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
conductivity,elem_charge,mass,power,time
m·t·P·σ·e
constants,em,mechanics
m·t⁻⁷·P⁻³·σ⁻²·e⁴
m = k₀ · t⁷·P³·σ²·e⁻⁴
null
1
3
7
17
15.6
-6.6
false
{"mass": "1", "time": "-7", "power": "-3", "conductivity": "-2", "elem_charge": "4"}
5
elem_charge,mass,power,resistivity,time
m·t·P·ρ_e·e
constants,em,mechanics
m·t⁻⁷·P⁻³·ρ_e²·e⁴
m = k₀ · t⁷·P³·ρ_e⁻²·e⁻⁴
null
1
3
7
17
15.6
-6.6
false
{"mass": "1", "time": "-7", "power": "-3", "resistivity": "2", "elem_charge": "4"}
5
amount,concentration,mass,power,time
m·t·P·n·c_n
chemistry,mechanics
m³·t⁻⁹·P⁻³·n²·c_n⁻²
n = k₀ · m⁻³ᐟ²·t⁹ᐟ²·P³ᐟ²·c_n
null
0
2
9
19
17.4
-7.9
false
{"mass": "3", "time": "-9", "power": "-3", "amount": "2", "concentration": "-2"}
5
concentration,mass,molar_mass,power,time
m·t·P·M_m·c_n
chemistry,mechanics
m⁵·t⁻⁹·P⁻³·M_m⁻²·c_n⁻²
M_m = k₀ · m⁵ᐟ²·t⁻⁹ᐟ²·P⁻³ᐟ²·c_n⁻¹
null
0
2
9
21
18.8
-9.3
false
{"mass": "5", "time": "-9", "power": "-3", "molar_mass": "-2", "concentration": "-2"}
5
mass,molar_energy,molar_mass,power,time
m·t·P·M_m·E_m
chemistry,mechanics
m·t⁻¹·P⁻¹·M_m⁻¹·E_m
m = k₀ · t·P·M_m·E_m⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "power": "-1", "molar_mass": "-1", "molar_energy": "1"}
5
concentration,mass,molar_energy,power,time
m·t·P·c_n·E_m
chemistry,mechanics
m³·t⁻⁷·P⁻¹·c_n⁻²·E_m⁻²
P = k₀ · m³·t⁻⁷·c_n⁻²·E_m⁻²
null
0
2
7
15
13.6
-4.1
false
{"mass": "3", "time": "-7", "power": "-1", "concentration": "-2", "molar_energy": "-2"}
6
boltzmann,concentration,gas_constant,mass,power,time
m·t·P·c_n·R·k_B
chemistry,constants,mechanics
m³·t⁻⁹·P⁻³·c_n⁻²·R⁻²·k_B²
c_n = k₀ · m³ᐟ²·t⁻⁹ᐟ²·P⁻³ᐟ²·R⁻¹·k_B
null
1
3
9
21
19.7
-10.7
false
{"mass": "3", "time": "-9", "power": "-3", "concentration": "-2", "gas_constant": "-2", "boltzmann": "2"}
5
cat_activity,concentration,mass,power,time
m·t·P·c_n·z
chemistry,mechanics
m³·t⁻⁷·P⁻³·c_n⁻²·z²
c_n = k₀ · m³ᐟ²·t⁻⁷ᐟ²·P⁻³ᐟ²·z
null
0
2
7
17
15
-5.5
false
{"mass": "3", "time": "-7", "power": "-3", "concentration": "-2", "cat_activity": "2"}
5
avogadro,concentration,mass,power,time
m·t·P·c_n·N_A
chemistry,constants,mechanics
m³·t⁻⁹·P⁻³·c_n⁻²·N_A⁻²
c_n = k₀ · m³ᐟ²·t⁻⁹ᐟ²·P⁻³ᐟ²·N_A⁻¹
null
1
3
9
19
18
-9
false
{"mass": "3", "time": "-9", "power": "-3", "concentration": "-2", "avogadro": "-2"}
5
illuminance,lum_intensity,mass,power,time
m·t·P·I_v·E_v
mechanics,photometry
m·t⁻³·P⁻¹·I_v·E_v⁻¹
m = k₀ · t³·P·I_v⁻¹·E_v
null
0
2
3
7
6
3.5
true
{"mass": "1", "time": "-3", "power": "-1", "lum_intensity": "1", "illuminance": "-1"}
5
lum_intensity,luminance,mass,power,time
m·t·P·I_v·L_v
mechanics,photometry
m·t⁻³·P⁻¹·I_v·L_v⁻¹
m = k₀ · t³·P·I_v⁻¹·L_v
null
0
2
3
7
6
3.5
true
{"mass": "1", "time": "-3", "power": "-1", "lum_intensity": "1", "luminance": "-1"}
4
light_speed,mass,power,time
m·t·P·c₀
constants,mechanics
m·t⁻¹·P⁻¹·c₀²
m = k₀ · t·P·c₀⁻²
null
1
2
2
5
3.8
5.7
true
