,mass,permeability,resistivity,time
m·t·E·μ₀·ρ_e
em,mechanics
m·t⁻¹·E⁻¹·μ₀⁻¹·ρ_e
m = k₀ · t·E·μ₀·ρ_e⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "energy": "-1", "permeability": "-1", "resistivity": "1"}
5
elem_charge,energy,mass,permeability,time
m·t·E·μ₀·e
constants,em,mechanics
m·t²·E·μ₀⁻²·e⁻⁴
m = k₀ · t⁻²·E⁻¹·μ₀²·e⁴
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "time": "2", "energy": "1", "permeability": "-2", "elem_charge": "-4"}
5
conductivity,elem_charge,energy,mass,time
m·t·E·σ·e
constants,em,mechanics
m·t⁻⁴·E⁻³·σ⁻²·e⁴
m = k₀ · t⁴·E³·σ²·e⁻⁴
null
1
3
4
14
12
-3
false
{"mass": "1", "time": "-4", "energy": "-3", "conductivity": "-2", "elem_charge": "4"}
5
elem_charge,energy,mass,resistivity,time
m·t·E·ρ_e·e
constants,em,mechanics
m·t⁻⁴·E⁻³·ρ_e²·e⁴
m = k₀ · t⁴·E³·ρ_e⁻²·e⁻⁴
null
1
3
4
14
12
-3
false
{"mass": "1", "time": "-4", "energy": "-3", "resistivity": "2", "elem_charge": "4"}
5
amount,concentration,energy,mass,time
m·t·E·n·c_n
chemistry,mechanics
m³·t⁻⁶·E⁻³·n²·c_n⁻²
n = k₀ · m⁻³ᐟ²·t³·E³ᐟ²·c_n
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "time": "-6", "energy": "-3", "amount": "2", "concentration": "-2"}
5
concentration,energy,mass,molar_mass,time
m·t·E·M_m·c_n
chemistry,mechanics
m⁵·t⁻⁶·E⁻³·M_m⁻²·c_n⁻²
M_m = k₀ · m⁵ᐟ²·t⁻³·E⁻³ᐟ²·c_n⁻¹
null
0
2
6
18
15.2
-5.7
false
{"mass": "5", "time": "-6", "energy": "-3", "molar_mass": "-2", "concentration": "-2"}
5
concentration,energy,mass,molar_energy,time
m·t·E·c_n·E_m
chemistry,mechanics
m³·t⁻⁶·E⁻¹·c_n⁻²·E_m⁻²
E = k₀ · m³·t⁻⁶·c_n⁻²·E_m⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "3", "time": "-6", "energy": "-1", "concentration": "-2", "molar_energy": "-2"}
6
boltzmann,concentration,energy,gas_constant,mass,time
m·t·E·c_n·R·k_B
chemistry,constants,mechanics
m³·t⁻⁶·E⁻³·c_n⁻²·R⁻²·k_B²
c_n = k₀ · m³ᐟ²·t⁻³·E⁻³ᐟ²·R⁻¹·k_B
null
1
3
6
18
16.1
-7.1
false
{"mass": "3", "time": "-6", "energy": "-3", "concentration": "-2", "gas_constant": "-2", "boltzmann": "2"}
5
cat_activity,concentration,energy,mass,time
m·t·E·c_n·z
chemistry,mechanics
m³·t⁻⁴·E⁻³·c_n⁻²·z²
c_n = k₀ · m³ᐟ²·t⁻²·E⁻³ᐟ²·z
null
0
2
4
14
11.4
-1.9
false
{"mass": "3", "time": "-4", "energy": "-3", "concentration": "-2", "cat_activity": "2"}
5
avogadro,concentration,energy,mass,time
m·t·E·c_n·N_A
chemistry,constants,mechanics
m³·t⁻⁶·E⁻³·c_n⁻²·N_A⁻²
c_n = k₀ · m³ᐟ²·t⁻³·E⁻³ᐟ²·N_A⁻¹
null
1
3
6
16
14.4
-5.4
false
{"mass": "3", "time": "-6", "energy": "-3", "concentration": "-2", "avogadro": "-2"}
5
energy,illuminance,lum_intensity,mass,time
m·t·E·I_v·E_v
mechanics,photometry
m·t⁻²·E⁻¹·I_v·E_v⁻¹
m = k₀ · t²·E·I_v⁻¹·E_v
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "energy": "-1", "lum_intensity": "1", "illuminance": "-1"}
5
energy,lum_intensity,luminance,mass,time
m·t·E·I_v·L_v
mechanics,photometry
