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
6
cat_activity,charge,concentration,length,mag_flux,mass
m·ℓ·q·Φ·c_n·z
chemistry,em,mechanics
m·ℓ⁻¹·q⁻¹·Φ⁻¹·c_n⁻¹·z
m = k₀ · ℓ·q·Φ·c_n·z⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "-1", "charge": "-1", "mag_flux": "-1", "concentration": "-1", "cat_activity": "1"}
7
boltzmann,charge,gas_constant,length,mag_flux,mass,molar_energy
m·ℓ·q·Φ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·q⁻²·Φ⁻²·E_m·R⁻¹·k_B
m = k₀ · ℓ⁻²·q²·Φ²·E_m⁻¹·R·k_B⁻¹
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "2", "charge": "-2", "mag_flux": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"}
6
cat_activity,charge,length,mag_flux,mass,molar_energy
m·ℓ·q·Φ·E_m·z
chemistry,em,mechanics
m²·ℓ⁴·q⁻³·Φ⁻³·E_m·z
E_m = k₀ · m⁻²·ℓ⁻⁴·q³·Φ³·z⁻¹
null
0
3
4
14
12.3
-3.3
false
{"mass": "2", "length": "4", "charge": "-3", "mag_flux": "-3", "molar_energy": "1", "cat_activity": "1"}
6
avogadro,charge,length,mag_flux,mass,molar_energy
m·ℓ·q·Φ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·q⁻²·Φ⁻²·E_m·N_A⁻¹
m = k₀ · ℓ⁻²·q²·Φ²·E_m⁻¹·N_A
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "charge": "-2", "mag_flux": "-2", "molar_energy": "1", "avogadro": "-1"}
7
boltzmann,cat_activity,charge,gas_constant,length,mag_flux,mass
m·ℓ·q·Φ·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·q⁻¹·Φ⁻¹·R·z·k_B⁻¹
m = k₀ · ℓ⁻²·q·Φ·R⁻¹·z⁻¹·k_B
null
1
4
2
8
8
0.5
false
{"mass": "1", "length": "2", "charge": "-1", "mag_flux": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"}
6
avogadro,cat_activity,charge,length,mag_flux,mass
m·ℓ·q·Φ·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·q⁻¹·Φ⁻¹·z·N_A
m = k₀ · ℓ⁻²·q·Φ·z⁻¹·N_A⁻¹
null
1
4
2
7
7
1.5
false
{"mass": "1", "length": "2", "charge": "-1", "mag_flux": "-1", "cat_activity": "1", "avogadro": "1"}
5
charge,length,light_speed,mag_flux,mass
m·ℓ·q·Φ·c₀
constants,em,mechanics
m·ℓ·q⁻¹·Φ⁻¹·c₀
m = k₀ · ℓ⁻¹·q·Φ·c₀⁻¹
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "charge": "-1", "mag_flux": "-1", "light_speed": "1"}
5
charge,grav_const,length,mag_flux,mass
m·ℓ·q·Φ·G
constants,em,mechanics
m³·ℓ·q⁻²·Φ⁻²·G
ℓ = k₀ · m⁻³·q²·Φ²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "3", "length": "1", "charge": "-2", "mag_flux": "-2", "grav_const": "1"}
5
charge,conductivity,length,mass,permittivity
m·ℓ·q·ε·σ
em,mechanics
m·ℓ³·q⁻²·ε⁻¹·σ²
m = k₀ · ℓ⁻³·q²·ε·σ⁻²
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "charge": "-2", "permittivity": "-1", "conductivity": "2"}
5
charge,length,mass,permittivity,resistivity
m·ℓ·q·ε·ρ_e
em,mechanics
m·ℓ³·q⁻²·ε⁻¹·ρ_e⁻²
m = k₀ · ℓ⁻³·q²·ε·ρ_e²
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "charge": "-2", "permittivity": "-1", "resistivity": "-2"}
6
amount,cat_activity,charge,length,mass,permittivity
m·ℓ·q·ε·n·z
chemistry,em,mechanics
m·ℓ³·q⁻²·ε·n⁻²·z²
m = k₀ · ℓ⁻³·q²·ε⁻¹·n²·z⁻²
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "3", "charge": "-2", "permittivity": "1", "amount": "-2", "cat_activity": "2"}
6
charge,length,mass,molar_energy,molar_mass,permittivity
m·ℓ·q·ε·M_m·E_m
chemistry,em,mechanics
m·ℓ·q⁻²·ε·M_m⁻¹·E_m
m = k₀ · ℓ⁻¹·q²·ε⁻¹·M_m·E_m⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "1", "charge": "-2", "permittivity": "1", "molar_mass": "-1", "molar_energy": "1"}
6
cat_activity,charge,length,mass,molar_mass,permittivity
m·ℓ·q·ε·M_m·z
chemistry,em,mechanics
m·ℓ⁻³·q²·ε⁻¹·M_m⁻²·z⁻²