{"mass": "1", "time": "-1", "power": "-1", "light_speed": "2"}
4
grav_const,mass,power,time
m·t·P·G
constants,mechanics
m⁵·t⁻⁵·P⁻³·G²
G = k₀ · m⁻⁵ᐟ²·t⁵ᐟ²·P³ᐟ²
null
1
2
5
15
12.3
-2.8
false
{"mass": "5", "time": "-5", "power": "-3", "grav_const": "2"}
4
ang_momentum,mass,momentum,time
m·t·p·Lₐ
mechanics
m·t⁻¹·p⁻²·Lₐ
m = k₀ · t·p²·Lₐ⁻¹
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "-1", "momentum": "-2", "ang_momentum": "1"}
4
action,mass,momentum,time
m·t·p·S
mechanics
m·t⁻¹·p⁻²·S
m = k₀ · t·p²·S⁻¹
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "-1", "momentum": "-2", "action": "1"}
4
inertia,mass,momentum,time
m·t·p·J
mechanics
m·t⁻²·p⁻²·J
m = k₀ · t²·p²·J⁻¹
null
0
1
2
6
3.9
6.1
true
{"mass": "1", "time": "-2", "momentum": "-2", "inertia": "1"}
4
mass,momentum,pressure,time
m·t·p·P_p
mechanics
m²·t⁻³·p⁻¹·P_p⁻¹
p = k₀ · m²·t⁻³·P_p⁻¹
null
0
1
3
7
5.1
4.9
true
{"mass": "2", "time": "-3", "momentum": "-1", "pressure": "-1"}
4
density,mass,momentum,time
m·t·p·ρ
mechanics
m⁴·t⁻³·p⁻³·ρ⁻¹
ρ = k₀ · m⁴·t⁻³·p⁻³
null
0
1
4
11
8.4
1.6
false
{"mass": "4", "time": "-3", "momentum": "-3", "density": "-1"}
4
mass,momentum,time,viscosity
m·t·p·μ
mechanics
m²·t⁻²·p⁻¹·μ⁻¹
p = k₀ · m²·t⁻²·μ⁻¹
null
0
1
2
6
3.9
6.1
true
{"mass": "2", "time": "-2", "momentum": "-1", "viscosity": "-1"}
4
kin_viscosity,mass,momentum,time
m·t·p·ν
mechanics
m²·t⁻¹·p⁻²·ν
t = k₀ · m²·p⁻²·ν
null
0
1
2
6
3.9
6.1
true
{"mass": "2", "time": "-1", "momentum": "-2", "kin_viscosity": "1"}
4
area,mass,momentum,time
m·t·p·A
mechanics
m²·t⁻²·p⁻²·A
A = k₀ · m⁻²·t²·p²
null
0
1
2
7
4.6
5.4
true
{"mass": "2", "time": "-2", "momentum": "-2", "area": "1"}
4
mass,momentum,time,volume
m·t·p·V
mechanics
m³·t⁻³·p⁻³·V
V = k₀ · m⁻³·t³·p³
null
0
1
3
10
7.2
2.8
false
{"mass": "3", "time": "-3", "momentum": "-3", "volume": "1"}
4
flowrate,mass,momentum,time
m·t·p·Q
mechanics
m³·t⁻²·p⁻³·Q
Q = k₀ · m⁻³·t²·p³
null
0
1
3
9
6.5
3.5
false
{"mass": "3", "time": "-2", "momentum": "-3", "flowrate": "1"}
6
concentration,gas_constant,mass,momentum,temperature,time
m·t·p·Θ·c_n·R
chemistry,mechanics,thermo
m²·t⁻³·p⁻¹·Θ⁻¹·c_n⁻¹·R⁻¹
p = k₀ · m²·t⁻³·Θ⁻¹·c_n⁻¹·R⁻¹
null
0
3
3
9
8.3
0.7
false
{"mass": "2", "time": "-3", "momentum": "-1", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,gas_constant,mass,momentum,temperature,time
m·t·p·Θ·R·z
chemistry,mechanics,thermo
m·t·p⁻²·Θ·R·z
m = k₀ · t⁻¹·p²·Θ⁻¹·R⁻¹·z⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "time": "1", "momentum": "-2", "temperature": "1", "gas_constant": "1", "cat_activity": "1"}
5
entropy,mass,momentum,thermal_cond,time
m·t·p·S_e·κ
mechanics,thermo
m·t⁻²·p⁻¹·S_e·κ⁻¹
m = k₀ · t²·p·S_e⁻¹·κ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "momentum": "-1", "entropy": "1", "thermal_cond": "-1"}
6
concentration,entropy,gas_constant,mass,momentum,time
m·t·p·S_e·c_n·R
chemistry,mechanics,thermo
