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
length,mass,temperature,thermal_cond,torque
m·ℓ·τ·Θ·κ
mechanics,thermo
m·ℓ⁴·τ⁻³·Θ²·κ²
m = k₀ · ℓ⁻⁴·τ³·Θ⁻²·κ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "torque": "-3", "temperature": "2", "thermal_cond": "2"}
6
cat_activity,gas_constant,length,mass,temperature,torque
m·ℓ·τ·Θ·R·z
chemistry,mechanics,thermo
m·ℓ²·τ⁻³·Θ²·R²·z²
m = k₀ · ℓ⁻²·τ³·Θ⁻²·R⁻²·z⁻²
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "torque": "-3", "temperature": "2", "gas_constant": "2", "cat_activity": "2"}
5
entropy,length,mass,thermal_cond,torque
m·ℓ·τ·S_e·κ
mechanics,thermo
m·ℓ⁴·τ⁻¹·S_e⁻²·κ²
m = k₀ · ℓ⁻⁴·τ·S_e²·κ⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-1", "entropy": "-2", "thermal_cond": "2"}
6
cat_activity,entropy,gas_constant,length,mass,torque
m·ℓ·τ·S_e·R·z
chemistry,mechanics,thermo
m·ℓ²·τ⁻¹·S_e⁻²·R²·z²
m = k₀ · ℓ⁻²·τ·S_e²·R⁻²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "torque": "-1", "entropy": "-2", "gas_constant": "2", "cat_activity": "2"}
5
heat_capacity,length,mass,thermal_cond,torque
m·ℓ·τ·C·κ
mechanics,thermo
m·ℓ⁴·τ⁻¹·C⁻²·κ²
m = k₀ · ℓ⁻⁴·τ·C²·κ⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-1", "heat_capacity": "-2", "thermal_cond": "2"}
6
cat_activity,gas_constant,heat_capacity,length,mass,torque
m·ℓ·τ·C·R·z
chemistry,mechanics,thermo
m·ℓ²·τ⁻¹·C⁻²·R²·z²
m = k₀ · ℓ⁻²·τ·C²·R⁻²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "torque": "-1", "heat_capacity": "-2", "gas_constant": "2", "cat_activity": "2"}
5
length,mass,specific_heat,thermal_cond,torque
m·ℓ·τ·c·κ
mechanics,thermo
m·ℓ⁻⁴·τ·c²·κ⁻²
m = k₀ · ℓ⁴·τ⁻¹·c⁻²·κ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "torque": "1", "specific_heat": "2", "thermal_cond": "-2"}
6
cat_activity,gas_constant,length,mass,specific_heat,torque
m·ℓ·τ·c·R·z
chemistry,mechanics,thermo
m·ℓ⁻²·τ·c²·R⁻²·z⁻²
m = k₀ · ℓ²·τ⁻¹·c⁻²·R²·z²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "torque": "1", "specific_heat": "2", "gas_constant": "-2", "cat_activity": "-2"}
5
expansion,length,mass,thermal_cond,torque
m·ℓ·τ·κ·β
mechanics,thermo
m·ℓ⁴·τ⁻³·κ²·β⁻²
m = k₀ · ℓ⁻⁴·τ³·κ⁻²·β²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "torque": "-3", "thermal_cond": "2", "expansion": "-2"}
6
amount,gas_constant,length,mass,thermal_cond,torque
m·ℓ·τ·κ·n·R
chemistry,mechanics,thermo
m·ℓ⁴·τ⁻¹·κ²·n⁻²·R⁻²
m = k₀ · ℓ⁻⁴·τ·κ⁻²·n²·R²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "torque": "-1", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_mass,thermal_cond,torque
m·ℓ·τ·κ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻⁴·τ·κ⁻²·M_m⁻²·R²
m = k₀ · ℓ⁴·τ⁻¹·κ²·M_m²·R⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "torque": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
concentration,gas_constant,length,mass,thermal_cond,torque
