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
6
cat_activity,gas_constant,length,mass,stiffness,temperature
m·ℓ·k·Θ·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁴·k⁻³·Θ²·R²·z²
m = k₀ · ℓ⁴·k³·Θ⁻²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "-4", "stiffness": "-3", "temperature": "2", "gas_constant": "2", "cat_activity": "2"}
5
entropy,length,mass,stiffness,thermal_cond
m·ℓ·k·S_e·κ
mechanics,thermo
m·ℓ²·k⁻¹·S_e⁻²·κ²
m = k₀ · ℓ⁻²·k·S_e²·κ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "stiffness": "-1", "entropy": "-2", "thermal_cond": "2"}
5
heat_capacity,length,mass,stiffness,thermal_cond
m·ℓ·k·C·κ
mechanics,thermo
m·ℓ²·k⁻¹·C⁻²·κ²
m = k₀ · ℓ⁻²·k·C²·κ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "stiffness": "-1", "heat_capacity": "-2", "thermal_cond": "2"}
5
length,mass,specific_heat,stiffness,thermal_cond
m·ℓ·k·c·κ
mechanics,thermo
m·ℓ⁻²·k·c²·κ⁻²
m = k₀ · ℓ²·k⁻¹·c⁻²·κ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "1", "specific_heat": "2", "thermal_cond": "-2"}
5
expansion,length,mass,specific_heat,stiffness
m·ℓ·k·c·β
mechanics,thermo
m·ℓ⁻²·k⁻¹·c·β⁻¹
m = k₀ · ℓ²·k·c⁻¹·β
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "stiffness": "-1", "specific_heat": "1", "expansion": "-1"}
6
gas_constant,length,mass,molar_energy,specific_heat,stiffness
m·ℓ·k·c·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·k⁻¹·c·E_m·R⁻¹
m = k₀ · ℓ²·k·c⁻¹·E_m⁻¹·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "stiffness": "-1", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"}
5
expansion,length,mass,stiffness,thermal_cond
m·ℓ·k·κ·β
mechanics,thermo
m·ℓ⁻²·k⁻³·κ²·β⁻²
m = k₀ · ℓ²·k³·κ⁻²·β²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-2", "stiffness": "-3", "thermal_cond": "2", "expansion": "-2"}
6
amount,gas_constant,length,mass,stiffness,thermal_cond
m·ℓ·k·κ·n·R
chemistry,mechanics,thermo
m·ℓ²·k⁻¹·κ²·n⁻²·R⁻²
m = k₀ · ℓ⁻²·k·κ⁻²·n²·R²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "stiffness": "-1", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_mass,stiffness,thermal_cond
m·ℓ·k·κ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·k·κ⁻²·M_m⁻²·R²
m = k₀ · ℓ²·k⁻¹·κ²·M_m²·R⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "stiffness": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
concentration,gas_constant,length,mass,stiffness,thermal_cond
m·ℓ·k·κ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻⁴·k⁻¹·κ²·c_n⁻²·R⁻²
m = k₀ · ℓ⁴·k·κ⁻²·c_n²·R²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "stiffness": "-1", "thermal_cond": "2", "concentration": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_energy,stiffness,thermal_cond
m·ℓ·k·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·k⁻³·κ²·E_m²·R⁻²
m = k₀ · ℓ²·k³·κ⁻²·E_m⁻²·R²
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "-2", "stiffness": "-3", "thermal_cond": "2", "molar_energy": "2", "gas_constant": "-2"}
6
avogadro,gas_constant,length,mass,stiffness,thermal_cond