m = k₀ · ℓ³·q⁻²·ε·M_m²·z²
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "-3", "charge": "2", "permittivity": "-1", "molar_mass": "-2", "cat_activity": "-2"}
6
cat_activity,charge,concentration,length,mass,permittivity
m·ℓ·q·ε·c_n·z
chemistry,em,mechanics
m·ℓ⁻³·q⁻²·ε·c_n⁻²·z²
m = k₀ · ℓ³·q²·ε⁻¹·c_n²·z⁻²
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "-3", "charge": "-2", "permittivity": "1", "concentration": "-2", "cat_activity": "2"}
6
cat_activity,charge,length,mass,molar_energy,permittivity
m·ℓ·q·ε·E_m·z
chemistry,em,mechanics
m·ℓ⁵·q⁻⁶·ε³·E_m²·z²
m = k₀ · ℓ⁻⁵·q⁶·ε⁻³·E_m⁻²·z⁻²
null
0
3
6
19
16.8
-7.8
false
{"mass": "1", "length": "5", "charge": "-6", "permittivity": "3", "molar_energy": "2", "cat_activity": "2"}
7
boltzmann,cat_activity,charge,gas_constant,length,mass,permittivity
m·ℓ·q·ε·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·ε·R²·z²·k_B⁻²
m = k₀ · ℓ⁻³·q²·ε⁻¹·R⁻²·z⁻²·k_B²
null
1
4
3
13
12
-3.5
false
{"mass": "1", "length": "3", "charge": "-2", "permittivity": "1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"}
6
avogadro,cat_activity,charge,length,mass,permittivity
m·ℓ·q·ε·z·N_A
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·ε·z²·N_A²
m = k₀ · ℓ⁻³·q²·ε⁻¹·z⁻²·N_A⁻²
null
1
4
3
11
10.3
-1.8
false
{"mass": "1", "length": "3", "charge": "-2", "permittivity": "1", "cat_activity": "2", "avogadro": "2"}
5
charge,length,light_speed,mass,permittivity
m·ℓ·q·ε·c₀
constants,em,mechanics
m·ℓ·q⁻²·ε·c₀²
m = k₀ · ℓ⁻¹·q²·ε⁻¹·c₀⁻²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "charge": "-2", "permittivity": "1", "light_speed": "2"}
5
charge,length,mass,permittivity,planck
m·ℓ·q·ε·h
constants,em,mechanics
m·ℓ·q²·ε⁻¹·h⁻²
m = k₀ · ℓ⁻¹·q⁻²·ε·h²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "charge": "2", "permittivity": "-1", "planck": "-2"}
4
charge,length,mass,permeability
m·ℓ·q·μ₀
em,mechanics
m·ℓ·q⁻²·μ₀⁻¹
m = k₀ · ℓ⁻¹·q²·μ₀
null
0
2
2
5
3.8
5.7
true
{"mass": "1", "length": "1", "charge": "-2", "permeability": "-1"}
6
amount,charge,conductivity,length,mass,molar_energy
m·ℓ·q·σ·n·E_m
chemistry,em,mechanics
m·ℓ⁴·q⁻⁴·σ²·n·E_m
m = k₀ · ℓ⁻⁴·q⁴·σ⁻²·n⁻¹·E_m⁻¹
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "4", "charge": "-4", "conductivity": "2", "amount": "1", "molar_energy": "1"}
6
amount,cat_activity,charge,conductivity,length,mass
m·ℓ·q·σ·n·z
chemistry,em,mechanics
m·ℓ³·q⁻²·σ·n⁻¹·z
m = k₀ · ℓ⁻³·q²·σ⁻¹·n·z⁻¹
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "3", "charge": "-2", "conductivity": "1", "amount": "-1", "cat_activity": "1"}
6
charge,conductivity,length,mass,molar_energy,molar_mass
m·ℓ·q·σ·M_m·E_m
chemistry,em,mechanics
m²·ℓ⁴·q⁻⁴·σ²·M_m⁻¹·E_m
M_m = k₀ · m²·ℓ⁴·q⁻⁴·σ²·E_m
null
0
3
4
14
12.3
-3.3
false
{"mass": "2", "length": "4", "charge": "-4", "conductivity": "2", "molar_mass": "-1", "molar_energy": "1"}
6
charge,concentration,conductivity,length,mass,molar_energy
m·ℓ·q·σ·c_n·E_m
chemistry,em,mechanics
m·ℓ⁷·q⁻⁴·σ²·c_n·E_m
m = k₀ · ℓ⁻⁷·q⁴·σ⁻²·c_n⁻¹·E_m⁻¹
null
0
3
7
16
15.2
-6.2
false
{"mass": "1", "length": "7", "charge": "-4", "conductivity": "2", "concentration": "1", "molar_energy": "1"}
7
boltzmann,charge,conductivity,gas_constant,length,mass,molar_energy
m·ℓ·q·σ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁴·q⁻⁴·σ²·E_m·R⁻¹·k_B
m = k₀ · ℓ⁻⁴·q⁴·σ⁻²·E_m⁻¹·R·k_B⁻¹
null
1
4
4
14
13.2
-4.7
false