m·t⁻²·E⁻¹·I_v·L_v⁻¹
m = k₀ · t²·E·I_v⁻¹·L_v
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "energy": "-1", "lum_intensity": "1", "luminance": "-1"}
4
energy,grav_const,mass,time
m·t·E·G
constants,mechanics
m⁵·t⁻²·E⁻³·G²
t = k₀ · m⁵ᐟ²·E⁻³ᐟ²·G
null
1
2
5
12
10.2
-0.7
false
{"mass": "5", "time": "-2", "energy": "-3", "grav_const": "2"}
4
mass,pressure,time,torque
m·t·τ·P_p
mechanics
m³·t⁻⁶·τ⁻¹·P_p⁻²
τ = k₀ · m³·t⁻⁶·P_p⁻²
null
0
1
6
12
10.1
-0.1
false
{"mass": "3", "time": "-6", "torque": "-1", "pressure": "-2"}
4
density,mass,time,torque
m·t·τ·ρ
mechanics
m⁵·t⁻⁶·τ⁻³·ρ⁻²
ρ = k₀ · m⁵ᐟ²·t⁻³·τ⁻³ᐟ²
null
0
1
6
16
12.9
-2.9
false
{"mass": "5", "time": "-6", "torque": "-3", "density": "-2"}
4
mass,time,torque,viscosity
m·t·τ·μ
mechanics
m³·t⁻⁴·τ⁻¹·μ⁻²
τ = k₀ · m³·t⁻⁴·μ⁻²
null
0
1
4
10
7.7
2.3
false
{"mass": "3", "time": "-4", "torque": "-1", "viscosity": "-2"}
4
kin_viscosity,mass,time,torque
m·t·τ·ν
mechanics
m·t⁻¹·τ⁻¹·ν
m = k₀ · t·τ·ν⁻¹
null
0
1
1
4
2
8
true
{"mass": "1", "time": "-1", "torque": "-1", "kin_viscosity": "1"}
4
area,mass,time,torque
m·t·τ·A
mechanics
m·t⁻²·τ⁻¹·A
m = k₀ · t²·τ·A⁻¹
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "-2", "torque": "-1", "area": "1"}
4
mass,time,torque,volume
m·t·τ·V
mechanics
m³·t⁻⁶·τ⁻³·V²
V = k₀ · m⁻³ᐟ²·t³·τ³ᐟ²
null
0
1
6
14
11.5
-1.5
false
{"mass": "3", "time": "-6", "torque": "-3", "volume": "2"}
4
flowrate,mass,time,torque
m·t·τ·Q
mechanics
m³·t⁻⁴·τ⁻³·Q²
Q = k₀ · m⁻³ᐟ²·t²·τ³ᐟ²
null
0
1
4
12
9.1
0.9
false
{"mass": "3", "time": "-4", "torque": "-3", "flowrate": "2"}
5
mass,temperature,thermal_cond,time,torque
m·t·τ·Θ·κ
mechanics,thermo
m·t⁻⁴·τ·Θ⁻²·κ⁻²
m = k₀ · t⁴·τ⁻¹·Θ²·κ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "1", "temperature": "-2", "thermal_cond": "-2"}
6
concentration,gas_constant,mass,temperature,time,torque
m·t·τ·Θ·c_n·R
chemistry,mechanics,thermo
m³·t⁻⁶·τ⁻¹·Θ⁻²·c_n⁻²·R⁻²
τ = k₀ · m³·t⁻⁶·Θ⁻²·c_n⁻²·R⁻²
null
0
3
6
16
14.7
-5.7
false
{"mass": "3", "time": "-6", "torque": "-1", "temperature": "-2", "concentration": "-2", "gas_constant": "-2"}
5
entropy,mass,thermal_cond,time,torque
m·t·τ·S_e·κ
mechanics,thermo
m·t⁻⁴·τ⁻¹·S_e²·κ⁻²
m = k₀ · t⁴·τ·S_e⁻²·κ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "-1", "entropy": "2", "thermal_cond": "-2"}
6
concentration,entropy,gas_constant,mass,time,torque
m·t·τ·S_e·c_n·R
chemistry,mechanics,thermo
m³·t⁻⁶·τ⁻³·S_e²·c_n⁻²·R⁻²
S_e = k₀ · m⁻³ᐟ²·t³·τ³ᐟ²·c_n·R
null
0
3
6
18
16.1
-7.1
false
{"mass": "3", "time": "-6", "torque": "-3", "entropy": "2", "concentration": "-2", "gas_constant": "-2"}
5
heat_capacity,mass,thermal_cond,time,torque
m·t·τ·C·κ
mechanics,thermo
m·t⁻⁴·τ⁻¹·C²·κ⁻²
m = k₀ · t⁴·τ·C⁻²·κ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "-1", "heat_capacity": "2", "thermal_cond": "-2"}
6
concentration,gas_constant,heat_capacity,mass,time,torque