m·ℓ·τ·κ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻²·τ⁻¹·κ²·c_n⁻²·R⁻²
m = k₀ · ℓ²·τ·κ⁻²·c_n²·R²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "torque": "-1", "thermal_cond": "2", "concentration": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_energy,thermal_cond,torque
m·ℓ·τ·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ⁴·τ⁻³·κ²·E_m²·R⁻²
m = k₀ · ℓ⁻⁴·τ³·κ⁻²·E_m⁻²·R²
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "4", "torque": "-3", "thermal_cond": "2", "molar_energy": "2", "gas_constant": "-2"}
6
avogadro,gas_constant,length,mass,thermal_cond,torque
m·ℓ·τ·κ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ⁴·τ⁻¹·κ²·R⁻²·N_A²
m = k₀ · ℓ⁻⁴·τ·κ⁻²·R²·N_A⁻²
null
1
4
4
12
11.5
-3
false
{"mass": "1", "length": "4", "torque": "-1", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"}
5
boltzmann,length,mass,thermal_cond,torque
m·ℓ·τ·κ·k_B
constants,mechanics,thermo
m·ℓ⁴·τ⁻¹·κ²·k_B⁻²
m = k₀ · ℓ⁻⁴·τ·κ⁻²·k_B²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "4", "torque": "-1", "thermal_cond": "2", "boltzmann": "-2"}
4
length,mass,thermal_diff,torque
m·ℓ·τ·α
mechanics,thermo
m·ℓ⁻²·τ⁻¹·α²
m = k₀ · ℓ²·τ·α⁻²
null
0
2
2
6
4.5
5
true
{"mass": "1", "length": "-2", "torque": "-1", "thermal_diff": "2"}
6
cat_activity,expansion,gas_constant,length,mass,torque
m·ℓ·τ·β·R·z
chemistry,mechanics,thermo
m·ℓ²·τ⁻³·β⁻²·R²·z²
m = k₀ · ℓ⁻²·τ³·β²·R⁻²·z⁻²
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "torque": "-3", "expansion": "-2", "gas_constant": "2", "cat_activity": "2"}
5
charge,current,length,mass,torque
m·ℓ·τ·q·i
em,mechanics
m·ℓ²·τ⁻¹·q⁻²·i²
m = k₀ · ℓ⁻²·τ·q²·i⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "charge": "-2", "current": "2"}
5
charge,length,mass,resistance,torque
m·ℓ·τ·q·R
em,mechanics
m·ℓ²·τ·q⁻⁴·R⁻²
m = k₀ · ℓ⁻²·τ⁻¹·q⁴·R²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "torque": "1", "charge": "-4", "resistance": "-2"}
5
bfield,charge,length,mass,torque
m·ℓ·τ·q·B
em,mechanics
m·ℓ⁻²·τ·q⁻²·B⁻²
m = k₀ · ℓ²·τ⁻¹·q²·B²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "torque": "1", "charge": "-2", "bfield": "-2"}
5
charge,length,mag_flux,mass,torque
m·ℓ·τ·q·Φ
em,mechanics
m·ℓ²·τ·q⁻²·Φ⁻²
m = k₀ · ℓ⁻²·τ⁻¹·q²·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "1", "charge": "-2", "mag_flux": "-2"}
5
charge,conductivity,length,mass,torque
m·ℓ·τ·q·σ
em,mechanics
m·ℓ⁴·τ·q⁻⁴·σ²
m = k₀ · ℓ⁻⁴·τ⁻¹·q⁴·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "torque": "1", "charge": "-4", "conductivity": "2"}
5
charge,length,mass,resistivity,torque
m·ℓ·τ·q·ρ_e
em,mechanics
m·ℓ⁴·τ·q⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁴·τ⁻¹·q⁴·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "torque": "1", "charge": "-4", "resistivity": "-2"}
5
current,length,mass,torque,voltage
m·ℓ·τ·i·U
em,mechanics
m·ℓ²·τ⁻³·i²·U²
