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
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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
acceleration,capacitance,elem_charge,frequency,mass
m·a·f·C_e·e
constants,em,mechanics
m·a²·f⁻²·C_e·e⁻²
m = k₀ · a⁻²·f²·C_e⁻¹·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "acceleration": "2", "frequency": "-2", "capacitance": "1", "elem_charge": "-2"}
5
acceleration,bfield,frequency,inductance,mass
m·a·f·L_e·B
em,mechanics
m·a⁻²·f⁶·L_e·B⁻²
m = k₀ · a²·f⁻⁶·L_e⁻¹·B²
null
0
2
6
12
11
-1.5
false
{"mass": "1", "acceleration": "-2", "frequency": "6", "inductance": "1", "bfield": "-2"}
5
acceleration,frequency,inductance,mag_flux,mass
m·a·f·L_e·Φ
em,mechanics
m·a²·f⁻²·L_e·Φ⁻²
m = k₀ · a⁻²·f²·L_e⁻¹·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "frequency": "-2", "inductance": "1", "mag_flux": "-2"}
5
acceleration,elem_charge,frequency,inductance,mass
m·a·f·L_e·e
constants,em,mechanics
m·a²·f⁻⁴·L_e⁻¹·e⁻²
m = k₀ · a⁻²·f⁴·L_e·e²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "acceleration": "2", "frequency": "-4", "inductance": "-1", "elem_charge": "-2"}
5
acceleration,efield,frequency,mass,permittivity
m·a·f·E_f·ε
em,mechanics
m·a⁻¹·f⁴·E_f⁻²·ε⁻¹
m = k₀ · a·f⁻⁴·E_f²·ε
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "acceleration": "-1", "frequency": "4", "efield": "-2", "permittivity": "-1"}
5
acceleration,efield,frequency,mass,permeability
m·a·f·E_f·μ₀
em,mechanics
m·a·f²·E_f⁻²·μ₀
m = k₀ · a⁻¹·f⁻²·E_f²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "acceleration": "1", "frequency": "2", "efield": "-2", "permeability": "1"}
5
acceleration,conductivity,efield,frequency,mass
m·a·f·E_f·σ
em,mechanics
m·a⁻¹·f⁵·E_f⁻²·σ⁻¹
m = k₀ · a·f⁻⁵·E_f²·σ
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "acceleration": "-1", "frequency": "5", "efield": "-2", "conductivity": "-1"}
5
acceleration,efield,frequency,mass,resistivity
m·a·f·E_f·ρ_e
em,mechanics
m·a⁻¹·f⁵·E_f⁻²·ρ_e
m = k₀ · a·f⁻⁵·E_f²·ρ_e⁻¹
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "acceleration": "-1", "frequency": "5", "efield": "-2", "resistivity": "1"}
5
acceleration,bfield,frequency,mass,permittivity
m·a·f·B·ε
em,mechanics
m·a⁻³·f⁶·B⁻²·ε⁻¹
m = k₀ · a³·f⁻⁶·B²·ε
null
0
2
6
13
11.7
-2.2
false
{"mass": "1", "acceleration": "-3", "frequency": "6", "bfield": "-2", "permittivity": "-1"}
5
acceleration,bfield,frequency,mass,permeability
m·a·f·B·μ₀
em,mechanics
m·a⁻¹·f⁴·B⁻²·μ₀
m = k₀ · a·f⁻⁴·B²·μ₀⁻¹
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "acceleration": "-1", "frequency": "4", "bfield": "-2", "permeability": "1"}
5
acceleration,bfield,conductivity,frequency,mass
m·a·f·B·σ
em,mechanics
m·a⁻³·f⁷·B⁻²·σ⁻¹
m = k₀ · a³·f⁻⁷·B²·σ
null
0
2
7
14
12.9
-3.4
false
{"mass": "1", "acceleration": "-3", "frequency": "7", "bfield": "-2", "conductivity": "-1"}
5
acceleration,bfield,frequency,mass,resistivity
m·a·f·B·ρ_e
em,mechanics
m·a⁻³·f⁷·B⁻²·ρ_e
m = k₀ · a³·f⁻⁷·B²·ρ_e⁻¹
