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
action,concentration,expansion,gas_constant,length,mass
m·ℓ·S·β·c_n·R
chemistry,mechanics,thermo
m·ℓ⁵·S⁻²·β⁻¹·c_n·R
m = k₀ · ℓ⁻⁵·S²·β·c_n⁻¹·R⁻¹
null
0
3
5
11
10.7
-1.7
false
{"mass": "1", "length": "5", "action": "-2", "expansion": "-1", "concentration": "1", "gas_constant": "1"}
6
action,cat_activity,expansion,gas_constant,length,mass
m·ℓ·S·β·R·z
chemistry,mechanics,thermo
m²·ℓ⁴·S⁻³·β⁻¹·R·z
β = k₀ · m²·ℓ⁴·S⁻³·R·z
null
0
3
4
12
10.9
-1.9
false
{"mass": "2", "length": "4", "action": "-3", "expansion": "-1", "gas_constant": "1", "cat_activity": "1"}
6
action,avogadro,expansion,gas_constant,length,mass
m·ℓ·S·β·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·S⁻²·β⁻¹·R·N_A⁻¹
m = k₀ · ℓ⁻²·S²·β·R⁻¹·N_A
null
1
4
2
8
7.7
0.8
false
{"mass": "1", "length": "2", "action": "-2", "expansion": "-1", "gas_constant": "1", "avogadro": "-1"}
5
action,boltzmann,expansion,length,mass
m·ℓ·S·β·k_B
constants,mechanics,thermo
m·ℓ²·S⁻²·β⁻¹·k_B
m = k₀ · ℓ⁻²·S²·β·k_B⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "action": "-2", "expansion": "-1", "boltzmann": "1"}
5
action,charge,current,length,mass
m·ℓ·S·q·i
em,mechanics
m·ℓ²·S⁻¹·q⁻¹·i
m = k₀ · ℓ⁻²·S·q·i⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "charge": "-1", "current": "1"}
5
action,charge,length,mass,voltage
m·ℓ·S·q·U
em,mechanics
m·ℓ²·S⁻²·q·U
m = k₀ · ℓ⁻²·S²·q⁻¹·U⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "action": "-2", "charge": "1", "voltage": "1"}
5
action,capacitance,charge,length,mass
m·ℓ·S·q·C_e
em,mechanics
m·ℓ²·S⁻²·q²·C_e⁻¹
m = k₀ · ℓ⁻²·S²·q⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "action": "-2", "charge": "2", "capacitance": "-1"}
5
action,charge,efield,length,mass
m·ℓ·S·q·E_f
em,mechanics
m·ℓ³·S⁻²·q·E_f
m = k₀ · ℓ⁻³·S²·q⁻¹·E_f⁻¹
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "3", "action": "-2", "charge": "1", "efield": "1"}
5
action,charge,length,mass,permittivity
m·ℓ·S·q·ε
em,mechanics
m·ℓ·S⁻²·q²·ε⁻¹
m = k₀ · ℓ⁻¹·S²·q⁻²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "action": "-2", "charge": "2", "permittivity": "-1"}
5
action,current,length,mass,voltage
m·ℓ·S·i·U
em,mechanics
m²·ℓ⁴·S⁻³·i·U
i = k₀ · m⁻²·ℓ⁻⁴·S³·U⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "2", "length": "4", "action": "-3", "current": "1", "voltage": "1"}
5
action,current,length,mass,resistance
m·ℓ·S·i·R
em,mechanics
m²·ℓ⁴·S⁻³·i²·R
R = k₀ · m⁻²·ℓ⁻⁴·S³·i⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "4", "action": "-3", "current": "2", "resistance": "1"}
5
action,capacitance,current,length,mass
m·ℓ·S·i·C_e
em,mechanics
m³·ℓ⁶·S⁻⁴·i²·C_e⁻¹
C_e = k₀ · m³·ℓ⁶·S⁻⁴·i²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "length": "6", "action": "-4", "current": "2", "capacitance": "-1"}
5
action,current,inductance,length,mass
m·ℓ·S·i·L_e
em,mechanics
m·ℓ²·S⁻²·i²·L_e