m = k₀ · ℓ⁻²·τ³·i⁻²·U⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "torque": "-3", "current": "2", "voltage": "2"}
5
current,length,mass,resistance,torque
m·ℓ·τ·i·R
em,mechanics
m·ℓ²·τ⁻³·i⁴·R²
m = k₀ · ℓ⁻²·τ³·i⁻⁴·R⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "torque": "-3", "current": "4", "resistance": "2"}
5
capacitance,current,length,mass,torque
m·ℓ·τ·i·C_e
em,mechanics
m·ℓ²·τ⁻²·i²·C_e⁻¹
m = k₀ · ℓ⁻²·τ²·i⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-2", "current": "2", "capacitance": "-1"}
5
current,efield,length,mass,torque
m·ℓ·τ·i·E_f
em,mechanics
m·ℓ⁴·τ⁻³·i²·E_f²
m = k₀ · ℓ⁻⁴·τ³·i⁻²·E_f⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "torque": "-3", "current": "2", "efield": "2"}
5
current,length,mass,permittivity,torque
m·ℓ·τ·i·ε
em,mechanics
m·ℓ·τ⁻²·i²·ε⁻¹
m = k₀ · ℓ⁻¹·τ²·i⁻²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "torque": "-2", "current": "2", "permittivity": "-1"}
5
current,elem_charge,length,mass,torque
m·ℓ·τ·i·e
constants,em,mechanics
m·ℓ²·τ⁻¹·i²·e⁻²
m = k₀ · ℓ⁻²·τ·i⁻²·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "torque": "-1", "current": "2", "elem_charge": "-2"}
5
length,mass,resistance,torque,voltage
m·ℓ·τ·U·R
em,mechanics
m·ℓ²·τ⁻³·U⁴·R⁻²
m = k₀ · ℓ⁻²·τ³·U⁻⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "torque": "-3", "voltage": "4", "resistance": "-2"}
5
inductance,length,mass,torque,voltage
m·ℓ·τ·U·L_e
em,mechanics
m·ℓ²·τ⁻²·U²·L_e⁻¹
m = k₀ · ℓ⁻²·τ²·U⁻²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-2", "voltage": "2", "inductance": "-1"}
5
bfield,length,mass,torque,voltage
m·ℓ·τ·U·B
em,mechanics
m·ℓ⁻²·τ⁻¹·U²·B⁻²
m = k₀ · ℓ²·τ·U⁻²·B²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "torque": "-1", "voltage": "2", "bfield": "-2"}
5
length,mag_flux,mass,torque,voltage
m·ℓ·τ·U·Φ
em,mechanics
m·ℓ²·τ⁻¹·U²·Φ⁻²
m = k₀ · ℓ⁻²·τ·U⁻²·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "voltage": "2", "mag_flux": "-2"}
5
length,mass,permeability,torque,voltage
m·ℓ·τ·U·μ₀
em,mechanics
m·ℓ·τ⁻²·U²·μ₀⁻¹
m = k₀ · ℓ⁻¹·τ²·U⁻²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "torque": "-2", "voltage": "2", "permeability": "-1"}
5
conductivity,length,mass,torque,voltage
m·ℓ·τ·U·σ
em,mechanics
m·ℓ⁴·τ⁻³·U⁴·σ²
m = k₀ · ℓ⁻⁴·τ³·U⁻⁴·σ⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "4", "torque": "-3", "voltage": "4", "conductivity": "2"}
5
length,mass,resistivity,torque,voltage
m·ℓ·τ·U·ρ_e
em,mechanics
m·ℓ⁴·τ⁻³·U⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁴·τ³·U⁻⁴·ρ_e²
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "4", "torque": "-3", "voltage": "4", "resistivity": "-2"}
5
capacitance,length,mass,resistance,torque
m·ℓ·τ·R·C_e
em,mechanics
m·ℓ²·τ⁻¹·R⁻²·C_e⁻²
m = k₀ · ℓ⁻²·τ·R²·C_e²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "resistance": "-2", "capacitance": "-2"}