null
0
2
7
14
12.9
-3.4
false
{"mass": "1", "acceleration": "-3", "frequency": "7", "bfield": "-2", "resistivity": "1"}
5
acceleration,frequency,mag_flux,mass,permittivity
m·a·f·Φ·ε
em,mechanics
m·a·f⁻²·Φ⁻²·ε⁻¹
m = k₀ · a⁻¹·f²·Φ²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "acceleration": "1", "frequency": "-2", "mag_flux": "-2", "permittivity": "-1"}
5
acceleration,frequency,mag_flux,mass,permeability
m·a·f·Φ·μ₀
em,mechanics
m·a³·f⁻⁴·Φ⁻²·μ₀
m = k₀ · a⁻³·f⁴·Φ²·μ₀⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "acceleration": "3", "frequency": "-4", "mag_flux": "-2", "permeability": "1"}
5
acceleration,conductivity,frequency,mag_flux,mass
m·a·f·Φ·σ
em,mechanics
m·a·f⁻¹·Φ⁻²·σ⁻¹
m = k₀ · a⁻¹·f·Φ²·σ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "1", "frequency": "-1", "mag_flux": "-2", "conductivity": "-1"}
5
acceleration,frequency,mag_flux,mass,resistivity
m·a·f·Φ·ρ_e
em,mechanics
m·a·f⁻¹·Φ⁻²·ρ_e
m = k₀ · a⁻¹·f·Φ²·ρ_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "1", "frequency": "-1", "mag_flux": "-2", "resistivity": "1"}
5
acceleration,elem_charge,frequency,mag_flux,mass
m·a·f·Φ·e
constants,em,mechanics
m·a²·f⁻³·Φ⁻¹·e⁻¹
m = k₀ · a⁻²·f³·Φ·e
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "acceleration": "2", "frequency": "-3", "mag_flux": "-1", "elem_charge": "-1"}
5
acceleration,elem_charge,frequency,mass,permittivity
m·a·f·ε·e
constants,em,mechanics
m·a³·f⁻⁴·ε·e⁻²
m = k₀ · a⁻³·f⁴·ε⁻¹·e²
null
1
3
4
11
9.9
-0.9
false
{"mass": "1", "acceleration": "3", "frequency": "-4", "permittivity": "1", "elem_charge": "-2"}
5
acceleration,elem_charge,frequency,mass,permeability
m·a·f·μ₀·e
constants,em,mechanics
m·a·f⁻²·μ₀⁻¹·e⁻²
m = k₀ · a⁻¹·f²·μ₀·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "acceleration": "1", "frequency": "-2", "permeability": "-1", "elem_charge": "-2"}
5
acceleration,conductivity,elem_charge,frequency,mass
m·a·f·σ·e
constants,em,mechanics
m·a³·f⁻⁵·σ·e⁻²
m = k₀ · a⁻³·f⁵·σ⁻¹·e²
null
1
3
5
12
11.1
-2.1
false
{"mass": "1", "acceleration": "3", "frequency": "-5", "conductivity": "1", "elem_charge": "-2"}
5
acceleration,elem_charge,frequency,mass,resistivity
m·a·f·ρ_e·e
constants,em,mechanics
m·a³·f⁻⁵·ρ_e⁻¹·e⁻²
m = k₀ · a⁻³·f⁵·ρ_e·e²
null
1
3
5
12
11.1
-2.1
false
{"mass": "1", "acceleration": "3", "frequency": "-5", "resistivity": "-1", "elem_charge": "-2"}
5
acceleration,amount,frequency,mass,molar_energy
m·a·f·n·E_m
chemistry,mechanics
m·a²·f⁻²·n⁻¹·E_m⁻¹
m = k₀ · a⁻²·f²·n·E_m
null
0
2
2
7
5.5
4
true
{"mass": "1", "acceleration": "2", "frequency": "-2", "amount": "-1", "molar_energy": "-1"}
5
acceleration,concentration,frequency,mass,molar_mass
m·a·f·M_m·c_n
chemistry,mechanics
m·a⁻³·f⁶·M_m⁻¹·c_n⁻¹
m = k₀ · a³·f⁻⁶·M_m·c_n
null
0
2
6
12
11
-1.5
false
{"mass": "1", "acceleration": "-3", "frequency": "6", "molar_mass": "-1", "concentration": "-1"}
5
acceleration,concentration,frequency,mass,molar_energy
m·a·f·c_n·E_m
chemistry,mechanics
m·a⁻¹·f⁴·c_n⁻¹·E_m⁻¹