m³·t⁻³·p⁻³·S_e·c_n⁻¹·R⁻¹
S_e = k₀ · m⁻³·t³·p³·c_n·R
null
0
3
3
12
10.4
-1.4
false
{"mass": "3", "time": "-3", "momentum": "-3", "entropy": "1", "concentration": "-1", "gas_constant": "-1"}
5
heat_capacity,mass,momentum,thermal_cond,time
m·t·p·C·κ
mechanics,thermo
m·t⁻²·p⁻¹·C·κ⁻¹
m = k₀ · t²·p·C⁻¹·κ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "momentum": "-1", "heat_capacity": "1", "thermal_cond": "-1"}
6
concentration,gas_constant,heat_capacity,mass,momentum,time
m·t·p·C·c_n·R
chemistry,mechanics,thermo
m³·t⁻³·p⁻³·C·c_n⁻¹·R⁻¹
C = k₀ · m⁻³·t³·p³·c_n·R
null
0
3
3
12
10.4
-1.4
false
{"mass": "3", "time": "-3", "momentum": "-3", "heat_capacity": "1", "concentration": "-1", "gas_constant": "-1"}
5
mass,momentum,specific_heat,thermal_cond,time
m·t·p·c·κ
mechanics,thermo
m²·t⁻²·p⁻¹·c·κ⁻¹
p = k₀ · m²·t⁻²·c·κ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "time": "-2", "momentum": "-1", "specific_heat": "1", "thermal_cond": "-1"}
6
concentration,gas_constant,mass,momentum,specific_heat,time
m·t·p·c·c_n·R
chemistry,mechanics,thermo
m⁴·t⁻³·p⁻³·c·c_n⁻¹·R⁻¹
c = k₀ · m⁻⁴·t³·p³·c_n·R
null
0
3
4
13
11.6
-2.6
false
{"mass": "4", "time": "-3", "momentum": "-3", "specific_heat": "1", "concentration": "-1", "gas_constant": "-1"}
6
amount,gas_constant,mass,momentum,thermal_cond,time
m·t·p·κ·n·R
chemistry,mechanics,thermo
m·t⁻²·p⁻¹·κ⁻¹·n·R
m = k₀ · t²·p·κ·n⁻¹·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "time": "-2", "momentum": "-1", "thermal_cond": "-1", "amount": "1", "gas_constant": "1"}
6
gas_constant,mass,molar_mass,momentum,thermal_cond,time
m·t·p·κ·M_m·R
chemistry,mechanics,thermo
m²·t⁻²·p⁻¹·κ⁻¹·M_m⁻¹·R
p = k₀ · m²·t⁻²·κ⁻¹·M_m⁻¹·R
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "time": "-2", "momentum": "-1", "thermal_cond": "-1", "molar_mass": "-1", "gas_constant": "1"}
6
concentration,gas_constant,mass,momentum,thermal_cond,time
m·t·p·κ·c_n·R
chemistry,mechanics,thermo
m²·t⁻¹·p⁻²·κ·c_n⁻¹·R⁻¹
t = k₀ · m²·p⁻²·κ·c_n⁻¹·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "time": "-1", "momentum": "-2", "thermal_cond": "1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,gas_constant,mass,momentum,thermal_cond,time
m·t·p·κ·R·z
chemistry,mechanics,thermo
m·t⁻¹·p⁻¹·κ⁻¹·R·z
m = k₀ · t·p·κ·R⁻¹·z⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "time": "-1", "momentum": "-1", "thermal_cond": "-1", "gas_constant": "1", "cat_activity": "1"}
6
avogadro,gas_constant,mass,momentum,thermal_cond,time
m·t·p·κ·R·N_A
chemistry,constants,mechanics,thermo
m·t⁻²·p⁻¹·κ⁻¹·R·N_A⁻¹
m = k₀ · t²·p·κ·R⁻¹·N_A
null
1
4
2
7
7
1.5
false
{"mass": "1", "time": "-2", "momentum": "-1", "thermal_cond": "-1", "gas_constant": "1", "avogadro": "-1"}
5
boltzmann,mass,momentum,thermal_cond,time
m·t·p·κ·k_B
constants,mechanics,thermo
m·t⁻²·p⁻¹·κ⁻¹·k_B
m = k₀ · t²·p·κ·k_B⁻¹