{"mass": "1", "length": "4", "charge": "-4", "conductivity": "2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"}
6
cat_activity,charge,conductivity,length,mass,molar_energy
m·ℓ·q·σ·E_m·z
chemistry,em,mechanics
m²·ℓ⁷·q⁻⁶·σ³·E_m·z
E_m = k₀ · m⁻²·ℓ⁻⁷·q⁶·σ⁻³·z⁻¹
null
0
3
7
20
18
-9
false
{"mass": "2", "length": "7", "charge": "-6", "conductivity": "3", "molar_energy": "1", "cat_activity": "1"}
6
avogadro,charge,conductivity,length,mass,molar_energy
m·ℓ·q·σ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·q⁻⁴·σ²·E_m·N_A⁻¹
m = k₀ · ℓ⁻⁴·q⁴·σ⁻²·E_m⁻¹·N_A
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "charge": "-4", "conductivity": "2", "molar_energy": "1", "avogadro": "-1"}
7
boltzmann,cat_activity,charge,conductivity,gas_constant,length,mass
m·ℓ·q·σ·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·σ·R·z·k_B⁻¹
m = k₀ · ℓ⁻³·q²·σ⁻¹·R⁻¹·z⁻¹·k_B
null
1
4
3
10
9.9
-1.4
false
{"mass": "1", "length": "3", "charge": "-2", "conductivity": "1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"}
6
avogadro,cat_activity,charge,conductivity,length,mass
m·ℓ·q·σ·z·N_A
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·σ·z·N_A
m = k₀ · ℓ⁻³·q²·σ⁻¹·z⁻¹·N_A⁻¹
null
1
4
3
9
8.9
-0.4
false
{"mass": "1", "length": "3", "charge": "-2", "conductivity": "1", "cat_activity": "1", "avogadro": "1"}
5
charge,conductivity,length,light_speed,mass
m·ℓ·q·σ·c₀
constants,em,mechanics
m·ℓ²·q⁻²·σ·c₀
m = k₀ · ℓ⁻²·q²·σ⁻¹·c₀⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "charge": "-2", "conductivity": "1", "light_speed": "1"}
5
charge,conductivity,grav_const,length,mass
m·ℓ·q·σ·G
constants,em,mechanics
m³·ℓ³·q⁻⁴·σ²·G
G = k₀ · m⁻³·ℓ⁻³·q⁴·σ⁻²
null
1
3
4
13
11.3
-2.3
false
{"mass": "3", "length": "3", "charge": "-4", "conductivity": "2", "grav_const": "1"}
6
amount,charge,length,mass,molar_energy,resistivity
m·ℓ·q·ρ_e·n·E_m
chemistry,em,mechanics
m·ℓ⁴·q⁻⁴·ρ_e⁻²·n·E_m
m = k₀ · ℓ⁻⁴·q⁴·ρ_e²·n⁻¹·E_m⁻¹
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "4", "charge": "-4", "resistivity": "-2", "amount": "1", "molar_energy": "1"}
6
amount,cat_activity,charge,length,mass,resistivity
m·ℓ·q·ρ_e·n·z
chemistry,em,mechanics
m·ℓ³·q⁻²·ρ_e⁻¹·n⁻¹·z
m = k₀ · ℓ⁻³·q²·ρ_e·n·z⁻¹
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "3", "charge": "-2", "resistivity": "-1", "amount": "-1", "cat_activity": "1"}
6
charge,length,mass,molar_energy,molar_mass,resistivity
m·ℓ·q·ρ_e·M_m·E_m
chemistry,em,mechanics
m²·ℓ⁴·q⁻⁴·ρ_e⁻²·M_m⁻¹·E_m
M_m = k₀ · m²·ℓ⁴·q⁻⁴·ρ_e⁻²·E_m
null
0
3
4
14
12.3
-3.3
false
{"mass": "2", "length": "4", "charge": "-4", "resistivity": "-2", "molar_mass": "-1", "molar_energy": "1"}
6
charge,concentration,length,mass,molar_energy,resistivity
m·ℓ·q·ρ_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁷·q⁻⁴·ρ_e⁻²·c_n·E_m
m = k₀ · ℓ⁻⁷·q⁴·ρ_e²·c_n⁻¹·E_m⁻¹
null
0
3
7
16
15.2
-6.2
false
{"mass": "1", "length": "7", "charge": "-4", "resistivity": "-2", "concentration": "1", "molar_energy": "1"}
7
boltzmann,charge,gas_constant,length,mass,molar_energy,resistivity
m·ℓ·q·ρ_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁴·q⁻⁴·ρ_e⁻²·E_m·R⁻¹·k_B
m = k₀ · ℓ⁻⁴·q⁴·ρ_e²·E_m⁻¹·R·k_B⁻¹
null
1
4
4
14
13.2
-4.7
false
{"mass": "1", "length": "4", "charge": "-4", "resistivity": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"}
6
cat_activity,charge,length,mass,molar_energy,resistivity
m·ℓ·q·ρ_e·E_m·z
chemistry,em,mechanics
m²·ℓ⁷·q⁻⁶·ρ_e⁻³·E_m·z
E_m = k₀ · m⁻²·ℓ⁻⁷·q⁶·ρ_e³·z⁻¹
null