m·ℓ·k·κ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·k⁻¹·κ²·R⁻²·N_A²
m = k₀ · ℓ⁻²·k·κ⁻²·R²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "stiffness": "-1", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"}
5
boltzmann,length,mass,stiffness,thermal_cond
m·ℓ·k·κ·k_B
constants,mechanics,thermo
m·ℓ²·k⁻¹·κ²·k_B⁻²
m = k₀ · ℓ⁻²·k·κ⁻²·k_B²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "stiffness": "-1", "thermal_cond": "2", "boltzmann": "-2"}
4
length,mass,stiffness,thermal_diff
m·ℓ·k·α
mechanics,thermo
m·ℓ⁻⁴·k⁻¹·α²
m = k₀ · ℓ⁴·k·α⁻²
null
0
2
4
8
6.9
2.6
false
{"mass": "1", "length": "-4", "stiffness": "-1", "thermal_diff": "2"}
6
expansion,gas_constant,length,mass,molar_mass,stiffness
m·ℓ·k·β·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·k⁻¹·β⁻¹·M_m⁻¹·R
m = k₀ · ℓ²·k·β·M_m·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "stiffness": "-1", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"}
6
cat_activity,expansion,gas_constant,length,mass,stiffness
m·ℓ·k·β·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁴·k⁻³·β⁻²·R²·z²
m = k₀ · ℓ⁴·k³·β²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "-4", "stiffness": "-3", "expansion": "-2", "gas_constant": "2", "cat_activity": "2"}
5
charge,length,mass,resistance,stiffness
m·ℓ·k·q·R
em,mechanics
m·ℓ⁴·k·q⁻⁴·R⁻²
m = k₀ · ℓ⁻⁴·k⁻¹·q⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "stiffness": "1", "charge": "-4", "resistance": "-2"}
5
charge,length,mag_flux,mass,stiffness
m·ℓ·k·q·Φ
em,mechanics
m·ℓ⁴·k·q⁻²·Φ⁻²
m = k₀ · ℓ⁻⁴·k⁻¹·q²·Φ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "stiffness": "1", "charge": "-2", "mag_flux": "-2"}
5
charge,conductivity,length,mass,stiffness
m·ℓ·k·q·σ
em,mechanics
m·ℓ⁶·k·q⁻⁴·σ²
m = k₀ · ℓ⁻⁶·k⁻¹·q⁴·σ⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "6", "stiffness": "1", "charge": "-4", "conductivity": "2"}
5
charge,length,mass,resistivity,stiffness
m·ℓ·k·q·ρ_e
em,mechanics
m·ℓ⁶·k·q⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁶·k⁻¹·q⁴·ρ_e²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "6", "stiffness": "1", "charge": "-4", "resistivity": "-2"}
5
current,length,mass,stiffness,voltage
m·ℓ·k·i·U
em,mechanics
m·ℓ⁻⁴·k⁻³·i²·U²
m = k₀ · ℓ⁴·k³·i⁻²·U⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "stiffness": "-3", "current": "2", "voltage": "2"}
5
current,length,mass,resistance,stiffness
m·ℓ·k·i·R
em,mechanics
m·ℓ⁻⁴·k⁻³·i⁴·R²
m = k₀ · ℓ⁴·k³·i⁻⁴·R⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "stiffness": "-3", "current": "4", "resistance": "2"}
5
capacitance,current,length,mass,stiffness
m·ℓ·k·i·C_e
em,mechanics
m·ℓ⁻²·k⁻²·i²·C_e⁻¹
m = k₀ · ℓ²·k²·i⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-2", "current": "2", "capacitance": "-1"}
5
current,efield,length,mass,stiffness
m·ℓ·k·i·E_f
em,mechanics
m·ℓ⁻²·k⁻³·i²·E_f²
m = k₀ · ℓ²·k³·i⁻²·E_f⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-2", "stiffness": "-3", "current": "2", "efield": "2"}