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "time": "-2", "momentum": "-1", "thermal_cond": "-1", "boltzmann": "1"}
4
mass,momentum,thermal_diff,time
m·t·p·α
mechanics,thermo
m²·t⁻¹·p⁻²·α
t = k₀ · m²·p⁻²·α
null
0
2
2
6
4.5
5
true
{"mass": "2", "time": "-1", "momentum": "-2", "thermal_diff": "1"}
6
concentration,expansion,gas_constant,mass,momentum,time
m·t·p·β·c_n·R
chemistry,mechanics,thermo
m²·t⁻³·p⁻¹·β·c_n⁻¹·R⁻¹
p = k₀ · m²·t⁻³·β·c_n⁻¹·R⁻¹
null
0
3
3
9
8.3
0.7
false
{"mass": "2", "time": "-3", "momentum": "-1", "expansion": "1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,expansion,gas_constant,mass,momentum,time
m·t·p·β·R·z
chemistry,mechanics,thermo
m·t·p⁻²·β⁻¹·R·z
m = k₀ · t⁻¹·p²·β·R⁻¹·z⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "time": "1", "momentum": "-2", "expansion": "-1", "gas_constant": "1", "cat_activity": "1"}
5
charge,mass,momentum,resistance,time
m·t·p·q·R
em,mechanics
m·t⁻¹·p⁻²·q²·R
m = k₀ · t·p²·q⁻²·R⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "time": "-1", "momentum": "-2", "charge": "2", "resistance": "1"}
5
charge,inductance,mass,momentum,time
m·t·p·q·L_e
em,mechanics
m·t⁻²·p⁻²·q²·L_e
m = k₀ · t²·p²·q⁻²·L_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "momentum": "-2", "charge": "2", "inductance": "1"}
5
charge,mag_flux,mass,momentum,time
m·t·p·q·Φ
em,mechanics
m·t⁻¹·p⁻²·q·Φ
m = k₀ · t·p²·q⁻¹·Φ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-1", "momentum": "-2", "charge": "1", "mag_flux": "1"}
5
charge,mass,momentum,permittivity,time
m·t·p·q·ε
em,mechanics
m²·t⁻¹·p⁻³·q²·ε⁻¹
t = k₀ · m²·p⁻³·q²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-1", "momentum": "-3", "charge": "2", "permittivity": "-1"}
5
charge,conductivity,mass,momentum,time
m·t·p·q·σ
em,mechanics
m²·t⁻²·p⁻³·q²·σ⁻¹
σ = k₀ · m²·t⁻²·p⁻³·q²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "time": "-2", "momentum": "-3", "charge": "2", "conductivity": "-1"}
5
charge,mass,momentum,resistivity,time
m·t·p·q·ρ_e
em,mechanics
m²·t⁻²·p⁻³·q²·ρ_e
ρ_e = k₀ · m⁻²·t²·p³·q⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "time": "-2", "momentum": "-3", "charge": "2", "resistivity": "1"}
5
current,mass,momentum,time,voltage
m·t·p·i·U
em,mechanics
m·t·p⁻²·i·U
m = k₀ · t⁻¹·p²·i⁻¹·U⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "1", "momentum": "-2", "current": "1", "voltage": "1"}
5
current,mass,momentum,resistance,time
m·t·p·i·R
em,mechanics
m·t·p⁻²·i²·R
m = k₀ · t⁻¹·p²·i⁻²·R⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "time": "1", "momentum": "-2", "current": "2", "resistance": "1"}
5
capacitance,current,mass,momentum,time
m·t·p·i·C_e
em,mechanics
m·t²·p⁻²·i²·C_e⁻¹
m = k₀ · t⁻²·p²·i⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "momentum": "-2", "current": "2", "capacitance": "-1"}
5
current,mass,momentum,permittivity,time
m·t·p·i·ε
em,mechanics
m²·t·p⁻³·i²·ε⁻¹