m = k₀ · ℓ⁻²·S²·i⁻²·L_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "action": "-2", "current": "2", "inductance": "1"}
5
action,current,efield,length,mass
m·ℓ·S·i·E_f
em,mechanics
m²·ℓ⁵·S⁻³·i·E_f
i = k₀ · m⁻²·ℓ⁻⁵·S³·E_f⁻¹
null
0
2
5
12
10.5
-1
false
{"mass": "2", "length": "5", "action": "-3", "current": "1", "efield": "1"}
5
action,bfield,current,length,mass
m·ℓ·S·i·B
em,mechanics
m·ℓ⁴·S⁻²·i·B
m = k₀ · ℓ⁻⁴·S²·i⁻¹·B⁻¹
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "4", "action": "-2", "current": "1", "bfield": "1"}
5
action,current,length,mag_flux,mass
m·ℓ·S·i·Φ
em,mechanics
m·ℓ²·S⁻²·i·Φ
m = k₀ · ℓ⁻²·S²·i⁻¹·Φ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "action": "-2", "current": "1", "mag_flux": "1"}
5
action,current,length,mass,permittivity
m·ℓ·S·i·ε
em,mechanics
m³·ℓ⁵·S⁻⁴·i²·ε⁻¹
ε = k₀ · m³·ℓ⁵·S⁻⁴·i²
null
0
2
5
15
12.6
-3.1
false
{"mass": "3", "length": "5", "action": "-4", "current": "2", "permittivity": "-1"}
5
action,current,length,mass,permeability
m·ℓ·S·i·μ₀
em,mechanics
m·ℓ³·S⁻²·i²·μ₀
m = k₀ · ℓ⁻³·S²·i⁻²·μ₀⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "action": "-2", "current": "2", "permeability": "1"}
5
action,conductivity,current,length,mass
m·ℓ·S·i·σ
em,mechanics
m²·ℓ³·S⁻³·i²·σ⁻¹
σ = k₀ · m²·ℓ³·S⁻³·i²
null
0
2
3
11
8.8
0.7
false
{"mass": "2", "length": "3", "action": "-3", "current": "2", "conductivity": "-1"}
5
action,current,length,mass,resistivity
m·ℓ·S·i·ρ_e
em,mechanics
m²·ℓ³·S⁻³·i²·ρ_e
ρ_e = k₀ · m⁻²·ℓ⁻³·S³·i⁻²
null
0
2
3
11
8.8
0.7
false
{"mass": "2", "length": "3", "action": "-3", "current": "2", "resistivity": "1"}
5
action,current,elem_charge,length,mass
m·ℓ·S·i·e
constants,em,mechanics
m·ℓ²·S⁻¹·i·e⁻¹
m = k₀ · ℓ⁻²·S·i⁻¹·e
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "action": "-1", "current": "1", "elem_charge": "-1"}
5
action,length,mass,resistance,voltage
m·ℓ·S·U·R
em,mechanics
m²·ℓ⁴·S⁻³·U²·R⁻¹
R = k₀ · m²·ℓ⁴·S⁻³·U²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "4", "action": "-3", "voltage": "2", "resistance": "-1"}
5
action,capacitance,length,mass,voltage
m·ℓ·S·U·C_e
em,mechanics
m·ℓ²·S⁻²·U²·C_e
m = k₀ · ℓ⁻²·S²·U⁻²·C_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "action": "-2", "voltage": "2", "capacitance": "1"}
5
action,inductance,length,mass,voltage
m·ℓ·S·U·L_e
em,mechanics
m³·ℓ⁶·S⁻⁴·U²·L_e⁻¹
L_e = k₀ · m³·ℓ⁶·S⁻⁴·U²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "length": "6", "action": "-4", "voltage": "2", "inductance": "-1"}
5
action,length,mag_flux,mass,voltage
m·ℓ·S·U·Φ
em,mechanics
m·ℓ²·S⁻¹·U·Φ⁻¹
m = k₀ · ℓ⁻²·S·U⁻¹·Φ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "voltage": "1", "mag_flux": "-1"}
5
action,length,mass,permittivity,voltage
m·ℓ·S·U·ε
em,mechanics
m·ℓ³·S⁻²·U²·ε
m = k₀ · ℓ⁻³·S²·U⁻²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "action": "-2", "voltage": "2", "permittivity": "1"}
5
action,length,mass,permeability,voltage