5
current,length,mass,permittivity,stiffness
m·ℓ·k·i·ε
em,mechanics
m·ℓ⁻³·k⁻²·i²·ε⁻¹
m = k₀ · ℓ³·k²·i⁻²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "stiffness": "-2", "current": "2", "permittivity": "-1"}
5
conductivity,current,length,mass,stiffness
m·ℓ·k·i·σ
em,mechanics
m·ℓ⁻⁶·k⁻³·i⁴·σ⁻²
m = k₀ · ℓ⁶·k³·i⁻⁴·σ²
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "-6", "stiffness": "-3", "current": "4", "conductivity": "-2"}
5
current,length,mass,resistivity,stiffness
m·ℓ·k·i·ρ_e
em,mechanics
m·ℓ⁻⁶·k⁻³·i⁴·ρ_e²
m = k₀ · ℓ⁶·k³·i⁻⁴·ρ_e⁻²
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "-6", "stiffness": "-3", "current": "4", "resistivity": "2"}
5
length,mass,resistance,stiffness,voltage
m·ℓ·k·U·R
em,mechanics
m·ℓ⁻⁴·k⁻³·U⁴·R⁻²
m = k₀ · ℓ⁴·k³·U⁻⁴·R²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "stiffness": "-3", "voltage": "4", "resistance": "-2"}
5
inductance,length,mass,stiffness,voltage
m·ℓ·k·U·L_e
em,mechanics
m·ℓ⁻²·k⁻²·U²·L_e⁻¹
m = k₀ · ℓ²·k²·U⁻²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-2", "voltage": "2", "inductance": "-1"}
5
bfield,length,mass,stiffness,voltage
m·ℓ·k·U·B
em,mechanics
m·ℓ⁻⁴·k⁻¹·U²·B⁻²
m = k₀ · ℓ⁴·k·U⁻²·B²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "stiffness": "-1", "voltage": "2", "bfield": "-2"}
5
length,mass,permeability,stiffness,voltage
m·ℓ·k·U·μ₀
em,mechanics
m·ℓ⁻³·k⁻²·U²·μ₀⁻¹
m = k₀ · ℓ³·k²·U⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "stiffness": "-2", "voltage": "2", "permeability": "-1"}
5
conductivity,length,mass,stiffness,voltage
m·ℓ·k·U·σ
em,mechanics
m·ℓ⁻²·k⁻³·U⁴·σ²
m = k₀ · ℓ²·k³·U⁻⁴·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-2", "stiffness": "-3", "voltage": "4", "conductivity": "2"}
5
length,mass,resistivity,stiffness,voltage
m·ℓ·k·U·ρ_e
em,mechanics
m·ℓ⁻²·k⁻³·U⁴·ρ_e⁻²
m = k₀ · ℓ²·k³·U⁻⁴·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-2", "stiffness": "-3", "voltage": "4", "resistivity": "-2"}
5
bfield,length,mass,resistance,stiffness
m·ℓ·k·R·B
em,mechanics
m·ℓ⁻⁴·k·R²·B⁻⁴
m = k₀ · ℓ⁴·k⁻¹·R⁻²·B⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "stiffness": "1", "resistance": "2", "bfield": "-4"}
5
length,mag_flux,mass,resistance,stiffness
m·ℓ·k·R·Φ
em,mechanics
m·ℓ⁴·k·R²·Φ⁻⁴
m = k₀ · ℓ⁻⁴·k⁻¹·R⁻²·Φ⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "stiffness": "1", "resistance": "2", "mag_flux": "-4"}
5
length,mass,permittivity,resistance,stiffness
m·ℓ·k·R·ε
em,mechanics
m·ℓ⁻²·k⁻¹·R⁻²·ε⁻²
m = k₀ · ℓ²·k·R²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-1", "resistance": "-2", "permittivity": "-2"}
5
length,mass,permeability,resistance,stiffness
m·ℓ·k·R·μ₀
em,mechanics
m·ℓ⁻²·k⁻¹·R²·μ₀⁻²
m = k₀ · ℓ²·k·R⁻²·μ₀²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-1", "resistance": "2", "permeability": "-2"}
5
elem_charge,length,mass,resistance,stiffness
m·ℓ·k·R·e
constants,em,mechanics
m·ℓ⁴·k·R⁻²·e⁻⁴