5
inductance,length,mass,resistance,torque
m·ℓ·τ·R·L_e
em,mechanics
m·ℓ²·τ⁻¹·R²·L_e⁻²
m = k₀ · ℓ⁻²·τ·R⁻²·L_e²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "resistance": "2", "inductance": "-2"}
5
efield,length,mass,resistance,torque
m·ℓ·τ·R·E_f
em,mechanics
m·ℓ⁶·τ⁻³·R⁻²·E_f⁴
m = k₀ · ℓ⁻⁶·τ³·R²·E_f⁻⁴
null
0
2
6
16
13.8
-4.3
false
{"mass": "1", "length": "6", "torque": "-3", "resistance": "-2", "efield": "4"}
5
bfield,length,mass,resistance,torque
m·ℓ·τ·R·B
em,mechanics
m·ℓ⁻⁶·τ·R²·B⁻⁴
m = k₀ · ℓ⁶·τ⁻¹·R⁻²·B⁴
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "torque": "1", "resistance": "2", "bfield": "-4"}
5
length,mag_flux,mass,resistance,torque
m·ℓ·τ·R·Φ
em,mechanics
m·ℓ²·τ·R²·Φ⁻⁴
m = k₀ · ℓ⁻²·τ⁻¹·R⁻²·Φ⁴
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "torque": "1", "resistance": "2", "mag_flux": "-4"}
5
elem_charge,length,mass,resistance,torque
m·ℓ·τ·R·e
constants,em,mechanics
m·ℓ²·τ·R⁻²·e⁻⁴
m = k₀ · ℓ⁻²·τ⁻¹·R²·e⁴
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "2", "torque": "1", "resistance": "-2", "elem_charge": "-4"}
5
capacitance,inductance,length,mass,torque
m·ℓ·τ·C_e·L_e
em,mechanics
m·ℓ²·τ⁻¹·C_e⁻¹·L_e⁻¹
m = k₀ · ℓ⁻²·τ·C_e·L_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "torque": "-1", "capacitance": "-1", "inductance": "-1"}
5
capacitance,length,mass,permeability,torque
m·ℓ·τ·C_e·μ₀
em,mechanics
m·ℓ·τ⁻¹·C_e⁻¹·μ₀⁻¹
m = k₀ · ℓ⁻¹·τ·C_e·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "torque": "-1", "capacitance": "-1", "permeability": "-1"}
5
capacitance,conductivity,length,mass,torque
m·ℓ·τ·C_e·σ
em,mechanics
m·ℓ⁴·τ⁻¹·C_e⁻²·σ²
m = k₀ · ℓ⁻⁴·τ·C_e²·σ⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-1", "capacitance": "-2", "conductivity": "2"}
5
capacitance,length,mass,resistivity,torque
m·ℓ·τ·C_e·ρ_e
em,mechanics
m·ℓ⁴·τ⁻¹·C_e⁻²·ρ_e⁻²
m = k₀ · ℓ⁻⁴·τ·C_e²·ρ_e²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-1", "capacitance": "-2", "resistivity": "-2"}
5
efield,inductance,length,mass,torque
m·ℓ·τ·L_e·E_f
em,mechanics
m·ℓ⁴·τ⁻²·L_e⁻¹·E_f²
m = k₀ · ℓ⁻⁴·τ²·L_e·E_f⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-2", "inductance": "-1", "efield": "2"}
5
inductance,length,mass,permittivity,torque
m·ℓ·τ·L_e·ε
em,mechanics
m·ℓ·τ⁻¹·L_e⁻¹·ε⁻¹
m = k₀ · ℓ⁻¹·τ·L_e·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "torque": "-1", "inductance": "-1", "permittivity": "-1"}
5
efield,length,mag_flux,mass,torque
m·ℓ·τ·E_f·Φ
em,mechanics
m·ℓ⁴·τ⁻¹·E_f²·Φ⁻²
m = k₀ · ℓ⁻⁴·τ·E_f⁻²·Φ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "torque": "-1", "efield": "2", "mag_flux": "-2"}
5
efield,length,mass,permeability,torque
m·ℓ·τ·E_f·μ₀
em,mechanics
m·ℓ³·τ⁻²·E_f²·μ₀⁻¹
m = k₀ · ℓ⁻³·τ²·E_f⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "torque": "-2", "efield": "2", "permeability": "-1"}
5