t = k₀ · m⁻²·p³·i⁻²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "1", "momentum": "-3", "current": "2", "permittivity": "-1"}
5
mass,momentum,resistance,time,voltage
m·t·p·U·R
em,mechanics
m·t·p⁻²·U²·R⁻¹
m = k₀ · t⁻¹·p²·U⁻²·R
null
0
2
2
7
5.5
4
true
{"mass": "1", "time": "1", "momentum": "-2", "voltage": "2", "resistance": "-1"}
5
inductance,mass,momentum,time,voltage
m·t·p·U·L_e
em,mechanics
m·t²·p⁻²·U²·L_e⁻¹
m = k₀ · t⁻²·p²·U⁻²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "2", "momentum": "-2", "voltage": "2", "inductance": "-1"}
5
efield,mass,momentum,time,voltage
m·t·p·U·E_f
em,mechanics
m·t⁻¹·p⁻¹·U·E_f⁻¹
m = k₀ · t·p·U⁻¹·E_f
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "momentum": "-1", "voltage": "1", "efield": "-1"}
5
bfield,mass,momentum,time,voltage
m·t·p·U·B
em,mechanics
m²·t⁻¹·p⁻²·U·B⁻¹
t = k₀ · m²·p⁻²·U·B⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "time": "-1", "momentum": "-2", "voltage": "1", "bfield": "-1"}
5
mass,momentum,permeability,time,voltage
m·t·p·U·μ₀
em,mechanics
m²·t·p⁻³·U²·μ₀⁻¹
t = k₀ · m⁻²·p³·U⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "1", "momentum": "-3", "voltage": "2", "permeability": "-1"}
5
bfield,mass,momentum,resistance,time
m·t·p·R·B
em,mechanics
m³·t⁻³·p⁻²·R·B⁻²
R = k₀ · m⁻³·t³·p²·B²
null
0
2
3
11
8.8
0.7
false
{"mass": "3", "time": "-3", "momentum": "-2", "resistance": "1", "bfield": "-2"}
5
mag_flux,mass,momentum,resistance,time
m·t·p·R·Φ
em,mechanics
m·t⁻¹·p⁻²·R⁻¹·Φ²
m = k₀ · t·p²·R·Φ⁻²
null
0
2
2
7
5.5
4
true
{"mass": "1", "time": "-1", "momentum": "-2", "resistance": "-1", "mag_flux": "2"}
5
conductivity,mass,momentum,resistance,time
m·t·p·R·σ
em,mechanics
m·t⁻¹·p⁻¹·R⁻¹·σ⁻¹
m = k₀ · t·p·R·σ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "momentum": "-1", "resistance": "-1", "conductivity": "-1"}
5
mass,momentum,resistance,resistivity,time
m·t·p·R·ρ_e
em,mechanics
m·t⁻¹·p⁻¹·R⁻¹·ρ_e
m = k₀ · t·p·R·ρ_e⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "momentum": "-1", "resistance": "-1", "resistivity": "1"}
5
elem_charge,mass,momentum,resistance,time
m·t·p·R·e
constants,em,mechanics
m·t⁻¹·p⁻²·R·e²
m = k₀ · t·p²·R⁻¹·e⁻²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "time": "-1", "momentum": "-2", "resistance": "1", "elem_charge": "2"}
5
bfield,capacitance,mass,momentum,time
m·t·p·C_e·B
em,mechanics
m³·t⁻²·p⁻²·C_e⁻¹·B⁻²
C_e = k₀ · m³·t⁻²·p⁻²·B⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "3", "time": "-2", "momentum": "-2", "capacitance": "-1", "bfield": "-2"}
5
capacitance,mag_flux,mass,momentum,time
m·t·p·C_e·Φ
em,mechanics
m·t⁻²·p⁻²·C_e·Φ²
m = k₀ · t²·p²·C_e⁻¹·Φ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "time": "-2", "momentum": "-2", "capacitance": "1", "mag_flux": "2"}
5
capacitance,mass,momentum,permittivity,time
m·t·p·C_e·ε
em,mechanics
m·t⁻¹·p⁻¹·C_e·ε⁻¹