m = k₀ · ℓ⁻⁴·k⁻¹·R²·e⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "1", "length": "4", "stiffness": "1", "resistance": "-2", "elem_charge": "-4"}
5
capacitance,length,mass,permeability,stiffness
m·ℓ·k·C_e·μ₀
em,mechanics
m·ℓ⁻¹·k⁻¹·C_e⁻¹·μ₀⁻¹
m = k₀ · ℓ·k·C_e·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "stiffness": "-1", "capacitance": "-1", "permeability": "-1"}
5
capacitance,conductivity,length,mass,stiffness
m·ℓ·k·C_e·σ
em,mechanics
m·ℓ²·k⁻¹·C_e⁻²·σ²
m = k₀ · ℓ⁻²·k·C_e²·σ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "stiffness": "-1", "capacitance": "-2", "conductivity": "2"}
5
capacitance,length,mass,resistivity,stiffness
m·ℓ·k·C_e·ρ_e
em,mechanics
m·ℓ²·k⁻¹·C_e⁻²·ρ_e⁻²
m = k₀ · ℓ⁻²·k·C_e²·ρ_e²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "stiffness": "-1", "capacitance": "-2", "resistivity": "-2"}
5
inductance,length,mass,permittivity,stiffness
m·ℓ·k·L_e·ε
em,mechanics
m·ℓ⁻¹·k⁻¹·L_e⁻¹·ε⁻¹
m = k₀ · ℓ·k·L_e·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "stiffness": "-1", "inductance": "-1", "permittivity": "-1"}
5
conductivity,inductance,length,mass,stiffness
m·ℓ·k·L_e·σ
em,mechanics
m·ℓ⁻²·k⁻¹·L_e⁻²·σ⁻²
m = k₀ · ℓ²·k·L_e²·σ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-1", "inductance": "-2", "conductivity": "-2"}
5
inductance,length,mass,resistivity,stiffness
m·ℓ·k·L_e·ρ_e
em,mechanics
m·ℓ⁻²·k⁻¹·L_e⁻²·ρ_e²
m = k₀ · ℓ²·k·L_e²·ρ_e⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-1", "inductance": "-2", "resistivity": "2"}
5
bfield,efield,length,mass,stiffness
m·ℓ·k·E_f·B
em,mechanics
m·ℓ⁻²·k⁻¹·E_f²·B⁻²
m = k₀ · ℓ²·k·E_f⁻²·B²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "stiffness": "-1", "efield": "2", "bfield": "-2"}
5
efield,length,mag_flux,mass,stiffness
m·ℓ·k·E_f·Φ
em,mechanics
m·ℓ²·k⁻¹·E_f²·Φ⁻²
m = k₀ · ℓ⁻²·k·E_f⁻²·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "stiffness": "-1", "efield": "2", "mag_flux": "-2"}
5
efield,length,mass,permeability,stiffness
m·ℓ·k·E_f·μ₀
em,mechanics
m·ℓ⁻¹·k⁻²·E_f²·μ₀⁻¹
m = k₀ · ℓ·k²·E_f⁻²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "stiffness": "-2", "efield": "2", "permeability": "-1"}
5
conductivity,efield,length,mass,stiffness
m·ℓ·k·E_f·σ
em,mechanics
m·ℓ²·k⁻³·E_f⁴·σ²
m = k₀ · ℓ⁻²·k³·E_f⁻⁴·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "stiffness": "-3", "efield": "4", "conductivity": "2"}
5
efield,length,mass,resistivity,stiffness
m·ℓ·k·E_f·ρ_e
em,mechanics
m·ℓ²·k⁻³·E_f⁴·ρ_e⁻²
m = k₀ · ℓ⁻²·k³·E_f⁻⁴·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "stiffness": "-3", "efield": "4", "resistivity": "-2"}
5
bfield,conductivity,length,mass,stiffness
m·ℓ·k·B·σ
em,mechanics
m·ℓ⁻⁶·k·B⁻⁴·σ⁻²
m = k₀ · ℓ⁶·k⁻¹·B⁴·σ²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "stiffness": "1", "bfield": "-4", "conductivity": "-2"}
5
bfield,length,mass,resistivity,stiffness
m·ℓ·k·B·ρ_e
em,mechanics
m·ℓ⁻⁶·k·B⁻⁴·ρ_e²