m·ℓ·S·U·μ₀
em,mechanics
m³·ℓ⁵·S⁻⁴·U²·μ₀⁻¹
μ₀ = k₀ · m³·ℓ⁵·S⁻⁴·U²
null
0
2
5
15
12.6
-3.1
false
{"mass": "3", "length": "5", "action": "-4", "voltage": "2", "permeability": "-1"}
5
action,conductivity,length,mass,voltage
m·ℓ·S·U·σ
em,mechanics
m²·ℓ⁵·S⁻³·U²·σ
σ = k₀ · m⁻²·ℓ⁻⁵·S³·U⁻²
null
0
2
5
13
11.2
-1.7
false
{"mass": "2", "length": "5", "action": "-3", "voltage": "2", "conductivity": "1"}
5
action,length,mass,resistivity,voltage
m·ℓ·S·U·ρ_e
em,mechanics
m²·ℓ⁵·S⁻³·U²·ρ_e⁻¹
ρ_e = k₀ · m²·ℓ⁵·S⁻³·U²
null
0
2
5
13
11.2
-1.7
false
{"mass": "2", "length": "5", "action": "-3", "voltage": "2", "resistivity": "-1"}
5
action,elem_charge,length,mass,voltage
m·ℓ·S·U·e
constants,em,mechanics
m·ℓ²·S⁻²·U·e
m = k₀ · ℓ⁻²·S²·U⁻¹·e⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "action": "-2", "voltage": "1", "elem_charge": "1"}
5
action,capacitance,length,mass,resistance
m·ℓ·S·R·C_e
em,mechanics
m·ℓ²·S⁻¹·R⁻¹·C_e⁻¹
m = k₀ · ℓ⁻²·S·R·C_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "resistance": "-1", "capacitance": "-1"}
5
action,inductance,length,mass,resistance
m·ℓ·S·R·L_e
em,mechanics
m·ℓ²·S⁻¹·R·L_e⁻¹
m = k₀ · ℓ⁻²·S·R⁻¹·L_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "resistance": "1", "inductance": "-1"}
5
action,efield,length,mass,resistance
m·ℓ·S·R·E_f
em,mechanics
m²·ℓ⁶·S⁻³·R⁻¹·E_f²
R = k₀ · m²·ℓ⁶·S⁻³·E_f²
null
0
2
6
14
12.4
-2.9
false
{"mass": "2", "length": "6", "action": "-3", "resistance": "-1", "efield": "2"}
5
action,length,mass,permittivity,resistance
m·ℓ·S·R·ε
em,mechanics
m·ℓ·S⁻¹·R⁻¹·ε⁻¹
m = k₀ · ℓ⁻¹·S·R·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "action": "-1", "resistance": "-1", "permittivity": "-1"}
5
action,length,mass,permeability,resistance
m·ℓ·S·R·μ₀
em,mechanics
m·ℓ·S⁻¹·R·μ₀⁻¹
m = k₀ · ℓ⁻¹·S·R⁻¹·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "action": "-1", "resistance": "1", "permeability": "-1"}
5
action,capacitance,inductance,length,mass
m·ℓ·S·C_e·L_e
em,mechanics
m²·ℓ⁴·S⁻²·C_e⁻¹·L_e⁻¹
C_e = k₀ · m²·ℓ⁴·S⁻²·L_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "length": "4", "action": "-2", "capacitance": "-1", "inductance": "-1"}
5
action,capacitance,efield,length,mass
m·ℓ·S·C_e·E_f
em,mechanics
m·ℓ⁴·S⁻²·C_e·E_f²
m = k₀ · ℓ⁻⁴·S²·C_e⁻¹·E_f⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "4", "action": "-2", "capacitance": "1", "efield": "2"}
5
action,capacitance,length,mass,permeability
m·ℓ·S·C_e·μ₀
em,mechanics
m²·ℓ³·S⁻²·C_e⁻¹·μ₀⁻¹
C_e = k₀ · m²·ℓ³·S⁻²·μ₀⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "length": "3", "action": "-2", "capacitance": "-1", "permeability": "-1"}
5
action,capacitance,conductivity,length,mass
m·ℓ·S·C_e·σ
em,mechanics
m·ℓ³·S⁻¹·C_e⁻¹·σ
m = k₀ · ℓ⁻³·S·C_e·σ⁻¹
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "3", "action": "-1", "capacitance": "-1", "conductivity": "1"}
5
action,capacitance,length,mass,resistivity
m·ℓ·S·C_e·ρ_e