m·t·τ·C·c_n·R
chemistry,mechanics,thermo
m³·t⁻⁶·τ⁻³·C²·c_n⁻²·R⁻²
C = k₀ · m⁻³ᐟ²·t³·τ³ᐟ²·c_n·R
null
0
3
6
18
16.1
-7.1
false
{"mass": "3", "time": "-6", "torque": "-3", "heat_capacity": "2", "concentration": "-2", "gas_constant": "-2"}
5
mass,specific_heat,thermal_cond,time,torque
m·t·τ·c·κ
mechanics,thermo
m³·t⁻⁴·τ⁻¹·c²·κ⁻²
τ = k₀ · m³·t⁻⁴·c²·κ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "3", "time": "-4", "torque": "-1", "specific_heat": "2", "thermal_cond": "-2"}
6
concentration,gas_constant,mass,specific_heat,time,torque
m·t·τ·c·c_n·R
chemistry,mechanics,thermo
m⁵·t⁻⁶·τ⁻³·c²·c_n⁻²·R⁻²
c = k₀ · m⁻⁵ᐟ²·t³·τ³ᐟ²·c_n·R
null
0
3
6
20
17.5
-8.5
false
{"mass": "5", "time": "-6", "torque": "-3", "specific_heat": "2", "concentration": "-2", "gas_constant": "-2"}
5
expansion,mass,thermal_cond,time,torque
m·t·τ·κ·β
mechanics,thermo
m·t⁻⁴·τ·κ⁻²·β²
m = k₀ · t⁴·τ⁻¹·κ²·β⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "1", "thermal_cond": "-2", "expansion": "2"}
6
amount,gas_constant,mass,thermal_cond,time,torque
m·t·τ·κ·n·R
chemistry,mechanics,thermo
m·t⁻⁴·τ⁻¹·κ⁻²·n²·R²
m = k₀ · t⁴·τ·κ²·n⁻²·R⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "time": "-4", "torque": "-1", "thermal_cond": "-2", "amount": "2", "gas_constant": "2"}
6
gas_constant,mass,molar_mass,thermal_cond,time,torque
m·t·τ·κ·M_m·R
chemistry,mechanics,thermo
m³·t⁻⁴·τ⁻¹·κ⁻²·M_m⁻²·R²
τ = k₀ · m³·t⁻⁴·κ⁻²·M_m⁻²·R²
null
0
3
4
14
12.3
-3.3
false
{"mass": "3", "time": "-4", "torque": "-1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
concentration,gas_constant,mass,thermal_cond,time,torque
m·t·τ·κ·c_n·R
chemistry,mechanics,thermo
m·t⁻¹·τ⁻¹·κ·c_n⁻¹·R⁻¹
m = k₀ · t·τ·κ⁻¹·c_n·R
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "time": "-1", "torque": "-1", "thermal_cond": "1", "concentration": "-1", "gas_constant": "-1"}
6
gas_constant,mass,molar_energy,thermal_cond,time,torque
m·t·τ·κ·E_m·R
chemistry,mechanics,thermo
m·t⁻⁴·τ·κ⁻²·E_m⁻²·R²
m = k₀ · t⁴·τ⁻¹·κ²·E_m²·R⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "time": "-4", "torque": "1", "thermal_cond": "-2", "molar_energy": "-2", "gas_constant": "2"}
6
cat_activity,gas_constant,mass,thermal_cond,time,torque
m·t·τ·κ·R·z
chemistry,mechanics,thermo
m·t⁻²·τ⁻¹·κ⁻²·R²·z²
m = k₀ · t²·τ·κ²·R⁻²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "time": "-2", "torque": "-1", "thermal_cond": "-2", "gas_constant": "2", "cat_activity": "2"}
6
avogadro,gas_constant,mass,thermal_cond,time,torque
m·t·τ·κ·R·N_A
chemistry,constants,mechanics,thermo
m·t⁻⁴·τ⁻¹·κ⁻²·R²·N_A⁻²
m = k₀ · t⁴·τ·κ²·R⁻²·N_A²
null
1
4
4
12
11.5
-3
false
{"mass": "1", "time": "-4", "torque": "-1", "thermal_cond": "-2", "gas_constant": "2", "avogadro": "-2"}
5
boltzmann,mass,thermal_cond,time,torque
m·t·τ·κ·k_B
constants,mechanics,thermo