m = k₀ · ℓ⁶·k⁻¹·B⁴·ρ_e⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "stiffness": "1", "bfield": "-4", "resistivity": "2"}
5
conductivity,length,mag_flux,mass,stiffness
m·ℓ·k·Φ·σ
em,mechanics
m·ℓ²·k·Φ⁻⁴·σ⁻²
m = k₀ · ℓ⁻²·k⁻¹·Φ⁴·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "stiffness": "1", "mag_flux": "-4", "conductivity": "-2"}
5
length,mag_flux,mass,resistivity,stiffness
m·ℓ·k·Φ·ρ_e
em,mechanics
m·ℓ²·k·Φ⁻⁴·ρ_e²
m = k₀ · ℓ⁻²·k⁻¹·Φ⁴·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "stiffness": "1", "mag_flux": "-4", "resistivity": "2"}
5
elem_charge,length,mag_flux,mass,stiffness
m·ℓ·k·Φ·e
constants,em,mechanics
m·ℓ⁴·k·Φ⁻²·e⁻²
m = k₀ · ℓ⁻⁴·k⁻¹·Φ²·e²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "4", "stiffness": "1", "mag_flux": "-2", "elem_charge": "-2"}
5
length,mass,permeability,permittivity,stiffness
m·ℓ·k·ε·μ₀
em,mechanics
m·ℓ⁻²·k⁻¹·ε⁻¹·μ₀⁻¹
m = k₀ · ℓ²·k·ε·μ₀
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "stiffness": "-1", "permittivity": "-1", "permeability": "-1"}
5
conductivity,length,mass,permeability,stiffness
m·ℓ·k·μ₀·σ
em,mechanics
m·ℓ⁻⁴·k⁻¹·μ₀⁻²·σ⁻²
m = k₀ · ℓ⁴·k·μ₀²·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "stiffness": "-1", "permeability": "-2", "conductivity": "-2"}
5
length,mass,permeability,resistivity,stiffness
m·ℓ·k·μ₀·ρ_e
em,mechanics
m·ℓ⁻⁴·k⁻¹·μ₀⁻²·ρ_e²
m = k₀ · ℓ⁴·k·μ₀²·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "stiffness": "-1", "permeability": "-2", "resistivity": "2"}
5
conductivity,elem_charge,length,mass,stiffness
m·ℓ·k·σ·e
constants,em,mechanics
m·ℓ⁶·k·σ²·e⁻⁴
m = k₀ · ℓ⁻⁶·k⁻¹·σ⁻²·e⁴
null
1
3
6
14
13
-4
false
{"mass": "1", "length": "6", "stiffness": "1", "conductivity": "2", "elem_charge": "-4"}
5
elem_charge,length,mass,resistivity,stiffness
m·ℓ·k·ρ_e·e
constants,em,mechanics
m·ℓ⁶·k·ρ_e⁻²·e⁻⁴
m = k₀ · ℓ⁻⁶·k⁻¹·ρ_e²·e⁴
null
1
3
6
14
13
-4
false
{"mass": "1", "length": "6", "stiffness": "1", "resistivity": "-2", "elem_charge": "-4"}
5
length,mass,molar_energy,molar_mass,stiffness
m·ℓ·k·M_m·E_m
chemistry,mechanics
m·ℓ⁻²·k⁻¹·M_m⁻¹·E_m
m = k₀ · ℓ²·k·M_m·E_m⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "stiffness": "-1", "molar_mass": "-1", "molar_energy": "1"}
5
cat_activity,concentration,length,mass,stiffness
m·ℓ·k·c_n·z
chemistry,mechanics
m·ℓ⁻⁶·k⁻¹·c_n⁻²·z²
m = k₀ · ℓ⁶·k·c_n²·z⁻²
null
0
2
6
12
11
-1.5
false
{"mass": "1", "length": "-6", "stiffness": "-1", "concentration": "-2", "cat_activity": "2"}
5
cat_activity,length,mass,molar_energy,stiffness
m·ℓ·k·E_m·z
chemistry,mechanics
m·ℓ⁻⁴·k⁻³·E_m²·z²
m = k₀ · ℓ⁴·k³·E_m⁻²·z⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "stiffness": "-3", "molar_energy": "2", "cat_activity": "2"}
4
length,light_speed,mass,stiffness
m·ℓ·k·c₀
constants,mechanics
m·ℓ⁻²·k⁻¹·c₀²
m = k₀ · ℓ²·k·c₀⁻²
null
1
2
2
6
4.5
5
true
{"mass": "1", "length": "-2", "stiffness": "-1", "light_speed": "2"}
4
grav_const,length,mass,stiffness
m·ℓ·k·G
constants,mechanics
m²·ℓ⁻³·k⁻¹·G
k = k₀ · m²·ℓ⁻³·G
null
1
2
3
7
5.7
3.8