em,mechanics
m·ℓ³·S⁻¹·C_e⁻¹·ρ_e⁻¹
m = k₀ · ℓ⁻³·S·C_e·ρ_e
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "3", "action": "-1", "capacitance": "-1", "resistivity": "-1"}
5
action,capacitance,elem_charge,length,mass
m·ℓ·S·C_e·e
constants,em,mechanics
m·ℓ²·S⁻²·C_e⁻¹·e²
m = k₀ · ℓ⁻²·S²·C_e·e⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "action": "-2", "capacitance": "-1", "elem_charge": "2"}
5
action,efield,inductance,length,mass
m·ℓ·S·L_e·E_f
em,mechanics
m³·ℓ⁸·S⁻⁴·L_e⁻¹·E_f²
L_e = k₀ · m³·ℓ⁸·S⁻⁴·E_f²
null
0
2
8
18
16.2
-6.7
false
{"mass": "3", "length": "8", "action": "-4", "inductance": "-1", "efield": "2"}
5
action,bfield,inductance,length,mass
m·ℓ·S·L_e·B
em,mechanics
m·ℓ⁶·S⁻²·L_e⁻¹·B²
m = k₀ · ℓ⁻⁶·S²·L_e·B⁻²
null
0
2
6
12
11
-1.5
false
{"mass": "1", "length": "6", "action": "-2", "inductance": "-1", "bfield": "2"}
5
action,inductance,length,mag_flux,mass
m·ℓ·S·L_e·Φ
em,mechanics
m·ℓ²·S⁻²·L_e⁻¹·Φ²
m = k₀ · ℓ⁻²·S²·L_e·Φ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "action": "-2", "inductance": "-1", "mag_flux": "2"}
5
action,inductance,length,mass,permittivity
m·ℓ·S·L_e·ε
em,mechanics
m²·ℓ³·S⁻²·L_e⁻¹·ε⁻¹
L_e = k₀ · m²·ℓ³·S⁻²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "length": "3", "action": "-2", "inductance": "-1", "permittivity": "-1"}
5
action,conductivity,inductance,length,mass
m·ℓ·S·L_e·σ
em,mechanics
m·ℓ·S⁻¹·L_e⁻¹·σ⁻¹
m = k₀ · ℓ⁻¹·S·L_e·σ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "action": "-1", "inductance": "-1", "conductivity": "-1"}
5
action,inductance,length,mass,resistivity
m·ℓ·S·L_e·ρ_e
em,mechanics
m·ℓ·S⁻¹·L_e⁻¹·ρ_e
m = k₀ · ℓ⁻¹·S·L_e·ρ_e⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "action": "-1", "inductance": "-1", "resistivity": "1"}
5
action,bfield,efield,length,mass
m·ℓ·S·E_f·B
em,mechanics
m·ℓ·S⁻¹·E_f·B⁻¹
m = k₀ · ℓ⁻¹·S·E_f⁻¹·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "action": "-1", "efield": "1", "bfield": "-1"}
5
action,efield,length,mag_flux,mass
m·ℓ·S·E_f·Φ
em,mechanics
m·ℓ³·S⁻¹·E_f·Φ⁻¹
m = k₀ · ℓ⁻³·S·E_f⁻¹·Φ
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "3", "action": "-1", "efield": "1", "mag_flux": "-1"}
5
action,efield,length,mass,permittivity
m·ℓ·S·E_f·ε
em,mechanics
m·ℓ⁵·S⁻²·E_f²·ε
m = k₀ · ℓ⁻⁵·S²·E_f⁻²·ε⁻¹
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "5", "action": "-2", "efield": "2", "permittivity": "1"}
5
action,efield,length,mass,permeability
m·ℓ·S·E_f·μ₀
em,mechanics
m³·ℓ⁷·S⁻⁴·E_f²·μ₀⁻¹
μ₀ = k₀ · m³·ℓ⁷·S⁻⁴·E_f²
null
0
2
7
17
15
-5.5
false
{"mass": "3", "length": "7", "action": "-4", "efield": "2", "permeability": "-1"}
5
action,conductivity,efield,length,mass
m·ℓ·S·E_f·σ
em,mechanics
m²·ℓ⁷·S⁻³·E_f²·σ
σ = k₀ · m⁻²·ℓ⁻⁷·S³·E_f⁻²
null
0
2
7
15
13.6
-4.1
false
{"mass": "2", "length": "7", "action": "-3", "efield": "2", "conductivity": "1"}
5
action,efield,length,mass,resistivity
m·ℓ·S·E_f·ρ_e
em,mechanics