0
3
7
20
18
-9
false
{"mass": "2", "length": "7", "charge": "-6", "resistivity": "-3", "molar_energy": "1", "cat_activity": "1"}
6
avogadro,charge,length,mass,molar_energy,resistivity
m·ℓ·q·ρ_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·q⁻⁴·ρ_e⁻²·E_m·N_A⁻¹
m = k₀ · ℓ⁻⁴·q⁴·ρ_e²·E_m⁻¹·N_A
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "charge": "-4", "resistivity": "-2", "molar_energy": "1", "avogadro": "-1"}
7
boltzmann,cat_activity,charge,gas_constant,length,mass,resistivity
m·ℓ·q·ρ_e·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·ρ_e⁻¹·R·z·k_B⁻¹
m = k₀ · ℓ⁻³·q²·ρ_e·R⁻¹·z⁻¹·k_B
null
1
4
3
10
9.9
-1.4
false
{"mass": "1", "length": "3", "charge": "-2", "resistivity": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"}
6
avogadro,cat_activity,charge,length,mass,resistivity
m·ℓ·q·ρ_e·z·N_A
chemistry,constants,em,mechanics
m·ℓ³·q⁻²·ρ_e⁻¹·z·N_A
m = k₀ · ℓ⁻³·q²·ρ_e·z⁻¹·N_A⁻¹
null
1
4
3
9
8.9
-0.4
false
{"mass": "1", "length": "3", "charge": "-2", "resistivity": "-1", "cat_activity": "1", "avogadro": "1"}
5
charge,length,light_speed,mass,resistivity
m·ℓ·q·ρ_e·c₀
constants,em,mechanics
m·ℓ²·q⁻²·ρ_e⁻¹·c₀
m = k₀ · ℓ⁻²·q²·ρ_e·c₀⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "charge": "-2", "resistivity": "-1", "light_speed": "1"}
5
charge,grav_const,length,mass,resistivity
m·ℓ·q·ρ_e·G
constants,em,mechanics
m³·ℓ³·q⁻⁴·ρ_e⁻²·G
G = k₀ · m⁻³·ℓ⁻³·q⁴·ρ_e²
null
1
3
4
13
11.3
-2.3
false
{"mass": "3", "length": "3", "charge": "-4", "resistivity": "-2", "grav_const": "1"}
5
capacitance,current,length,mass,voltage
m·ℓ·i·U·C_e
em,mechanics
m·ℓ²·i²·U⁻⁴·C_e⁻³
m = k₀ · ℓ⁻²·i⁻²·U⁴·C_e³
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "current": "2", "voltage": "-4", "capacitance": "-3"}
5
current,inductance,length,mass,voltage
m·ℓ·i·U·L_e
em,mechanics
m·ℓ²·i⁻⁴·U²·L_e⁻³
m = k₀ · ℓ⁻²·i⁴·U⁻²·L_e³
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "current": "-4", "voltage": "2", "inductance": "-3"}
5
bfield,current,length,mass,voltage
m·ℓ·i·U·B
em,mechanics
m·ℓ⁻⁴·i⁻¹·U²·B⁻³
m = k₀ · ℓ⁴·i·U⁻²·B³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-4", "current": "-1", "voltage": "2", "bfield": "-3"}
5
current,length,mag_flux,mass,voltage
m·ℓ·i·U·Φ
em,mechanics
m·ℓ²·i⁻¹·U²·Φ⁻³
m = k₀ · ℓ⁻²·i·U⁻²·Φ³
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "2", "current": "-1", "voltage": "2", "mag_flux": "-3"}
5
current,length,mass,permittivity,voltage
m·ℓ·i·U·ε
em,mechanics
m·ℓ⁻¹·i²·U⁻⁴·ε⁻³
m = k₀ · ℓ·i⁻²·U⁴·ε³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-1", "current": "2", "voltage": "-4", "permittivity": "-3"}
5
current,length,mass,permeability,voltage
m·ℓ·i·U·μ₀
em,mechanics
m·ℓ⁻¹·i⁻⁴·U²·μ₀⁻³
m = k₀ · ℓ·i⁴·U⁻²·μ₀³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-1", "current": "-4", "voltage": "2", "permeability": "-3"}
6
amount,current,length,mass,molar_energy,voltage
m·ℓ·i·U·n·E_m
chemistry,em,mechanics
m·ℓ²·i²·U²·n⁻³·E_m⁻³
m = k₀ · ℓ⁻²·i⁻²·U⁻²·n³·E_m³
null
0
3
3
13
11.1
-2.1
false
{"mass": "1", "length": "2", "current": "2", "voltage": "2", "amount": "-3", "molar_energy": "-3"}
6
amount,cat_activity,current,length,mass,voltage
m·ℓ·i·U·n·z
chemistry,em,mechanics
m·ℓ²·i⁻¹·U⁻¹·n⁻³·z³
m = k₀ · ℓ⁻²·i·U·n³·z⁻³
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "2", "current": "-1", "voltage": "-1", "amount": "-3", "cat_activity": "3"}
6
current,length,mass,molar_energy,molar_mass,voltage