true
{"mass": "2", "length": "-3", "stiffness": "-1", "grav_const": "1"}
4
length,mass,planck,stiffness
m·ℓ·k·h
constants,mechanics
m·ℓ⁴·k·h⁻²
m = k₀ · ℓ⁻⁴·k⁻¹·h²
null
1
2
4
8
6.9
2.6
false
{"mass": "1", "length": "4", "stiffness": "1", "planck": "-2"}
4
flowrate,length,mass,surf_tension
m·ℓ·γ·Q
mechanics
m·ℓ⁻⁶·γ⁻¹·Q²
m = k₀ · ℓ⁶·γ·Q⁻²
null
0
1
6
10
8.7
1.3
false
{"mass": "1", "length": "-6", "surf_tension": "-1", "flowrate": "2"}
5
length,mass,specific_heat,surf_tension,temperature
m·ℓ·γ·Θ·c
mechanics,thermo
m·ℓ⁻²·γ⁻¹·Θ·c
m = k₀ · ℓ²·γ·Θ⁻¹·c⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "surf_tension": "-1", "temperature": "1", "specific_heat": "1"}
5
length,mass,surf_tension,temperature,thermal_cond
m·ℓ·γ·Θ·κ
mechanics,thermo
m·ℓ⁻²·γ⁻³·Θ²·κ²
m = k₀ · ℓ²·γ³·Θ⁻²·κ⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-2", "surf_tension": "-3", "temperature": "2", "thermal_cond": "2"}
6
gas_constant,length,mass,molar_mass,surf_tension,temperature
m·ℓ·γ·Θ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·γ⁻¹·Θ·M_m⁻¹·R
m = k₀ · ℓ²·γ·Θ⁻¹·M_m·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "surf_tension": "-1", "temperature": "1", "molar_mass": "-1", "gas_constant": "1"}
6
cat_activity,gas_constant,length,mass,surf_tension,temperature
m·ℓ·γ·Θ·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁴·γ⁻³·Θ²·R²·z²
m = k₀ · ℓ⁴·γ³·Θ⁻²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "-4", "surf_tension": "-3", "temperature": "2", "gas_constant": "2", "cat_activity": "2"}
5
entropy,length,mass,surf_tension,thermal_cond
m·ℓ·γ·S_e·κ
mechanics,thermo
m·ℓ²·γ⁻¹·S_e⁻²·κ²
m = k₀ · ℓ⁻²·γ·S_e²·κ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "surf_tension": "-1", "entropy": "-2", "thermal_cond": "2"}
5
heat_capacity,length,mass,surf_tension,thermal_cond
m·ℓ·γ·C·κ
mechanics,thermo
m·ℓ²·γ⁻¹·C⁻²·κ²
m = k₀ · ℓ⁻²·γ·C²·κ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "surf_tension": "-1", "heat_capacity": "-2", "thermal_cond": "2"}
5
length,mass,specific_heat,surf_tension,thermal_cond
m·ℓ·γ·c·κ
mechanics,thermo
m·ℓ⁻²·γ·c²·κ⁻²
m = k₀ · ℓ²·γ⁻¹·c⁻²·κ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "surf_tension": "1", "specific_heat": "2", "thermal_cond": "-2"}
5
expansion,length,mass,specific_heat,surf_tension
m·ℓ·γ·c·β
mechanics,thermo
m·ℓ⁻²·γ⁻¹·c·β⁻¹
m = k₀ · ℓ²·γ·c⁻¹·β
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "surf_tension": "-1", "specific_heat": "1", "expansion": "-1"}
6
gas_constant,length,mass,molar_energy,specific_heat,surf_tension
m·ℓ·γ·c·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·γ⁻¹·c·E_m·R⁻¹
m = k₀ · ℓ²·γ·c⁻¹·E_m⁻¹·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "surf_tension": "-1", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"}
5
expansion,length,mass,surf_tension,thermal_cond
m·ℓ·γ·κ·β
mechanics,thermo
m·ℓ⁻²·γ⁻³·κ²·β⁻²
m = k₀ · ℓ²·γ³·κ⁻²·β²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-2", "surf_tension": "-3", "thermal_cond": "2", "expansion": "-2"}