m²·ℓ⁷·S⁻³·E_f²·ρ_e⁻¹
ρ_e = k₀ · m²·ℓ⁷·S⁻³·E_f²
null
0
2
7
15
13.6
-4.1
false
{"mass": "2", "length": "7", "action": "-3", "efield": "2", "resistivity": "-1"}
5
action,efield,elem_charge,length,mass
m·ℓ·S·E_f·e
constants,em,mechanics
m·ℓ³·S⁻²·E_f·e
m = k₀ · ℓ⁻³·S²·E_f⁻¹·e⁻¹
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "3", "action": "-2", "efield": "1", "elem_charge": "1"}
5
action,bfield,length,mass,permeability
m·ℓ·S·B·μ₀
em,mechanics
m·ℓ⁵·S⁻²·B²·μ₀⁻¹
m = k₀ · ℓ⁻⁵·S²·B⁻²·μ₀
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "5", "action": "-2", "bfield": "2", "permeability": "-1"}
5
action,length,mag_flux,mass,permeability
m·ℓ·S·Φ·μ₀
em,mechanics
m·ℓ·S⁻²·Φ²·μ₀⁻¹
m = k₀ · ℓ⁻¹·S²·Φ⁻²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "action": "-2", "mag_flux": "2", "permeability": "-1"}
5
action,length,mass,permeability,permittivity
m·ℓ·S·ε·μ₀
em,mechanics
m²·ℓ²·S⁻²·ε⁻¹·μ₀⁻¹
ε = k₀ · m²·ℓ²·S⁻²·μ₀⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "length": "2", "action": "-2", "permittivity": "-1", "permeability": "-1"}
5
action,conductivity,length,mass,permittivity
m·ℓ·S·ε·σ
em,mechanics
m·ℓ²·S⁻¹·ε⁻¹·σ
m = k₀ · ℓ⁻²·S·ε·σ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "permittivity": "-1", "conductivity": "1"}
5
action,length,mass,permittivity,resistivity
m·ℓ·S·ε·ρ_e
em,mechanics
m·ℓ²·S⁻¹·ε⁻¹·ρ_e⁻¹
m = k₀ · ℓ⁻²·S·ε·ρ_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "permittivity": "-1", "resistivity": "-1"}
5
action,elem_charge,length,mass,permittivity
m·ℓ·S·ε·e
constants,em,mechanics
m·ℓ·S⁻²·ε⁻¹·e²
m = k₀ · ℓ⁻¹·S²·ε·e⁻²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "action": "-2", "permittivity": "-1", "elem_charge": "2"}
5
action,amount,length,mass,molar_energy
m·ℓ·S·n·E_m
chemistry,mechanics
m·ℓ²·S⁻²·n·E_m
m = k₀ · ℓ⁻²·S²·n⁻¹·E_m⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "action": "-2", "amount": "1", "molar_energy": "1"}
5
action,amount,cat_activity,length,mass
m·ℓ·S·n·z
chemistry,mechanics
m·ℓ²·S⁻¹·n⁻¹·z
m = k₀ · ℓ⁻²·S·n·z⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "action": "-1", "amount": "-1", "cat_activity": "1"}
5
action,length,mass,molar_energy,molar_mass
m·ℓ·S·M_m·E_m
chemistry,mechanics
m²·ℓ²·S⁻²·M_m⁻¹·E_m
M_m = k₀ · m²·ℓ²·S⁻²·E_m
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "length": "2", "action": "-2", "molar_mass": "-1", "molar_energy": "1"}
5
action,concentration,length,mass,molar_energy
m·ℓ·S·c_n·E_m
chemistry,mechanics
m·ℓ⁵·S⁻²·c_n·E_m
m = k₀ · ℓ⁻⁵·S²·c_n⁻¹·E_m⁻¹
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "length": "5", "action": "-2", "concentration": "1", "molar_energy": "1"}
5
action,cat_activity,concentration,length,mass
m·ℓ·S·c_n·z
chemistry,mechanics
m·ℓ⁻¹·S⁻¹·c_n⁻¹·z
m = k₀ · ℓ·S·c_n·z⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "action": "-1", "concentration": "-1", "cat_activity": "1"}
6