m·ℓ·i·U·M_m·E_m
chemistry,em,mechanics
m²·ℓ⁻²·i⁻²·U⁻²·M_m⁻³·E_m³
m = k₀ · ℓ·i·U·M_m³ᐟ²·E_m⁻³ᐟ²
null
0
3
3
14
11.8
-2.8
false
{"mass": "2", "length": "-2", "current": "-2", "voltage": "-2", "molar_mass": "-3", "molar_energy": "3"}
6
cat_activity,current,length,mass,molar_mass,voltage
m·ℓ·i·U·M_m·z
chemistry,em,mechanics
m²·ℓ⁻²·i·U·M_m⁻³·z⁻³
i = k₀ · m⁻²·ℓ²·U⁻¹·M_m³·z³
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "-2", "current": "1", "voltage": "1", "molar_mass": "-3", "cat_activity": "-3"}
6
concentration,current,length,mass,molar_energy,voltage
m·ℓ·i·U·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁷·i²·U²·c_n⁻³·E_m⁻³
m = k₀ · ℓ⁷·i⁻²·U⁻²·c_n³·E_m³
null
0
3
7
18
16.6
-7.6
false
{"mass": "1", "length": "-7", "current": "2", "voltage": "2", "concentration": "-3", "molar_energy": "-3"}
6
cat_activity,concentration,current,length,mass,voltage
m·ℓ·i·U·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁷·i⁻¹·U⁻¹·c_n⁻³·z³
m = k₀ · ℓ⁷·i·U·c_n³·z⁻³
null
0
3
7
16
15.2
-6.2
false
{"mass": "1", "length": "-7", "current": "-1", "voltage": "-1", "concentration": "-3", "cat_activity": "3"}
7
boltzmann,current,gas_constant,length,mass,molar_energy,voltage
m·ℓ·i·U·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·i²·U²·E_m⁻³·R³·k_B⁻³
m = k₀ · ℓ⁻²·i⁻²·U⁻²·E_m³·R⁻³·k_B³
null
1
4
3
16
14.1
-5.6
false
{"mass": "1", "length": "2", "current": "2", "voltage": "2", "molar_energy": "-3", "gas_constant": "3", "boltzmann": "-3"}
6
avogadro,current,length,mass,molar_energy,voltage
m·ℓ·i·U·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·i²·U²·E_m⁻³·N_A³
m = k₀ · ℓ⁻²·i⁻²·U⁻²·E_m³·N_A⁻³
null
1
4
3
13
11.7
-3.2
false
{"mass": "1", "length": "2", "current": "2", "voltage": "2", "molar_energy": "-3", "avogadro": "3"}
7
boltzmann,cat_activity,current,gas_constant,length,mass,voltage
m·ℓ·i·U·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·i⁻¹·U⁻¹·R³·z³·k_B⁻³
m = k₀ · ℓ⁻²·i·U·R⁻³·z⁻³·k_B³
null
1
4
3
14
12.7
-4.2
false
{"mass": "1", "length": "2", "current": "-1", "voltage": "-1", "gas_constant": "3", "cat_activity": "3", "boltzmann": "-3"}
6
avogadro,cat_activity,current,length,mass,voltage
m·ℓ·i·U·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·i⁻¹·U⁻¹·z³·N_A³
m = k₀ · ℓ⁻²·i·U·z⁻³·N_A⁻³
null
1
4
3
11
10.3
-1.8
false
{"mass": "1", "length": "2", "current": "-1", "voltage": "-1", "cat_activity": "3", "avogadro": "3"}
5
current,length,light_speed,mass,voltage
m·ℓ·i·U·c₀
constants,em,mechanics
m·ℓ⁻¹·i⁻¹·U⁻¹·c₀³
m = k₀ · ℓ·i·U·c₀⁻³
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "-1", "current": "-1", "voltage": "-1", "light_speed": "3"}
5
current,grav_const,length,mass,voltage
m·ℓ·i·U·G
constants,em,mechanics
m⁵·ℓ⁻⁵·i⁻²·U⁻²·G³
i = k₀ · m⁵ᐟ²·ℓ⁻⁵ᐟ²·U⁻¹·G³ᐟ²
null
1
3
5
17
14.6
-5.6
false
{"mass": "5", "length": "-5", "current": "-2", "voltage": "-2", "grav_const": "3"}
5
current,length,mass,planck,voltage
m·ℓ·i·U·h
constants,em,mechanics
m²·ℓ⁴·i·U·h⁻³
i = k₀ · m⁻²·ℓ⁻⁴·U⁻¹·h³
null
1
3
4
11
9.9
-0.9
false
{"mass": "2", "length": "4", "current": "1", "voltage": "1", "planck": "-3"}
5
current,elem_charge,length,mass,voltage
m·ℓ·i·U·e
constants,em,mechanics
m·ℓ²·i²·U⁻¹·e⁻³
m = k₀ · ℓ⁻²·i⁻²·U·e³
null
1
3
3
9
8
1
false
{"mass": "1", "length": "2", "current": "2", "voltage": "-1", "elem_charge": "-3"}
5
capacitance,current,length,mass,resistance
m·ℓ·i·R·C_e
em,mechanics
m·ℓ²·i⁻²·R⁻⁴·C_e⁻³
m = k₀ · ℓ⁻²·i²·R⁴·C_e³