m = k₀ · t·p·C_e⁻¹·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "momentum": "-1", "capacitance": "1", "permittivity": "-1"}
5
capacitance,mass,momentum,permeability,time
m·t·p·C_e·μ₀
em,mechanics
m·t·p⁻¹·C_e⁻¹·μ₀⁻¹
m = k₀ · t⁻¹·p·C_e·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "1", "momentum": "-1", "capacitance": "-1", "permeability": "-1"}
5
capacitance,conductivity,mass,momentum,time
m·t·p·C_e·σ
em,mechanics
m·t⁻²·p⁻¹·C_e·σ⁻¹
m = k₀ · t²·p·C_e⁻¹·σ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "momentum": "-1", "capacitance": "1", "conductivity": "-1"}
5
capacitance,mass,momentum,resistivity,time
m·t·p·C_e·ρ_e
em,mechanics
m·t⁻²·p⁻¹·C_e·ρ_e
m = k₀ · t²·p·C_e⁻¹·ρ_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "momentum": "-1", "capacitance": "1", "resistivity": "1"}
5
bfield,inductance,mass,momentum,time
m·t·p·L_e·B
em,mechanics
m³·t⁻⁴·p⁻²·L_e·B⁻²
L_e = k₀ · m⁻³·t⁴·p²·B²
null
0
2
4
12
10
-0.5
false
{"mass": "3", "time": "-4", "momentum": "-2", "inductance": "1", "bfield": "-2"}
5
inductance,mass,momentum,permittivity,time
m·t·p·L_e·ε
em,mechanics
m·t·p⁻¹·L_e⁻¹·ε⁻¹
m = k₀ · t⁻¹·p·L_e·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "1", "momentum": "-1", "inductance": "-1", "permittivity": "-1"}
5
inductance,mass,momentum,permeability,time
m·t·p·L_e·μ₀
em,mechanics
m·t⁻¹·p⁻¹·L_e·μ₀⁻¹
m = k₀ · t·p·L_e⁻¹·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "time": "-1", "momentum": "-1", "inductance": "1", "permeability": "-1"}
5
elem_charge,inductance,mass,momentum,time
m·t·p·L_e·e
constants,em,mechanics
m·t⁻²·p⁻²·L_e·e²
m = k₀ · t²·p²·L_e⁻¹·e⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "time": "-2", "momentum": "-2", "inductance": "1", "elem_charge": "2"}
5
efield,mag_flux,mass,momentum,time
m·t·p·E_f·Φ
em,mechanics
m·t⁻²·p⁻¹·E_f⁻¹·Φ
m = k₀ · t²·p·E_f·Φ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "-2", "momentum": "-1", "efield": "-1", "mag_flux": "1"}
5
efield,mass,momentum,permittivity,time
m·t·p·E_f·ε
em,mechanics
m²·t⁻³·p⁻¹·E_f⁻²·ε⁻¹
p = k₀ · m²·t⁻³·E_f⁻²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-3", "momentum": "-1", "efield": "-2", "permittivity": "-1"}
5
conductivity,efield,mass,momentum,time
m·t·p·E_f·σ
em,mechanics
m²·t⁻⁴·p⁻¹·E_f⁻²·σ⁻¹
p = k₀ · m²·t⁻⁴·E_f⁻²·σ⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "time": "-4", "momentum": "-1", "efield": "-2", "conductivity": "-1"}
5
efield,mass,momentum,resistivity,time
m·t·p·E_f·ρ_e
em,mechanics
m²·t⁻⁴·p⁻¹·E_f⁻²·ρ_e
p = k₀ · m²·t⁻⁴·E_f⁻²·ρ_e
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "time": "-4", "momentum": "-1", "efield": "-2", "resistivity": "1"}
5
bfield,mag_flux,mass,momentum,time
m·t·p·B·Φ
em,mechanics
m²·t⁻²·p⁻²·B⁻¹·Φ
B = k₀ · m²·t⁻²·p⁻²·Φ
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "time": "-2", "momentum": "-2", "bfield": "-1", "mag_flux": "1"}
5
bfield,mass,momentum,permittivity,time