action,boltzmann,gas_constant,length,mass,molar_energy
m·ℓ·S·E_m·R·k_B
chemistry,constants,mechanics
m·ℓ²·S⁻²·E_m·R⁻¹·k_B
m = k₀ · ℓ⁻²·S²·E_m⁻¹·R·k_B⁻¹
null
1
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "action": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"}
5
action,cat_activity,length,mass,molar_energy
m·ℓ·S·E_m·z
chemistry,mechanics
m²·ℓ⁴·S⁻³·E_m·z
E_m = k₀ · m⁻²·ℓ⁻⁴·S³·z⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "2", "length": "4", "action": "-3", "molar_energy": "1", "cat_activity": "1"}
5
action,avogadro,length,mass,molar_energy
m·ℓ·S·E_m·N_A
chemistry,constants,mechanics
m·ℓ²·S⁻²·E_m·N_A⁻¹
m = k₀ · ℓ⁻²·S²·E_m⁻¹·N_A
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "action": "-2", "molar_energy": "1", "avogadro": "-1"}
6
action,boltzmann,cat_activity,gas_constant,length,mass
m·ℓ·S·R·z·k_B
chemistry,constants,mechanics
m·ℓ²·S⁻¹·R·z·k_B⁻¹
m = k₀ · ℓ⁻²·S·R⁻¹·z⁻¹·k_B
null
1
3
2
7
6.4
2.6
false
{"mass": "1", "length": "2", "action": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"}
5
action,avogadro,cat_activity,length,mass
m·ℓ·S·z·N_A
chemistry,constants,mechanics
m·ℓ²·S⁻¹·z·N_A
m = k₀ · ℓ⁻²·S·z⁻¹·N_A⁻¹
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "action": "-1", "cat_activity": "1", "avogadro": "1"}
4
action,length,light_speed,mass
m·ℓ·S·c₀
constants,mechanics
m·ℓ·S⁻¹·c₀
m = k₀ · ℓ⁻¹·S·c₀⁻¹
null
1
2
1
4
2.6
6.9
true
{"mass": "1", "length": "1", "action": "-1", "light_speed": "1"}
4
action,grav_const,length,mass
m·ℓ·S·G
constants,mechanics
m³·ℓ·S⁻²·G
ℓ = k₀ · m⁻³·S²·G⁻¹
null
1
2
3
7
5.7
3.8
true
{"mass": "3", "length": "1", "action": "-2", "grav_const": "1"}
3
inertia,length,mass
m·ℓ·J
mechanics
m·ℓ²·J⁻¹
m = k₀ · ℓ⁻²·J
null
0
1
2
4
2.2
7.8
true
{"mass": "1", "length": "2", "inertia": "-1"}
4
length,mass,pressure,viscosity
m·ℓ·P_p·μ
mechanics
m·ℓ⁻¹·P_p·μ⁻²
m = k₀ · ℓ·P_p⁻¹·μ²
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "length": "-1", "pressure": "1", "viscosity": "-2"}
4
kin_viscosity,length,mass,pressure
m·ℓ·P_p·ν
mechanics
m·ℓ⁻⁵·P_p⁻¹·ν²
m = k₀ · ℓ⁵·P_p·ν⁻²
null
0
1
5
9
7.5
2.5
false
{"mass": "1", "length": "-5", "pressure": "-1", "kin_viscosity": "2"}
4
length,mass,omega,pressure
m·ℓ·P_p·ω
mechanics
m·ℓ⁻¹·P_p⁻¹·ω²
m = k₀ · ℓ·P_p·ω⁻²
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "length": "-1", "pressure": "-1", "omega": "2"}
4
frequency,length,mass,pressure
m·ℓ·P_p·f
mechanics
m·ℓ⁻¹·P_p⁻¹·f²
m = k₀ · ℓ·P_p·f⁻²
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "length": "-1", "pressure": "-1", "frequency": "2"}
4
flowrate,length,mass,pressure
m·ℓ·P_p·Q
mechanics
m·ℓ⁻⁷·P_p⁻¹·Q²
m = k₀ · ℓ⁷·P_p·Q⁻²
null
0
1
7
11
9.9
0.1
false
{"mass": "1", "length": "-7", "pressure": "-1", "flowrate": "2"}
5
length,mass,pressure,specific_heat,temperature
m·ℓ·P_p·Θ·c
mechanics,thermo
m·ℓ⁻³·P_p⁻¹·Θ·c
m = k₀ · ℓ³·P_p·Θ⁻¹·c⁻¹
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "-3", "pressure": "-1", "temperature": "1", "specific_heat": "1"}