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "current": "-2", "resistance": "-4", "capacitance": "-3"}
5
current,inductance,length,mass,resistance
m·ℓ·i·R·L_e
em,mechanics
m·ℓ²·i⁻²·R²·L_e⁻³
m = k₀ · ℓ⁻²·i²·R⁻²·L_e³
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "current": "-2", "resistance": "2", "inductance": "-3"}
5
bfield,current,length,mass,resistance
m·ℓ·i·R·B
em,mechanics
m·ℓ⁻⁴·i·R²·B⁻³
m = k₀ · ℓ⁴·i⁻¹·R⁻²·B³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-4", "current": "1", "resistance": "2", "bfield": "-3"}
5
current,length,mag_flux,mass,resistance
m·ℓ·i·R·Φ
em,mechanics
m·ℓ²·i·R²·Φ⁻³
m = k₀ · ℓ⁻²·i⁻¹·R⁻²·Φ³
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "2", "current": "1", "resistance": "2", "mag_flux": "-3"}
5
current,length,mass,permittivity,resistance
m·ℓ·i·R·ε
em,mechanics
m·ℓ⁻¹·i⁻²·R⁻⁴·ε⁻³
m = k₀ · ℓ·i²·R⁴·ε³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-1", "current": "-2", "resistance": "-4", "permittivity": "-3"}
5
current,length,mass,permeability,resistance
m·ℓ·i·R·μ₀
em,mechanics
m·ℓ⁻¹·i⁻²·R²·μ₀⁻³
m = k₀ · ℓ·i²·R⁻²·μ₀³
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-1", "current": "-2", "resistance": "2", "permeability": "-3"}
6
amount,current,length,mass,molar_energy,resistance
m·ℓ·i·R·n·E_m
chemistry,em,mechanics
m·ℓ²·i⁴·R²·n⁻³·E_m⁻³
m = k₀ · ℓ⁻²·i⁻⁴·R⁻²·n³·E_m³
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "2", "current": "4", "resistance": "2", "amount": "-3", "molar_energy": "-3"}
6
amount,cat_activity,current,length,mass,resistance
m·ℓ·i·R·n·z
chemistry,em,mechanics
m·ℓ²·i⁻²·R⁻¹·n⁻³·z³
m = k₀ · ℓ⁻²·i²·R·n³·z⁻³
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "current": "-2", "resistance": "-1", "amount": "-3", "cat_activity": "3"}
6
current,length,mass,molar_energy,molar_mass,resistance
m·ℓ·i·R·M_m·E_m
chemistry,em,mechanics
m²·ℓ⁻²·i⁻⁴·R⁻²·M_m⁻³·E_m³
m = k₀ · ℓ·i²·R·M_m³ᐟ²·E_m⁻³ᐟ²
null
0
3
4
16
13.7
-4.7
false
{"mass": "2", "length": "-2", "current": "-4", "resistance": "-2", "molar_mass": "-3", "molar_energy": "3"}
6
cat_activity,current,length,mass,molar_mass,resistance
m·ℓ·i·R·M_m·z
chemistry,em,mechanics
m²·ℓ⁻²·i²·R·M_m⁻³·z⁻³
R = k₀ · m⁻²·ℓ²·i⁻²·M_m³·z³
null
0
3
3
13
11.1
-2.1
false
{"mass": "2", "length": "-2", "current": "2", "resistance": "1", "molar_mass": "-3", "cat_activity": "-3"}
6
concentration,current,length,mass,molar_energy,resistance
m·ℓ·i·R·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁷·i⁴·R²·c_n⁻³·E_m⁻³
m = k₀ · ℓ⁷·i⁻⁴·R⁻²·c_n³·E_m³
null
0
3
7
20
18
-9
false
{"mass": "1", "length": "-7", "current": "4", "resistance": "2", "concentration": "-3", "molar_energy": "-3"}
6
cat_activity,concentration,current,length,mass,resistance
m·ℓ·i·R·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁷·i⁻²·R⁻¹·c_n⁻³·z³
m = k₀ · ℓ⁷·i²·R·c_n³·z⁻³
null
0
3
7
17
15.9
-6.9
false
{"mass": "1", "length": "-7", "current": "-2", "resistance": "-1", "concentration": "-3", "cat_activity": "3"}
7
boltzmann,current,gas_constant,length,mass,molar_energy,resistance
m·ℓ·i·R·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·i⁴·R²·E_m⁻³·R³·k_B⁻³
m = k₀ · ℓ⁻²·i⁻⁴·R⁻²·E_m³·R⁻³·k_B³
null
1
4
4
18
16
-7.5
false
{"mass": "1", "length": "2", "current": "4", "resistance": "2", "molar_energy": "-3", "gas_constant": "3", "boltzmann": "-3"}
6
avogadro,current,length,mass,molar_energy,resistance