m·t·p·B·ε
em,mechanics
m⁴·t⁻³·p⁻³·B⁻²·ε⁻¹
ε = k₀ · m⁴·t⁻³·p⁻³·B⁻²
null
0
2
4
13
10.7
-1.2
false
{"mass": "4", "time": "-3", "momentum": "-3", "bfield": "-2", "permittivity": "-1"}
5
bfield,mass,momentum,permeability,time
m·t·p·B·μ₀
em,mechanics
m²·t⁻³·p⁻¹·B⁻²·μ₀
p = k₀ · m²·t⁻³·B⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-3", "momentum": "-1", "bfield": "-2", "permeability": "1"}
5
bfield,conductivity,mass,momentum,time
m·t·p·B·σ
em,mechanics
m⁴·t⁻⁴·p⁻³·B⁻²·σ⁻¹
σ = k₀ · m⁴·t⁻⁴·p⁻³·B⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "4", "time": "-4", "momentum": "-3", "bfield": "-2", "conductivity": "-1"}
5
bfield,mass,momentum,resistivity,time
m·t·p·B·ρ_e
em,mechanics
m⁴·t⁻⁴·p⁻³·B⁻²·ρ_e
ρ_e = k₀ · m⁻⁴·t⁴·p³·B²
null
0
2
4
14
11.4
-1.9
false
{"mass": "4", "time": "-4", "momentum": "-3", "bfield": "-2", "resistivity": "1"}
5
mag_flux,mass,momentum,permeability,time
m·t·p·Φ·μ₀
em,mechanics
m²·t⁻¹·p⁻³·Φ²·μ₀⁻¹
t = k₀ · m²·p⁻³·Φ²·μ₀⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "time": "-1", "momentum": "-3", "mag_flux": "2", "permeability": "-1"}
5
elem_charge,mag_flux,mass,momentum,time
m·t·p·Φ·e
constants,em,mechanics
m·t⁻¹·p⁻²·Φ·e
m = k₀ · t·p²·Φ⁻¹·e⁻¹
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "time": "-1", "momentum": "-2", "mag_flux": "1", "elem_charge": "1"}
5
elem_charge,mass,momentum,permittivity,time
m·t·p·ε·e
constants,em,mechanics
m²·t⁻¹·p⁻³·ε⁻¹·e²
t = k₀ · m²·p⁻³·ε⁻¹·e²
null
1
3
3
9
8
1
false
{"mass": "2", "time": "-1", "momentum": "-3", "permittivity": "-1", "elem_charge": "2"}
5
conductivity,mass,momentum,permeability,time
m·t·p·μ₀·σ
em,mechanics
m²·t⁻¹·p⁻²·μ₀⁻¹·σ⁻¹
t = k₀ · m²·p⁻²·μ₀⁻¹·σ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "time": "-1", "momentum": "-2", "permeability": "-1", "conductivity": "-1"}
5
mass,momentum,permeability,resistivity,time
m·t·p·μ₀·ρ_e
em,mechanics
m²·t⁻¹·p⁻²·μ₀⁻¹·ρ_e
t = k₀ · m²·p⁻²·μ₀⁻¹·ρ_e
null
0
2
2
7
5.5
4
true
{"mass": "2", "time": "-1", "momentum": "-2", "permeability": "-1", "resistivity": "1"}
5
conductivity,elem_charge,mass,momentum,time
m·t·p·σ·e
constants,em,mechanics
m²·t⁻²·p⁻³·σ⁻¹·e²
σ = k₀ · m²·t⁻²·p⁻³·e²
null
1
3
3
10
8.7
0.3
false
{"mass": "2", "time": "-2", "momentum": "-3", "conductivity": "-1", "elem_charge": "2"}
5
elem_charge,mass,momentum,resistivity,time
m·t·p·ρ_e·e
constants,em,mechanics
m²·t⁻²·p⁻³·ρ_e·e²
ρ_e = k₀ · m⁻²·t²·p³·e⁻²
null
1
3
3
10
8.7
0.3
false
{"mass": "2", "time": "-2", "momentum": "-3", "resistivity": "1", "elem_charge": "2"}
5
amount,concentration,mass,momentum,time
m·t·p·n·c_n
chemistry,mechanics
m³·t⁻³·p⁻³·n·c_n⁻¹
n = k₀ · m⁻³·t³·p³·c_n
null
0
2
3
11
8.8
0.7
false
{"mass": "3", "time": "-3", "momentum": "-3", "amount": "1", "concentration": "-1"}
5
concentration,mass,molar_mass,momentum,time
m·t·p·M_m·c_n
chemistry,mechanics
m⁴·t⁻³·p⁻³·M_m⁻¹·c_n⁻¹
M_m = k₀ · m⁴·t⁻³·p⁻³·c_n⁻¹