conductivity,efield,length,mass,torque
m·ℓ·τ·E_f·σ
em,mechanics
m·ℓ⁸·τ⁻³·E_f⁴·σ²
m = k₀ · ℓ⁻⁸·τ³·E_f⁻⁴·σ⁻²
null
0
2
8
18
16.2
-6.7
false
{"mass": "1", "length": "8", "torque": "-3", "efield": "4", "conductivity": "2"}
5
efield,length,mass,resistivity,torque
m·ℓ·τ·E_f·ρ_e
em,mechanics
m·ℓ⁸·τ⁻³·E_f⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁸·τ³·E_f⁻⁴·ρ_e²
null
0
2
8
18
16.2
-6.7
false
{"mass": "1", "length": "8", "torque": "-3", "efield": "4", "resistivity": "-2"}
5
bfield,conductivity,length,mass,torque
m·ℓ·τ·B·σ
em,mechanics
m·ℓ⁻⁸·τ·B⁻⁴·σ⁻²
m = k₀ · ℓ⁸·τ⁻¹·B⁴·σ²
null
0
2
8
16
14.8
-5.3
false
{"mass": "1", "length": "-8", "torque": "1", "bfield": "-4", "conductivity": "-2"}
5
bfield,length,mass,resistivity,torque
m·ℓ·τ·B·ρ_e
em,mechanics
m·ℓ⁻⁸·τ·B⁻⁴·ρ_e²
m = k₀ · ℓ⁸·τ⁻¹·B⁴·ρ_e⁻²
null
0
2
8
16
14.8
-5.3
false
{"mass": "1", "length": "-8", "torque": "1", "bfield": "-4", "resistivity": "2"}
5
bfield,elem_charge,length,mass,torque
m·ℓ·τ·B·e
constants,em,mechanics
m·ℓ⁻²·τ·B⁻²·e⁻²
m = k₀ · ℓ²·τ⁻¹·B²·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "-2", "torque": "1", "bfield": "-2", "elem_charge": "-2"}
5
elem_charge,length,mag_flux,mass,torque
m·ℓ·τ·Φ·e
constants,em,mechanics
m·ℓ²·τ·Φ⁻²·e⁻²
m = k₀ · ℓ⁻²·τ⁻¹·Φ²·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "torque": "1", "mag_flux": "-2", "elem_charge": "-2"}
5
conductivity,length,mass,permittivity,torque
m·ℓ·τ·ε·σ
em,mechanics
m·ℓ²·τ⁻¹·ε⁻²·σ²
m = k₀ · ℓ⁻²·τ·ε²·σ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "permittivity": "-2", "conductivity": "2"}
5
length,mass,permittivity,resistivity,torque
m·ℓ·τ·ε·ρ_e
em,mechanics
m·ℓ²·τ⁻¹·ε⁻²·ρ_e⁻²
m = k₀ · ℓ⁻²·τ·ε²·ρ_e²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "permittivity": "-2", "resistivity": "-2"}
5
conductivity,length,mass,permeability,torque
m·ℓ·τ·μ₀·σ
em,mechanics
m·ℓ⁻²·τ⁻¹·μ₀⁻²·σ⁻²
m = k₀ · ℓ²·τ·μ₀²·σ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "torque": "-1", "permeability": "-2", "conductivity": "-2"}
5
length,mass,permeability,resistivity,torque
m·ℓ·τ·μ₀·ρ_e
em,mechanics
m·ℓ⁻²·τ⁻¹·μ₀⁻²·ρ_e²
m = k₀ · ℓ²·τ·μ₀²·ρ_e⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "torque": "-1", "permeability": "-2", "resistivity": "2"}
5
conductivity,elem_charge,length,mass,torque
m·ℓ·τ·σ·e
constants,em,mechanics
m·ℓ⁴·τ·σ²·e⁻⁴
m = k₀ · ℓ⁻⁴·τ⁻¹·σ⁻²·e⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "1", "length": "4", "torque": "1", "conductivity": "2", "elem_charge": "-4"}
5
elem_charge,length,mass,resistivity,torque
m·ℓ·τ·ρ_e·e
constants,em,mechanics
m·ℓ⁴·τ·ρ_e⁻²·e⁻⁴
m = k₀ · ℓ⁻⁴·τ⁻¹·ρ_e²·e⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "1", "length": "4", "torque": "1", "resistivity": "-2", "elem_charge": "-4"}
5
amount,cat_activity,length,mass,torque
m·ℓ·τ·n·z
chemistry,mechanics
m·ℓ²·τ⁻¹·n⁻²·z²