m·ℓ·i·R·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·i⁴·R²·E_m⁻³·N_A³
m = k₀ · ℓ⁻²·i⁻⁴·R⁻²·E_m³·N_A⁻³
null
1
4
4
15
13.6
-5.1
false
{"mass": "1", "length": "2", "current": "4", "resistance": "2", "molar_energy": "-3", "avogadro": "3"}
7
boltzmann,cat_activity,current,gas_constant,length,mass,resistance
m·ℓ·i·R·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·i⁻²·R⁻¹·R³·z³·k_B⁻³
m = k₀ · ℓ⁻²·i²·R·R⁻³·z⁻³·k_B³
null
1
4
3
15
13.4
-4.9
false
{"mass": "1", "length": "2", "current": "-2", "resistance": "-1", "gas_constant": "3", "cat_activity": "3", "boltzmann": "-3"}
6
avogadro,cat_activity,current,length,mass,resistance
m·ℓ·i·R·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·i⁻²·R⁻¹·z³·N_A³
m = k₀ · ℓ⁻²·i²·R·z⁻³·N_A⁻³
null
1
4
3
12
11
-2.5
false
{"mass": "1", "length": "2", "current": "-2", "resistance": "-1", "cat_activity": "3", "avogadro": "3"}
5
current,length,light_speed,mass,resistance
m·ℓ·i·R·c₀
constants,em,mechanics
m·ℓ⁻¹·i⁻²·R⁻¹·c₀³
m = k₀ · ℓ·i²·R·c₀⁻³
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "-1", "current": "-2", "resistance": "-1", "light_speed": "3"}
5
current,grav_const,length,mass,resistance
m·ℓ·i·R·G
constants,em,mechanics
m⁵·ℓ⁻⁵·i⁻⁴·R⁻²·G³
R = k₀ · m⁵ᐟ²·ℓ⁻⁵ᐟ²·i⁻²·G³ᐟ²
null
1
3
5
19
16
-7
false
{"mass": "5", "length": "-5", "current": "-4", "resistance": "-2", "grav_const": "3"}
5
current,length,mass,planck,resistance
m·ℓ·i·R·h
constants,em,mechanics
m²·ℓ⁴·i²·R·h⁻³
R = k₀ · m⁻²·ℓ⁻⁴·i⁻²·h³
null
1
3
4
12
10.6
-1.6
false
{"mass": "2", "length": "4", "current": "2", "resistance": "1", "planck": "-3"}
5
current,elem_charge,length,mass,resistance
m·ℓ·i·R·e
constants,em,mechanics
m·ℓ²·i·R⁻¹·e⁻³
m = k₀ · ℓ⁻²·i⁻¹·R·e³
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "2", "current": "1", "resistance": "-1", "elem_charge": "-3"}
5
capacitance,current,inductance,length,mass
m·ℓ·i·C_e·L_e
em,mechanics
m·ℓ²·i⁻²·C_e⁻¹·L_e⁻²
m = k₀ · ℓ⁻²·i²·C_e·L_e²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "current": "-2", "capacitance": "-1", "inductance": "-2"}
5
capacitance,current,efield,length,mass
m·ℓ·i·C_e·E_f
em,mechanics
m·ℓ⁻²·i²·C_e⁻³·E_f⁻⁴
m = k₀ · ℓ²·i⁻²·C_e³·E_f⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-2", "current": "2", "capacitance": "-3", "efield": "-4"}
5
capacitance,conductivity,current,length,mass
m·ℓ·i·C_e·σ
em,mechanics
m·ℓ⁶·i⁻²·C_e⁻³·σ⁴
m = k₀ · ℓ⁻⁶·i²·C_e³·σ⁻⁴
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "6", "current": "-2", "capacitance": "-3", "conductivity": "4"}
5
capacitance,current,length,mass,resistivity
m·ℓ·i·C_e·ρ_e
em,mechanics
m·ℓ⁶·i⁻²·C_e⁻³·ρ_e⁻⁴
m = k₀ · ℓ⁻⁶·i²·C_e³·ρ_e⁴
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "6", "current": "-2", "capacitance": "-3", "resistivity": "-4"}
6
amount,capacitance,current,length,mass,molar_energy
m·ℓ·i·C_e·n·E_m
chemistry,em,mechanics
m·ℓ²·i²·C_e⁻¹·n⁻²·E_m⁻²
m = k₀ · ℓ⁻²·i⁻²·C_e·n²·E_m²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "current": "2", "capacitance": "-1", "amount": "-2", "molar_energy": "-2"}
6
amount,capacitance,cat_activity,current,length,mass
m·ℓ·i·C_e·n·z
chemistry,em,mechanics
m·ℓ²·i⁻²·C_e·n⁻⁴·z⁴
m = k₀ · ℓ⁻²·i²·C_e⁻¹·n⁴·z⁻⁴
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "2", "current": "-2", "capacitance": "1", "amount": "-4", "cat_activity": "4"}
6
capacitance,current,length,mass,molar_energy,molar_mass
m·ℓ·i·C_e·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻²·i⁻²·C_e·M_m⁻²·E_m²