6
amount,gas_constant,length,mass,surf_tension,thermal_cond
m·ℓ·γ·κ·n·R
chemistry,mechanics,thermo
m·ℓ²·γ⁻¹·κ²·n⁻²·R⁻²
m = k₀ · ℓ⁻²·γ·κ⁻²·n²·R²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "surf_tension": "-1", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_mass,surf_tension,thermal_cond
m·ℓ·γ·κ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·γ·κ⁻²·M_m⁻²·R²
m = k₀ · ℓ²·γ⁻¹·κ²·M_m²·R⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "surf_tension": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
concentration,gas_constant,length,mass,surf_tension,thermal_cond
m·ℓ·γ·κ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻⁴·γ⁻¹·κ²·c_n⁻²·R⁻²
m = k₀ · ℓ⁴·γ·κ⁻²·c_n²·R²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "surf_tension": "-1", "thermal_cond": "2", "concentration": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_energy,surf_tension,thermal_cond
m·ℓ·γ·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·γ⁻³·κ²·E_m²·R⁻²
m = k₀ · ℓ²·γ³·κ⁻²·E_m⁻²·R²
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "-2", "surf_tension": "-3", "thermal_cond": "2", "molar_energy": "2", "gas_constant": "-2"}
6
avogadro,gas_constant,length,mass,surf_tension,thermal_cond
m·ℓ·γ·κ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·γ⁻¹·κ²·R⁻²·N_A²
m = k₀ · ℓ⁻²·γ·κ⁻²·R²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "surf_tension": "-1", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"}
5
boltzmann,length,mass,surf_tension,thermal_cond
m·ℓ·γ·κ·k_B
constants,mechanics,thermo
m·ℓ²·γ⁻¹·κ²·k_B⁻²
m = k₀ · ℓ⁻²·γ·κ⁻²·k_B²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "surf_tension": "-1", "thermal_cond": "2", "boltzmann": "-2"}
4
length,mass,surf_tension,thermal_diff
m·ℓ·γ·α
mechanics,thermo
m·ℓ⁻⁴·γ⁻¹·α²
m = k₀ · ℓ⁴·γ·α⁻²
null
0
2
4
8
6.9
2.6
false
{"mass": "1", "length": "-4", "surf_tension": "-1", "thermal_diff": "2"}
6
expansion,gas_constant,length,mass,molar_mass,surf_tension
m·ℓ·γ·β·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·γ⁻¹·β⁻¹·M_m⁻¹·R
m = k₀ · ℓ²·γ·β·M_m·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "surf_tension": "-1", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"}
6
cat_activity,expansion,gas_constant,length,mass,surf_tension
m·ℓ·γ·β·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁴·γ⁻³·β⁻²·R²·z²
m = k₀ · ℓ⁴·γ³·β²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "-4", "surf_tension": "-3", "expansion": "-2", "gas_constant": "2", "cat_activity": "2"}
5
charge,length,mass,resistance,surf_tension
m·ℓ·γ·q·R
em,mechanics
m·ℓ⁴·γ·q⁻⁴·R⁻²
m = k₀ · ℓ⁻⁴·γ⁻¹·q⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "surf_tension": "1", "charge": "-4", "resistance": "-2"}
5
charge,length,mag_flux,mass,surf_tension
m·ℓ·γ·q·Φ
em,mechanics
m·ℓ⁴·γ·q⁻²·Φ⁻²
m = k₀ · ℓ⁻⁴·γ⁻¹·q²·Φ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "surf_tension": "1", "charge": "-2", "mag_flux": "-2"}