m·t⁻⁴·τ⁻¹·κ⁻²·k_B²
m = k₀ · t⁴·τ·κ²·k_B⁻²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "time": "-4", "torque": "-1", "thermal_cond": "-2", "boltzmann": "2"}
4
mass,thermal_diff,time,torque
m·t·τ·α
mechanics,thermo
m·t⁻¹·τ⁻¹·α
m = k₀ · t·τ·α⁻¹
null
0
2
1
4
2.6
6.9
true
{"mass": "1", "time": "-1", "torque": "-1", "thermal_diff": "1"}
6
concentration,expansion,gas_constant,mass,time,torque
m·t·τ·β·c_n·R
chemistry,mechanics,thermo
m³·t⁻⁶·τ⁻¹·β²·c_n⁻²·R⁻²
τ = k₀ · m³·t⁻⁶·β²·c_n⁻²·R⁻²
null
0
3
6
16
14.7
-5.7
false
{"mass": "3", "time": "-6", "torque": "-1", "expansion": "2", "concentration": "-2", "gas_constant": "-2"}
5
charge,efield,mass,time,torque
m·t·τ·q·E_f
em,mechanics
m·t⁻²·τ·q⁻²·E_f⁻²
m = k₀ · t²·τ⁻¹·q²·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "1", "charge": "-2", "efield": "-2"}
5
charge,mass,permittivity,time,torque
m·t·τ·q·ε
em,mechanics
m·t⁻²·τ⁻³·q⁴·ε⁻²
m = k₀ · t²·τ³·q⁻⁴·ε²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "-2", "torque": "-3", "charge": "4", "permittivity": "-2"}
5
charge,mass,permeability,time,torque
m·t·τ·q·μ₀
em,mechanics
m·t²·τ·q⁻⁴·μ₀⁻²
m = k₀ · t⁻²·τ⁻¹·q⁴·μ₀²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "2", "torque": "1", "charge": "-4", "permeability": "-2"}
5
charge,conductivity,mass,time,torque
m·t·τ·q·σ
em,mechanics
m·t⁻⁴·τ⁻³·q⁴·σ⁻²
m = k₀ · t⁴·τ³·q⁻⁴·σ²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "time": "-4", "torque": "-3", "charge": "4", "conductivity": "-2"}
5
charge,mass,resistivity,time,torque
m·t·τ·q·ρ_e
em,mechanics
m·t⁻⁴·τ⁻³·q⁴·ρ_e²
m = k₀ · t⁴·τ³·q⁻⁴·ρ_e⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "time": "-4", "torque": "-3", "charge": "4", "resistivity": "2"}
5
current,efield,mass,time,torque
m·t·τ·i·E_f
em,mechanics
m·t⁻⁴·τ·i⁻²·E_f⁻²
m = k₀ · t⁴·τ⁻¹·i²·E_f²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "1", "current": "-2", "efield": "-2"}
5
current,mass,permittivity,time,torque
m·t·τ·i·ε
em,mechanics
m·t²·τ⁻³·i⁴·ε⁻²
m = k₀ · t⁻²·τ³·i⁻⁴·ε²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "2", "torque": "-3", "current": "4", "permittivity": "-2"}
5
current,mass,permeability,time,torque
m·t·τ·i·μ₀
em,mechanics
m·t⁻²·τ·i⁻⁴·μ₀⁻²
m = k₀ · t²·τ⁻¹·i⁴·μ₀²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-2", "torque": "1", "current": "-4", "permeability": "-2"}
5
efield,mass,time,torque,voltage
m·t·τ·U·E_f
em,mechanics
m·t⁻²·τ⁻¹·U²·E_f⁻²
m = k₀ · t²·τ·U⁻²·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "-1", "voltage": "2", "efield": "-2"}
5
bfield,mass,time,torque,voltage
m·t·τ·U·B
em,mechanics
m·t⁻¹·τ⁻¹·U·B⁻¹
m = k₀ · t·τ·U⁻¹·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "torque": "-1", "voltage": "1", "bfield": "-1"}
5
mass,permittivity,time,torque,voltage
m·t·τ·U·ε
em,mechanics
m·t⁻²·τ·U⁻⁴·ε⁻²