m = k₀ · ℓ²·i²·C_e⁻¹·M_m²·E_m⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "current": "-2", "capacitance": "1", "molar_mass": "-2", "molar_energy": "2"}
6
capacitance,cat_activity,current,length,mass,molar_mass
m·ℓ·i·C_e·M_m·z
chemistry,em,mechanics
m³·ℓ⁻²·i²·C_e⁻¹·M_m⁻⁴·z⁻⁴
C_e = k₀ · m³·ℓ⁻²·i²·M_m⁻⁴·z⁻⁴
null
0
3
4
16
13.7
-4.7
false
{"mass": "3", "length": "-2", "current": "2", "capacitance": "-1", "molar_mass": "-4", "cat_activity": "-4"}
6
capacitance,concentration,current,length,mass,molar_energy
m·ℓ·i·C_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁴·i²·C_e⁻¹·c_n⁻²·E_m⁻²
m = k₀ · ℓ⁴·i⁻²·C_e·c_n²·E_m²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "current": "2", "capacitance": "-1", "concentration": "-2", "molar_energy": "-2"}
6
capacitance,cat_activity,concentration,current,length,mass
m·ℓ·i·C_e·c_n·z
chemistry,em,mechanics
m·ℓ⁻¹⁰·i⁻²·C_e·c_n⁻⁴·z⁴
m = k₀ · ℓ¹⁰·i²·C_e⁻¹·c_n⁴·z⁻⁴
null
0
3
10
22
20.9
-11.9
false
{"mass": "1", "length": "-10", "current": "-2", "capacitance": "1", "concentration": "-4", "cat_activity": "4"}
7
boltzmann,capacitance,current,gas_constant,length,mass,molar_energy
m·ℓ·i·C_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·i²·C_e⁻¹·E_m⁻²·R²·k_B⁻²
m = k₀ · ℓ⁻²·i⁻²·C_e·E_m²·R⁻²·k_B²
null
1
4
2
12
10.8
-2.3
false
{"mass": "1", "length": "2", "current": "2", "capacitance": "-1", "molar_energy": "-2", "gas_constant": "2", "boltzmann": "-2"}
6
capacitance,cat_activity,current,length,mass,molar_energy
m·ℓ·i·C_e·E_m·z
chemistry,em,mechanics
m·ℓ²·i⁶·C_e⁻³·E_m⁻⁴·z⁻⁴
m = k₀ · ℓ⁻²·i⁻⁶·C_e³·E_m⁴·z⁴
null
0
3
6
20
17.5
-8.5
false
{"mass": "1", "length": "2", "current": "6", "capacitance": "-3", "molar_energy": "-4", "cat_activity": "-4"}
6
avogadro,capacitance,current,length,mass,molar_energy
m·ℓ·i·C_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·i²·C_e⁻¹·E_m⁻²·N_A²
m = k₀ · ℓ⁻²·i⁻²·C_e·E_m²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "current": "2", "capacitance": "-1", "molar_energy": "-2", "avogadro": "2"}
7
boltzmann,capacitance,cat_activity,current,gas_constant,length,mass
m·ℓ·i·C_e·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·i⁻²·C_e·R⁴·z⁴·k_B⁻⁴
m = k₀ · ℓ⁻²·i²·C_e⁻¹·R⁻⁴·z⁻⁴·k_B⁴
null
1
4
4
18
16
-7.5
false
{"mass": "1", "length": "2", "current": "-2", "capacitance": "1", "gas_constant": "4", "cat_activity": "4", "boltzmann": "-4"}
6
avogadro,capacitance,cat_activity,current,length,mass
m·ℓ·i·C_e·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·i⁻²·C_e·z⁴·N_A⁴
m = k₀ · ℓ⁻²·i²·C_e⁻¹·z⁻⁴·N_A⁻⁴
null
1
4
4
14
12.9
-4.4
false
{"mass": "1", "length": "2", "current": "-2", "capacitance": "1", "cat_activity": "4", "avogadro": "4"}
5
capacitance,current,length,light_speed,mass
m·ℓ·i·C_e·c₀
constants,em,mechanics
m·ℓ⁻²·i⁻²·C_e·c₀⁴
m = k₀ · ℓ²·i²·C_e⁻¹·c₀⁻⁴
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "-2", "current": "-2", "capacitance": "1", "light_speed": "4"}
5
capacitance,current,grav_const,length,mass
m·ℓ·i·C_e·G
constants,em,mechanics
m³·ℓ⁻⁴·i⁻²·C_e·G²
C_e = k₀ · m⁻³·ℓ⁴·i²·G⁻²
null
1
3
4
12
10.6
-1.6
false
{"mass": "3", "length": "-4", "current": "-2", "capacitance": "1", "grav_const": "2"}
5
capacitance,current,length,mass,planck
m·ℓ·i·C_e·h
constants,em,mechanics
m³·ℓ⁶·i²·C_e⁻¹·h⁻⁴
C_e = k₀ · m³·ℓ⁶·i²·h⁻⁴
null
1
3
6
16
14.4
-5.4
false
{"mass": "3", "length": "6", "current": "2", "capacitance": "-1", "planck": "-4"}