m = k₀ · ℓ⁻²·τ·n²·z⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "torque": "-1", "amount": "-2", "cat_activity": "2"}
5
cat_activity,length,mass,molar_mass,torque
m·ℓ·τ·M_m·z
chemistry,mechanics
m·ℓ⁻²·τ·M_m⁻²·z⁻²
m = k₀ · ℓ²·τ⁻¹·M_m²·z²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "torque": "1", "molar_mass": "-2", "cat_activity": "-2"}
5
cat_activity,concentration,length,mass,torque
m·ℓ·τ·c_n·z
chemistry,mechanics
m·ℓ⁻⁴·τ⁻¹·c_n⁻²·z²
m = k₀ · ℓ⁴·τ·c_n²·z⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "torque": "-1", "concentration": "-2", "cat_activity": "2"}
5
cat_activity,length,mass,molar_energy,torque
m·ℓ·τ·E_m·z
chemistry,mechanics
m·ℓ²·τ⁻³·E_m²·z²
m = k₀ · ℓ⁻²·τ³·E_m⁻²·z⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "torque": "-3", "molar_energy": "2", "cat_activity": "2"}
6
boltzmann,cat_activity,gas_constant,length,mass,torque
m·ℓ·τ·R·z·k_B
chemistry,constants,mechanics
m·ℓ²·τ⁻¹·R²·z²·k_B⁻²
m = k₀ · ℓ⁻²·τ·R⁻²·z⁻²·k_B²
null
1
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "torque": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"}
5
avogadro,cat_activity,length,mass,torque
m·ℓ·τ·z·N_A
chemistry,constants,mechanics
m·ℓ²·τ⁻¹·z²·N_A²
m = k₀ · ℓ⁻²·τ·z⁻²·N_A⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "torque": "-1", "cat_activity": "2", "avogadro": "2"}
4
grav_const,length,mass,torque
m·ℓ·τ·G
constants,mechanics
m²·ℓ⁻¹·τ⁻¹·G
ℓ = k₀ · m²·τ⁻¹·G
null
1
2
2
5
3.8
5.7
true
{"mass": "2", "length": "-1", "torque": "-1", "grav_const": "1"}
4
length,mass,planck,torque
m·ℓ·τ·h
constants,mechanics
m·ℓ²·τ·h⁻²
m = k₀ · ℓ⁻²·τ⁻¹·h²
null
1
2
2
6
4.5
5
true
{"mass": "1", "length": "2", "torque": "1", "planck": "-2"}
4
length,mass,momentum,power
m·ℓ·P·p
mechanics
m²·ℓ·P·p⁻³
ℓ = k₀ · m⁻²·P⁻¹·p³
null
0
1
3
7
5.1
4.9
true
{"mass": "2", "length": "1", "power": "1", "momentum": "-3"}
4
ang_momentum,length,mass,power
m·ℓ·P·Lₐ
mechanics
m²·ℓ⁴·P·Lₐ⁻³
P = k₀ · m⁻²·ℓ⁻⁴·Lₐ³
null
0
1
4
10
7.7
2.3
false
{"mass": "2", "length": "4", "power": "1", "ang_momentum": "-3"}
4
action,length,mass,power
m·ℓ·P·S
mechanics
m²·ℓ⁴·P·S⁻³
P = k₀ · m⁻²·ℓ⁻⁴·S³
null
0
1
4
10
7.7
2.3
false
{"mass": "2", "length": "4", "power": "1", "action": "-3"}
4
length,mass,power,pressure
m·ℓ·P·P_p
mechanics
m·ℓ⁻⁷·P²·P_p⁻³
m = k₀ · ℓ⁷·P⁻²·P_p³
null
0
1
7
13
11.3
-1.3
false
{"mass": "1", "length": "-7", "power": "2", "pressure": "-3"}
4
length,mass,power,viscosity
m·ℓ·P·μ
mechanics
m²·ℓ⁻⁵·P·μ⁻³
P = k₀ · m⁻²·ℓ⁵·μ³
null
0
1
5
11
8.9
1.1
false
{"mass": "2", "length": "-5", "power": "1", "viscosity": "-3"}
4
kin_viscosity,length,mass,power
m·ℓ·P·ν
mechanics
m·ℓ⁻⁴·P⁻¹·ν³
m = k₀ · ℓ⁴·P·ν⁻³
null
0
1
4
9
7
3
false
{"mass": "1", "length": "-4", "power": "-1", "kin_viscosity": "3"}
4
length,mass,omega,power
m·ℓ·P·ω
mechanics
m·ℓ²·P⁻¹·ω³
m = k₀ · ℓ⁻²·P·ω⁻³
null
0
1
3
7
5.1
4.9
true