5
length,mass,pressure,temperature,thermal_cond
m·ℓ·P_p·Θ·κ
mechanics,thermo
m·ℓ⁻⁵·P_p⁻³·Θ²·κ²
m = k₀ · ℓ⁵·P_p³·Θ⁻²·κ⁻²
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "-5", "pressure": "-3", "temperature": "2", "thermal_cond": "2"}
6
gas_constant,length,mass,molar_mass,pressure,temperature
m·ℓ·P_p·Θ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻³·P_p⁻¹·Θ·M_m⁻¹·R
m = k₀ · ℓ³·P_p·Θ⁻¹·M_m·R⁻¹
null
0
3
3
8
7.6
1.4
false
{"mass": "1", "length": "-3", "pressure": "-1", "temperature": "1", "molar_mass": "-1", "gas_constant": "1"}
6
cat_activity,gas_constant,length,mass,pressure,temperature
m·ℓ·P_p·Θ·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁷·P_p⁻³·Θ²·R²·z²
m = k₀ · ℓ⁷·P_p³·Θ⁻²·R⁻²·z⁻²
null
0
3
7
17
15.9
-6.9
false
{"mass": "1", "length": "-7", "pressure": "-3", "temperature": "2", "gas_constant": "2", "cat_activity": "2"}
5
entropy,length,mass,pressure,thermal_cond
m·ℓ·P_p·S_e·κ
mechanics,thermo
m·ℓ·P_p⁻¹·S_e⁻²·κ²
m = k₀ · ℓ⁻¹·P_p·S_e²·κ⁻²
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "pressure": "-1", "entropy": "-2", "thermal_cond": "2"}
6
cat_activity,entropy,gas_constant,length,mass,pressure
m·ℓ·P_p·S_e·R·z
chemistry,mechanics,thermo
m·ℓ⁻¹·P_p⁻¹·S_e⁻²·R²·z²
m = k₀ · ℓ·P_p·S_e²·R⁻²·z⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-1", "pressure": "-1", "entropy": "-2", "gas_constant": "2", "cat_activity": "2"}
5
heat_capacity,length,mass,pressure,thermal_cond
m·ℓ·P_p·C·κ
mechanics,thermo
m·ℓ·P_p⁻¹·C⁻²·κ²
m = k₀ · ℓ⁻¹·P_p·C²·κ⁻²
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "pressure": "-1", "heat_capacity": "-2", "thermal_cond": "2"}
6
cat_activity,gas_constant,heat_capacity,length,mass,pressure
m·ℓ·P_p·C·R·z
chemistry,mechanics,thermo
m·ℓ⁻¹·P_p⁻¹·C⁻²·R²·z²
m = k₀ · ℓ·P_p·C²·R⁻²·z⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-1", "pressure": "-1", "heat_capacity": "-2", "gas_constant": "2", "cat_activity": "2"}
5
length,mass,pressure,specific_heat,thermal_cond
m·ℓ·P_p·c·κ
mechanics,thermo
m·ℓ⁻¹·P_p·c²·κ⁻²
m = k₀ · ℓ·P_p⁻¹·c⁻²·κ²
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "pressure": "1", "specific_heat": "2", "thermal_cond": "-2"}
5
expansion,length,mass,pressure,specific_heat
m·ℓ·P_p·c·β
mechanics,thermo
m·ℓ⁻³·P_p⁻¹·c·β⁻¹
m = k₀ · ℓ³·P_p·c⁻¹·β
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "-3", "pressure": "-1", "specific_heat": "1", "expansion": "-1"}
6
gas_constant,length,mass,molar_energy,pressure,specific_heat
m·ℓ·P_p·c·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻³·P_p⁻¹·c·E_m·R⁻¹
m = k₀ · ℓ³·P_p·c⁻¹·E_m⁻¹·R
null
0
3
3
8
7.6
1.4
false
{"mass": "1", "length": "-3", "pressure": "-1", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"}
6
cat_activity,gas_constant,length,mass,pressure,specific_heat
m·ℓ·P_p·c·R·z
chemistry,mechanics,thermo
m·ℓ·P_p·c²·R⁻²·z⁻²