m = k₀ · a·f⁻⁴·c_n·E_m
null
0
2
4
8
7.2
2.3
false
{"mass": "1", "acceleration": "-1", "frequency": "4", "concentration": "-1", "molar_energy": "-1"}
6
acceleration,boltzmann,frequency,gas_constant,mass,molar_energy
m·a·f·E_m·R·k_B
chemistry,constants,mechanics
m·a²·f⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · a⁻²·f²·E_m·R⁻¹·k_B
null
1
3
2
8
7.1
1.9
false
{"mass": "1", "acceleration": "2", "frequency": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
5
acceleration,cat_activity,frequency,mass,molar_energy
m·a·f·E_m·z
chemistry,mechanics
m·a²·f⁻¹·E_m⁻¹·z⁻¹
m = k₀ · a⁻²·f·E_m·z
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "frequency": "-1", "molar_energy": "-1", "cat_activity": "-1"}
5
acceleration,avogadro,frequency,mass,molar_energy
m·a·f·E_m·N_A
chemistry,constants,mechanics
m·a²·f⁻²·E_m⁻¹·N_A
m = k₀ · a⁻²·f²·E_m·N_A⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "acceleration": "2", "frequency": "-2", "molar_energy": "-1", "avogadro": "1"}
4
acceleration,frequency,grav_const,mass
m·a·f·G
constants,mechanics
m·a⁻³·f⁴·G
m = k₀ · a³·f⁻⁴·G⁻¹
null
1
2
4
9
7.6
1.9
false
{"mass": "1", "acceleration": "-3", "frequency": "4", "grav_const": "1"}
4
acceleration,frequency,mass,planck
m·a·f·h
constants,mechanics
m·a²·f⁻³·h⁻¹
m = k₀ · a⁻²·f³·h
null
1
2
3
7
5.7
3.8
true
{"mass": "1", "acceleration": "2", "frequency": "-3", "planck": "-1"}
4
acceleration,area,mass,stiffness
m·a·k·A
mechanics
m²·a²·k⁻²·A⁻¹
A = k₀ · m²·a²·k⁻²
null
0
1
2
7
4.6
5.4
true
{"mass": "2", "acceleration": "2", "stiffness": "-2", "area": "-1"}
4
acceleration,mass,stiffness,volume
m·a·k·V
mechanics
m³·a³·k⁻³·V⁻¹
V = k₀ · m³·a³·k⁻³
null
0
1
3
10
7.2
2.8
false
{"mass": "3", "acceleration": "3", "stiffness": "-3", "volume": "-1"}
4
acceleration,flowrate,mass,stiffness
m·a·k·Q
mechanics
m⁵·a⁶·k⁻⁵·Q⁻²
Q = k₀ · m⁵ᐟ²·a³·k⁻⁵ᐟ²
null
0
1
6
18
14.3
-4.3
false
{"mass": "5", "acceleration": "6", "stiffness": "-5", "flowrate": "-2"}
5
acceleration,entropy,mass,stiffness,temperature
m·a·k·Θ·S_e
mechanics,thermo
m²·a²·k⁻¹·Θ⁻¹·S_e⁻¹
k = k₀ · m²·a²·Θ⁻¹·S_e⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "entropy": "-1"}
5
acceleration,heat_capacity,mass,stiffness,temperature
m·a·k·Θ·C
mechanics,thermo
m²·a²·k⁻¹·Θ⁻¹·C⁻¹
k = k₀ · m²·a²·Θ⁻¹·C⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "heat_capacity": "-1"}
5
acceleration,mass,specific_heat,stiffness,temperature
m·a·k·Θ·c
mechanics,thermo
m·a²·k⁻¹·Θ⁻¹·c⁻¹
m = k₀ · a⁻²·k·Θ·c
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "specific_heat": "-1"}
5
acceleration,mass,stiffness,temperature,thermal_cond
m·a·k·Θ·κ
mechanics,thermo
m·a²·k·Θ⁻²·κ⁻²
m = k₀ · a⁻²·k⁻¹·Θ²·κ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "stiffness": "1", "temperature": "-2", "thermal_cond": "-2"}
6
acceleration,amount,gas_constant,mass,stiffness,temperature
m·a·k·Θ·n·R
chemistry,mechanics,thermo
m²·a²·k⁻¹·Θ⁻¹·n⁻¹·R⁻¹
k = k₀ · m²·a²·Θ⁻¹·n⁻¹·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "amount": "-1", "gas_constant": "-1"}