{"mass": "1", "length": "2", "power": "-1", "omega": "3"}
4
frequency,length,mass,power
m·ℓ·P·f
mechanics
m·ℓ²·P⁻¹·f³
m = k₀ · ℓ⁻²·P·f⁻³
null
0
1
3
7
5.1
4.9
true
{"mass": "1", "length": "2", "power": "-1", "frequency": "3"}
4
length,mass,power,stiffness
m·ℓ·P·k
mechanics
m·ℓ⁻⁴·P²·k⁻³
m = k₀ · ℓ⁴·P⁻²·k³
null
0
1
4
10
7.7
2.3
false
{"mass": "1", "length": "-4", "power": "2", "stiffness": "-3"}
4
length,mass,power,surf_tension
m·ℓ·P·γ
mechanics
m·ℓ⁻⁴·P²·γ⁻³
m = k₀ · ℓ⁴·P⁻²·γ³
null
0
1
4
10
7.7
2.3
false
{"mass": "1", "length": "-4", "power": "2", "surf_tension": "-3"}
4
flowrate,length,mass,power
m·ℓ·P·Q
mechanics
m·ℓ⁻⁷·P⁻¹·Q³
m = k₀ · ℓ⁷·P·Q⁻³
null
0
1
7
12
10.6
-0.6
false
{"mass": "1", "length": "-7", "power": "-1", "flowrate": "3"}
5
entropy,length,mass,power,temperature
m·ℓ·P·Θ·S_e
mechanics,thermo
m·ℓ²·P²·Θ⁻³·S_e⁻³
m = k₀ · ℓ⁻²·P⁻²·Θ³·S_e³
null
0
2
3
11
8.8
0.7
false
{"mass": "1", "length": "2", "power": "2", "temperature": "-3", "entropy": "-3"}
5
heat_capacity,length,mass,power,temperature
m·ℓ·P·Θ·C
mechanics,thermo
m·ℓ²·P²·Θ⁻³·C⁻³
m = k₀ · ℓ⁻²·P⁻²·Θ³·C³
null
0
2
3
11
8.8
0.7
false
{"mass": "1", "length": "2", "power": "2", "temperature": "-3", "heat_capacity": "-3"}
5
length,mass,power,specific_heat,temperature
m·ℓ·P·Θ·c
mechanics,thermo
m²·ℓ⁻²·P⁻²·Θ³·c³
m = k₀ · ℓ·P·Θ⁻³ᐟ²·c⁻³ᐟ²
null
0
2
3
12
9.5
0
false
{"mass": "2", "length": "-2", "power": "-2", "temperature": "3", "specific_heat": "3"}
6
amount,gas_constant,length,mass,power,temperature
m·ℓ·P·Θ·n·R
chemistry,mechanics,thermo
m·ℓ²·P²·Θ⁻³·n⁻³·R⁻³
m = k₀ · ℓ⁻²·P⁻²·Θ³·n³·R³
null
0
3
3
14
11.8
-2.8
false
{"mass": "1", "length": "2", "power": "2", "temperature": "-3", "amount": "-3", "gas_constant": "-3"}
6
gas_constant,length,mass,molar_mass,power,temperature
m·ℓ·P·Θ·M_m·R
chemistry,mechanics,thermo
m²·ℓ⁻²·P⁻²·Θ³·M_m⁻³·R³
m = k₀ · ℓ·P·Θ⁻³ᐟ²·M_m³ᐟ²·R⁻³ᐟ²
null
0
3
3
15
12.5
-3.5
false
{"mass": "2", "length": "-2", "power": "-2", "temperature": "3", "molar_mass": "-3", "gas_constant": "3"}
6
concentration,gas_constant,length,mass,power,temperature
m·ℓ·P·Θ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻⁷·P²·Θ⁻³·c_n⁻³·R⁻³
m = k₀ · ℓ⁷·P⁻²·Θ³·c_n³·R³
null
0
3
7
19
17.3
-8.3
false
{"mass": "1", "length": "-7", "power": "2", "temperature": "-3", "concentration": "-3", "gas_constant": "-3"}
6
avogadro,gas_constant,length,mass,power,temperature
m·ℓ·P·Θ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·P²·Θ⁻³·R⁻³·N_A³
m = k₀ · ℓ⁻²·P⁻²·Θ³·R³·N_A⁻³
null
1
4
3
14
12.4
-3.9
false
{"mass": "1", "length": "2", "power": "2", "temperature": "-3", "gas_constant": "-3", "avogadro": "3"}
5
boltzmann,length,mass,power,temperature
m·ℓ·P·Θ·k_B
constants,mechanics,thermo
m·ℓ²·P²·Θ⁻³·k_B⁻³
m = k₀ · ℓ⁻²·P⁻²·Θ³·k_B³
null
1
3
3
11
9.4
-0.4
false
{"mass": "1", "length": "2", "power": "2", "temperature": "-3", "boltzmann": "-3"}