m = k₀ · ℓ⁻¹·P_p⁻¹·c⁻²·R²·z²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "pressure": "1", "specific_heat": "2", "gas_constant": "-2", "cat_activity": "-2"}
5
expansion,length,mass,pressure,thermal_cond
m·ℓ·P_p·κ·β
mechanics,thermo
m·ℓ⁻⁵·P_p⁻³·κ²·β⁻²
m = k₀ · ℓ⁵·P_p³·κ⁻²·β²
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "-5", "pressure": "-3", "thermal_cond": "2", "expansion": "-2"}
6
amount,gas_constant,length,mass,pressure,thermal_cond
m·ℓ·P_p·κ·n·R
chemistry,mechanics,thermo
m·ℓ·P_p⁻¹·κ²·n⁻²·R⁻²
m = k₀ · ℓ⁻¹·P_p·κ⁻²·n²·R²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "pressure": "-1", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_mass,pressure,thermal_cond
m·ℓ·P_p·κ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻¹·P_p·κ⁻²·M_m⁻²·R²
m = k₀ · ℓ·P_p⁻¹·κ²·M_m²·R⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-1", "pressure": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
concentration,gas_constant,length,mass,pressure,thermal_cond
m·ℓ·P_p·κ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻⁵·P_p⁻¹·κ²·c_n⁻²·R⁻²
m = k₀ · ℓ⁵·P_p·κ⁻²·c_n²·R²
null
0
3
5
13
12.1
-3.1
false
{"mass": "1", "length": "-5", "pressure": "-1", "thermal_cond": "2", "concentration": "-2", "gas_constant": "-2"}
6
gas_constant,length,mass,molar_energy,pressure,thermal_cond
m·ℓ·P_p·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻⁵·P_p⁻³·κ²·E_m²·R⁻²
m = k₀ · ℓ⁵·P_p³·κ⁻²·E_m⁻²·R²
null
0
3
5
15
13.5
-4.5
false
{"mass": "1", "length": "-5", "pressure": "-3", "thermal_cond": "2", "molar_energy": "2", "gas_constant": "-2"}
6
avogadro,gas_constant,length,mass,pressure,thermal_cond
m·ℓ·P_p·κ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ·P_p⁻¹·κ²·R⁻²·N_A²
m = k₀ · ℓ⁻¹·P_p·κ⁻²·R²·N_A⁻²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "1", "pressure": "-1", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"}
5
boltzmann,length,mass,pressure,thermal_cond
m·ℓ·P_p·κ·k_B
constants,mechanics,thermo
m·ℓ·P_p⁻¹·κ²·k_B⁻²
m = k₀ · ℓ⁻¹·P_p·κ⁻²·k_B²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "pressure": "-1", "thermal_cond": "2", "boltzmann": "-2"}
4
length,mass,pressure,thermal_diff
m·ℓ·P_p·α
mechanics,thermo
m·ℓ⁻⁵·P_p⁻¹·α²
m = k₀ · ℓ⁵·P_p·α⁻²
null
0
2
5
9
8.1
1.4
false
{"mass": "1", "length": "-5", "pressure": "-1", "thermal_diff": "2"}
6
expansion,gas_constant,length,mass,molar_mass,pressure
m·ℓ·P_p·β·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻³·P_p⁻¹·β⁻¹·M_m⁻¹·R
m = k₀ · ℓ³·P_p·β·M_m·R⁻¹
null
0
3
3
8
7.6
1.4
false
{"mass": "1", "length": "-3", "pressure": "-1", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"}
6
cat_activity,expansion,gas_constant,length,mass,pressure
m·ℓ·P_p·β·R·z
chemistry,mechanics,thermo
m·ℓ⁻⁷·P_p⁻³·β⁻²·R²·z²
m = k₀ · ℓ⁷·P_p³·β²·R⁻²·z⁻²
null
0
3
7
17
15.9
-6.9
false
{"mass": "1", "length": "-7", "pressure": "-3", "expansion": "-2", "gas_constant": "2", "cat_activity": "2"}