5
charge,conductivity,length,mass,surf_tension
m·ℓ·γ·q·σ
em,mechanics
m·ℓ⁶·γ·q⁻⁴·σ²
m = k₀ · ℓ⁻⁶·γ⁻¹·q⁴·σ⁻²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "6", "surf_tension": "1", "charge": "-4", "conductivity": "2"}
5
charge,length,mass,resistivity,surf_tension
m·ℓ·γ·q·ρ_e
em,mechanics
m·ℓ⁶·γ·q⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁶·γ⁻¹·q⁴·ρ_e²
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "6", "surf_tension": "1", "charge": "-4", "resistivity": "-2"}
5
current,length,mass,surf_tension,voltage
m·ℓ·γ·i·U
em,mechanics
m·ℓ⁻⁴·γ⁻³·i²·U²
m = k₀ · ℓ⁴·γ³·i⁻²·U⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "surf_tension": "-3", "current": "2", "voltage": "2"}
5
current,length,mass,resistance,surf_tension
m·ℓ·γ·i·R
em,mechanics
m·ℓ⁻⁴·γ⁻³·i⁴·R²
m = k₀ · ℓ⁴·γ³·i⁻⁴·R⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "surf_tension": "-3", "current": "4", "resistance": "2"}
5
capacitance,current,length,mass,surf_tension
m·ℓ·γ·i·C_e
em,mechanics
m·ℓ⁻²·γ⁻²·i²·C_e⁻¹
m = k₀ · ℓ²·γ²·i⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "surf_tension": "-2", "current": "2", "capacitance": "-1"}
5
current,efield,length,mass,surf_tension
m·ℓ·γ·i·E_f
em,mechanics
m·ℓ⁻²·γ⁻³·i²·E_f²
m = k₀ · ℓ²·γ³·i⁻²·E_f⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-2", "surf_tension": "-3", "current": "2", "efield": "2"}
5
current,length,mass,permittivity,surf_tension
m·ℓ·γ·i·ε
em,mechanics
m·ℓ⁻³·γ⁻²·i²·ε⁻¹
m = k₀ · ℓ³·γ²·i⁻²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "surf_tension": "-2", "current": "2", "permittivity": "-1"}
5
conductivity,current,length,mass,surf_tension
m·ℓ·γ·i·σ
em,mechanics
m·ℓ⁻⁶·γ⁻³·i⁴·σ⁻²
m = k₀ · ℓ⁶·γ³·i⁻⁴·σ²
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "-6", "surf_tension": "-3", "current": "4", "conductivity": "-2"}
5
current,length,mass,resistivity,surf_tension
m·ℓ·γ·i·ρ_e
em,mechanics
m·ℓ⁻⁶·γ⁻³·i⁴·ρ_e²
m = k₀ · ℓ⁶·γ³·i⁻⁴·ρ_e⁻²
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "-6", "surf_tension": "-3", "current": "4", "resistivity": "2"}
5
length,mass,resistance,surf_tension,voltage
m·ℓ·γ·U·R
em,mechanics
m·ℓ⁻⁴·γ⁻³·U⁴·R⁻²
m = k₀ · ℓ⁴·γ³·U⁻⁴·R²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "surf_tension": "-3", "voltage": "4", "resistance": "-2"}
5
inductance,length,mass,surf_tension,voltage
m·ℓ·γ·U·L_e
em,mechanics
m·ℓ⁻²·γ⁻²·U²·L_e⁻¹
m = k₀ · ℓ²·γ²·U⁻²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "surf_tension": "-2", "voltage": "2", "inductance": "-1"}
5
bfield,length,mass,surf_tension,voltage
m·ℓ·γ·U·B
em,mechanics
m·ℓ⁻⁴·γ⁻¹·U²·B⁻²
m = k₀ · ℓ⁴·γ·U⁻²·B²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "surf_tension": "-1", "voltage": "2", "bfield": "-2"}
5
length,mass,permeability,surf_tension,voltage
m·ℓ·γ·U·μ₀
em,mechanics
m·ℓ⁻³·γ⁻²·U²·μ₀⁻¹
m = k₀ · ℓ³·γ²·U⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "surf_tension": "-2", "voltage": "2", "permeability": "-1"}