5
entropy,length,mass,power,thermal_cond
m·ℓ·P·S_e·κ
mechanics,thermo
m·ℓ⁵·P⁻¹·S_e⁻³·κ³
m = k₀ · ℓ⁻⁵·P·S_e³·κ⁻³
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "5", "power": "-1", "entropy": "-3", "thermal_cond": "3"}
5
entropy,expansion,length,mass,power
m·ℓ·P·S_e·β
mechanics,thermo
m·ℓ²·P²·S_e⁻³·β³
m = k₀ · ℓ⁻²·P⁻²·S_e³·β⁻³
null
0
2
3
11
8.8
0.7
false
{"mass": "1", "length": "2", "power": "2", "entropy": "-3", "expansion": "3"}
6
entropy,gas_constant,length,mass,molar_energy,power
m·ℓ·P·S_e·E_m·R
chemistry,mechanics,thermo
m·ℓ²·P²·S_e⁻³·E_m⁻³·R³
m = k₀ · ℓ⁻²·P⁻²·S_e³·E_m³·R⁻³
null
0
3
3
14
11.8
-2.8
false
{"mass": "1", "length": "2", "power": "2", "entropy": "-3", "molar_energy": "-3", "gas_constant": "3"}
6
cat_activity,entropy,gas_constant,length,mass,power
m·ℓ·P·S_e·R·z
chemistry,mechanics,thermo
m·ℓ²·P⁻¹·S_e⁻³·R³·z³
m = k₀ · ℓ⁻²·P·S_e³·R⁻³·z⁻³
null
0
3
3
13
11.1
-2.1
false
{"mass": "1", "length": "2", "power": "-1", "entropy": "-3", "gas_constant": "3", "cat_activity": "3"}
5
heat_capacity,length,mass,power,thermal_cond
m·ℓ·P·C·κ
mechanics,thermo
m·ℓ⁵·P⁻¹·C⁻³·κ³
m = k₀ · ℓ⁻⁵·P·C³·κ⁻³
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "5", "power": "-1", "heat_capacity": "-3", "thermal_cond": "3"}
5
expansion,heat_capacity,length,mass,power
m·ℓ·P·C·β
mechanics,thermo
m·ℓ²·P²·C⁻³·β³
m = k₀ · ℓ⁻²·P⁻²·C³·β⁻³
null
0
2
3
11
8.8
0.7
false
{"mass": "1", "length": "2", "power": "2", "heat_capacity": "-3", "expansion": "3"}
6
gas_constant,heat_capacity,length,mass,molar_energy,power
m·ℓ·P·C·E_m·R
chemistry,mechanics,thermo
m·ℓ²·P²·C⁻³·E_m⁻³·R³
m = k₀ · ℓ⁻²·P⁻²·C³·E_m³·R⁻³
null
0
3
3
14
11.8
-2.8
false
{"mass": "1", "length": "2", "power": "2", "heat_capacity": "-3", "molar_energy": "-3", "gas_constant": "3"}
6
cat_activity,gas_constant,heat_capacity,length,mass,power
m·ℓ·P·C·R·z
chemistry,mechanics,thermo
m·ℓ²·P⁻¹·C⁻³·R³·z³
m = k₀ · ℓ⁻²·P·C³·R⁻³·z⁻³
null
0
3
3
13
11.1
-2.1
false
{"mass": "1", "length": "2", "power": "-1", "heat_capacity": "-3", "gas_constant": "3", "cat_activity": "3"}
5
length,mass,power,specific_heat,thermal_cond
m·ℓ·P·c·κ
mechanics,thermo
m²·ℓ⁻⁵·P·c³·κ⁻³
P = k₀ · m⁻²·ℓ⁵·c⁻³·κ³
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "-5", "power": "1", "specific_heat": "3", "thermal_cond": "-3"}
5
expansion,length,mass,power,specific_heat
m·ℓ·P·c·β
mechanics,thermo
m²·ℓ⁻²·P⁻²·c³·β⁻³
m = k₀ · ℓ·P·c⁻³ᐟ²·β³ᐟ²
null
0
2
3
12
9.5
0
false
{"mass": "2", "length": "-2", "power": "-2", "specific_heat": "3", "expansion": "-3"}
6
gas_constant,length,mass,molar_energy,power,specific_heat
m·ℓ·P·c·E_m·R
chemistry,mechanics,thermo
m²·ℓ⁻²·P⁻²·c³·E_m³·R⁻³
m = k₀ · ℓ·P·c⁻³ᐟ²·E_m⁻³ᐟ²·R³ᐟ²
null
0
3
3
15
12.5
-3.5
false
{"mass": "2", "length": "-2", "power": "-2", "specific_heat": "3", "molar_energy": "3", "gas_constant": "-3"}