m = k₀ · t²·τ⁻¹·U⁴·ε²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-2", "torque": "1", "voltage": "-4", "permittivity": "-2"}
5
mass,permeability,time,torque,voltage
m·t·τ·U·μ₀
em,mechanics
m·t²·τ⁻³·U⁴·μ₀⁻²
m = k₀ · t⁻²·τ³·U⁻⁴·μ₀²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "2", "torque": "-3", "voltage": "4", "permeability": "-2"}
5
conductivity,mass,time,torque,voltage
m·t·τ·U·σ
em,mechanics
m·t⁻⁴·τ·U⁻⁴·σ⁻²
m = k₀ · t⁴·τ⁻¹·U⁴·σ²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "-4", "torque": "1", "voltage": "-4", "conductivity": "-2"}
5
mass,resistivity,time,torque,voltage
m·t·τ·U·ρ_e
em,mechanics
m·t⁻⁴·τ·U⁻⁴·ρ_e²
m = k₀ · t⁴·τ⁻¹·U⁴·ρ_e⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "time": "-4", "torque": "1", "voltage": "-4", "resistivity": "2"}
5
bfield,mass,resistance,time,torque
m·t·τ·R·B
em,mechanics
m²·t⁻³·τ⁻¹·R·B⁻²
τ = k₀ · m²·t⁻³·R·B⁻²
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-3", "torque": "-1", "resistance": "1", "bfield": "-2"}
5
conductivity,mass,resistance,time,torque
m·t·τ·R·σ
em,mechanics
m·t⁻²·τ⁻¹·R⁻²·σ⁻²
m = k₀ · t²·τ·R²·σ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "-1", "resistance": "-2", "conductivity": "-2"}
5
mass,resistance,resistivity,time,torque
m·t·τ·R·ρ_e
em,mechanics
m·t⁻²·τ⁻¹·R⁻²·ρ_e²
m = k₀ · t²·τ·R²·ρ_e⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "-1", "resistance": "-2", "resistivity": "2"}
5
bfield,capacitance,mass,time,torque
m·t·τ·C_e·B
em,mechanics
m²·t⁻²·τ⁻¹·C_e⁻¹·B⁻²
τ = k₀ · m²·t⁻²·C_e⁻¹·B⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "time": "-2", "torque": "-1", "capacitance": "-1", "bfield": "-2"}
5
capacitance,mass,permittivity,time,torque
m·t·τ·C_e·ε
em,mechanics
m·t⁻²·τ⁻¹·C_e²·ε⁻²
m = k₀ · t²·τ·C_e⁻²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "-1", "capacitance": "2", "permittivity": "-2"}
5
capacitance,mass,permeability,time,torque
m·t·τ·C_e·μ₀
em,mechanics
m·t²·τ⁻¹·C_e⁻²·μ₀⁻²
m = k₀ · t⁻²·τ·C_e²·μ₀²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "torque": "-1", "capacitance": "-2", "permeability": "-2"}
5
capacitance,conductivity,mass,time,torque
m·t·τ·C_e·σ
em,mechanics
m·t⁻⁴·τ⁻¹·C_e²·σ⁻²
m = k₀ · t⁴·τ·C_e⁻²·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "-1", "capacitance": "2", "conductivity": "-2"}
5
capacitance,mass,resistivity,time,torque
m·t·τ·C_e·ρ_e
em,mechanics
m·t⁻⁴·τ⁻¹·C_e²·ρ_e²
m = k₀ · t⁴·τ·C_e⁻²·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "-1", "capacitance": "2", "resistivity": "2"}
5
bfield,inductance,mass,time,torque
m·t·τ·L_e·B
em,mechanics
m²·t⁻⁴·τ⁻¹·L_e·B⁻²
τ = k₀ · m²·t⁻⁴·L_e·B⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "time": "-4", "torque": "-1", "inductance": "1", "bfield": "-2"}
5
inductance,mass,permittivity,time,torque
m·t·τ·L_e·ε
em,mechanics
m·t²·τ⁻¹·L_e⁻²·ε⁻²