null
0
2
4
12
10
-0.5
false
{"mass": "4", "time": "-3", "momentum": "-3", "molar_mass": "-1", "concentration": "-1"}
5
concentration,mass,molar_energy,momentum,time
m·t·p·c_n·E_m
chemistry,mechanics
m²·t⁻³·p⁻¹·c_n⁻¹·E_m⁻¹
p = k₀ · m²·t⁻³·c_n⁻¹·E_m⁻¹
null
0
2
3
8
6.7
2.8
true
{"mass": "2", "time": "-3", "momentum": "-1", "concentration": "-1", "molar_energy": "-1"}
6
boltzmann,concentration,gas_constant,mass,momentum,time
m·t·p·c_n·R·k_B
chemistry,constants,mechanics
m³·t⁻³·p⁻³·c_n⁻¹·R⁻¹·k_B
c_n = k₀ · m³·t⁻³·p⁻³·R⁻¹·k_B
null
1
3
3
12
10.4
-1.4
false
{"mass": "3", "time": "-3", "momentum": "-3", "concentration": "-1", "gas_constant": "-1", "boltzmann": "1"}
5
cat_activity,concentration,mass,momentum,time
m·t·p·c_n·z
chemistry,mechanics
m³·t⁻²·p⁻³·c_n⁻¹·z
c_n = k₀ · m³·t⁻²·p⁻³·z
null
0
2
3
10
8.1
1.4
false
{"mass": "3", "time": "-2", "momentum": "-3", "concentration": "-1", "cat_activity": "1"}
5
avogadro,concentration,mass,momentum,time
m·t·p·c_n·N_A
chemistry,constants,mechanics
m³·t⁻³·p⁻³·c_n⁻¹·N_A⁻¹
c_n = k₀ · m³·t⁻³·p⁻³·N_A⁻¹
null
1
3
3
11
9.4
-0.4
false
{"mass": "3", "time": "-3", "momentum": "-3", "concentration": "-1", "avogadro": "-1"}
5
cat_activity,mass,molar_energy,momentum,time
m·t·p·E_m·z
chemistry,mechanics
m·t·p⁻²·E_m·z
m = k₀ · t⁻¹·p²·E_m⁻¹·z⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "time": "1", "momentum": "-2", "molar_energy": "1", "cat_activity": "1"}
5
illuminance,lum_intensity,mass,momentum,time
m·t·p·I_v·E_v
mechanics,photometry
m²·t⁻²·p⁻²·I_v·E_v⁻¹
I_v = k₀ · m⁻²·t²·p²·E_v
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "time": "-2", "momentum": "-2", "lum_intensity": "1", "illuminance": "-1"}
5
lum_intensity,luminance,mass,momentum,time
m·t·p·I_v·L_v
mechanics,photometry
m²·t⁻²·p⁻²·I_v·L_v⁻¹
I_v = k₀ · m⁻²·t²·p²·L_v
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "time": "-2", "momentum": "-2", "lum_intensity": "1", "luminance": "-1"}
4
grav_const,mass,momentum,time
m·t·p·G
constants,mechanics
m⁴·t⁻¹·p⁻³·G
t = k₀ · m⁴·p⁻³·G
null
1
2
4
9
7.6
1.9
false
{"mass": "4", "time": "-1", "momentum": "-3", "grav_const": "1"}
4
mass,momentum,planck,time
m·t·p·h
constants,mechanics
m·t⁻¹·p⁻²·h
m = k₀ · t·p²·h⁻¹
null
1
2
2
5
3.8
5.7
true
{"mass": "1", "time": "-1", "momentum": "-2", "planck": "1"}
4
ang_momentum,mass,pressure,time
m·t·Lₐ·P_p
mechanics
m³·t⁻⁵·Lₐ⁻¹·P_p⁻²
Lₐ = k₀ · m³·t⁻⁵·P_p⁻²
null
0
1
5
11
8.9
1.1
false
{"mass": "3", "time": "-5", "ang_momentum": "-1", "pressure": "-2"}
4
ang_momentum,density,mass,time
m·t·Lₐ·ρ
mechanics
m⁵·t⁻³·Lₐ⁻³·ρ⁻²
ρ = k₀ · m⁵ᐟ²·t⁻³ᐟ²·Lₐ⁻³ᐟ²
null
0
1
5
13
10.3
-0.3
false
{"mass": "5", "time": "-3", "ang_momentum": "-3", "density": "-2"}
4
ang_momentum,mass,time,viscosity
m·t·Lₐ·μ
mechanics
m³·t⁻³·Lₐ⁻¹·μ⁻²
Lₐ = k₀ · m³·t⁻³·μ⁻²
null
0
1
3
9
6.5
3.5
false
{"mass": "3", "time": "-3", "ang_momentum": "-1", "viscosity": "-2"}