m = k₀ · t⁻²·τ·L_e²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "torque": "-1", "inductance": "-2", "permittivity": "-2"}
5
inductance,mass,permeability,time,torque
m·t·τ·L_e·μ₀
em,mechanics
m·t⁻²·τ⁻¹·L_e²·μ₀⁻²
m = k₀ · t²·τ·L_e⁻²·μ₀²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "torque": "-1", "inductance": "2", "permeability": "-2"}
5
efield,mag_flux,mass,time,torque
m·t·τ·E_f·Φ
em,mechanics
m·t⁻⁴·τ⁻¹·E_f⁻²·Φ²
m = k₀ · t⁴·τ·E_f²·Φ⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "time": "-4", "torque": "-1", "efield": "-2", "mag_flux": "2"}
5
efield,mass,permittivity,time,torque
m·t·τ·E_f·ε
em,mechanics
m³·t⁻⁶·τ⁻¹·E_f⁻⁴·ε⁻²
τ = k₀ · m³·t⁻⁶·E_f⁻⁴·ε⁻²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "time": "-6", "torque": "-1", "efield": "-4", "permittivity": "-2"}
5
efield,mass,permeability,time,torque
m·t·τ·E_f·μ₀
em,mechanics
m·t⁻⁶·τ·E_f⁻⁴·μ₀²
m = k₀ · t⁶·τ⁻¹·E_f⁴·μ₀⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "time": "-6", "torque": "1", "efield": "-4", "permeability": "2"}
5
conductivity,efield,mass,time,torque
m·t·τ·E_f·σ
em,mechanics
m³·t⁻⁸·τ⁻¹·E_f⁻⁴·σ⁻²
τ = k₀ · m³·t⁻⁸·E_f⁻⁴·σ⁻²
null
0
2
8
18
16.2
-6.7
false
{"mass": "3", "time": "-8", "torque": "-1", "efield": "-4", "conductivity": "-2"}
5
efield,mass,resistivity,time,torque
m·t·τ·E_f·ρ_e
em,mechanics
m³·t⁻⁸·τ⁻¹·E_f⁻⁴·ρ_e²
τ = k₀ · m³·t⁻⁸·E_f⁻⁴·ρ_e²
null
0
2
8
18
16.2
-6.7
false
{"mass": "3", "time": "-8", "torque": "-1", "efield": "-4", "resistivity": "2"}
5
efield,elem_charge,mass,time,torque
m·t·τ·E_f·e
constants,em,mechanics
m·t⁻²·τ·E_f⁻²·e⁻²
m = k₀ · t²·τ⁻¹·E_f²·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "time": "-2", "torque": "1", "efield": "-2", "elem_charge": "-2"}
5
bfield,mag_flux,mass,time,torque
m·t·τ·B·Φ
em,mechanics
m·t⁻²·τ⁻¹·B⁻¹·Φ
m = k₀ · t²·τ·B·Φ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "torque": "-1", "bfield": "-1", "mag_flux": "1"}
5
bfield,mass,permittivity,time,torque
m·t·τ·B·ε
em,mechanics
m⁵·t⁻⁶·τ⁻³·B⁻⁴·ε⁻²
ε = k₀ · m⁵ᐟ²·t⁻³·τ⁻³ᐟ²·B⁻²
null
0
2
6
20
16.6
-7.1
false
{"mass": "5", "time": "-6", "torque": "-3", "bfield": "-4", "permittivity": "-2"}
5
bfield,mass,permeability,time,torque
m·t·τ·B·μ₀
em,mechanics
m³·t⁻⁶·τ⁻¹·B⁻⁴·μ₀²
τ = k₀ · m³·t⁻⁶·B⁻⁴·μ₀²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "time": "-6", "torque": "-1", "bfield": "-4", "permeability": "2"}
5
bfield,conductivity,mass,time,torque
m·t·τ·B·σ
em,mechanics
m⁵·t⁻⁸·τ⁻³·B⁻⁴·σ⁻²
σ = k₀ · m⁵ᐟ²·t⁻⁴·τ⁻³ᐟ²·B⁻²
null
0
2
8
22
19
-9.5
false
{"mass": "5", "time": "-8", "torque": "-3", "bfield": "-4", "conductivity": "-2"}
5
bfield,mass,resistivity,time,torque
m·t·τ·B·ρ_e
em,mechanics
m⁵·t⁻⁸·τ⁻³·B⁻⁴·ρ_e²
ρ_e = k₀ · m⁻⁵ᐟ²·t⁴·τ³ᐟ²·B²
null
0
2
8
22
19
-9.5
false
{"mass": "5", "time": "-8", "torque": "-3", "bfield": "-4", "resistivity": "2"}