6
acceleration,gas_constant,mass,molar_mass,stiffness,temperature
m·a·k·Θ·M_m·R
chemistry,mechanics,thermo
m·a²·k⁻¹·Θ⁻¹·M_m·R⁻¹
m = k₀ · a⁻²·k·Θ·M_m⁻¹·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "molar_mass": "1", "gas_constant": "-1"}
6
acceleration,concentration,gas_constant,mass,stiffness,temperature
m·a·k·Θ·c_n·R
chemistry,mechanics,thermo
m·a·k⁻²·Θ·c_n·R
m = k₀ · a⁻¹·k²·Θ⁻¹·c_n⁻¹·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "1", "stiffness": "-2", "temperature": "1", "concentration": "1", "gas_constant": "1"}
6
acceleration,cat_activity,gas_constant,mass,stiffness,temperature
m·a·k·Θ·R·z
chemistry,mechanics,thermo
m³·a⁴·k⁻¹·Θ⁻²·R⁻²·z⁻²
k = k₀ · m³·a⁴·Θ⁻²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "3", "acceleration": "4", "stiffness": "-1", "temperature": "-2", "gas_constant": "-2", "cat_activity": "-2"}
6
acceleration,avogadro,gas_constant,mass,stiffness,temperature
m·a·k·Θ·R·N_A
chemistry,constants,mechanics,thermo
m²·a²·k⁻¹·Θ⁻¹·R⁻¹·N_A
k = k₀ · m²·a²·Θ⁻¹·R⁻¹·N_A
null
1
4
2
8
7.7
0.8
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "gas_constant": "-1", "avogadro": "1"}
5
acceleration,boltzmann,mass,stiffness,temperature
m·a·k·Θ·k_B
constants,mechanics,thermo
m²·a²·k⁻¹·Θ⁻¹·k_B⁻¹
k = k₀ · m²·a²·Θ⁻¹·k_B⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "temperature": "-1", "boltzmann": "-1"}
5
acceleration,entropy,mass,stiffness,thermal_cond
m·a·k·S_e·κ
mechanics,thermo
m³·a²·k⁻³·S_e⁻²·κ²
a = k₀ · m⁻³ᐟ²·k³ᐟ²·S_e·κ⁻¹
null
0
2
3
12
9.5
0
false
{"mass": "3", "acceleration": "2", "stiffness": "-3", "entropy": "-2", "thermal_cond": "2"}
5
acceleration,entropy,expansion,mass,stiffness
m·a·k·S_e·β
mechanics,thermo
m²·a²·k⁻¹·S_e⁻¹·β
k = k₀ · m²·a²·S_e⁻¹·β
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "entropy": "-1", "expansion": "1"}
6
acceleration,concentration,entropy,gas_constant,mass,stiffness
m·a·k·S_e·c_n·R
chemistry,mechanics,thermo
m³·a³·k⁻³·S_e⁻¹·c_n·R
S_e = k₀ · m³·a³·k⁻³·c_n·R
null
0
3
3
12
10.4
-1.4
false
{"mass": "3", "acceleration": "3", "stiffness": "-3", "entropy": "-1", "concentration": "1", "gas_constant": "1"}
6
acceleration,entropy,gas_constant,mass,molar_energy,stiffness
m·a·k·S_e·E_m·R
chemistry,mechanics,thermo
m²·a²·k⁻¹·S_e⁻¹·E_m⁻¹·R
k = k₀ · m²·a²·S_e⁻¹·E_m⁻¹·R
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "entropy": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
acceleration,heat_capacity,mass,stiffness,thermal_cond
m·a·k·C·κ
mechanics,thermo
m³·a²·k⁻³·C⁻²·κ²
a = k₀ · m⁻³ᐟ²·k³ᐟ²·C·κ⁻¹
null
0
2
3
12
9.5
0
false
{"mass": "3", "acceleration": "2", "stiffness": "-3", "heat_capacity": "-2", "thermal_cond": "2"}
5
acceleration,expansion,heat_capacity,mass,stiffness
m·a·k·C·β
mechanics,thermo
m²·a²·k⁻¹·C⁻¹·β
k = k₀ · m²·a²·C⁻¹·β
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "heat_capacity": "-1", "expansion": "1"}
6
acceleration,concentration,gas_constant,heat_capacity,mass,stiffness
m·a·k·C·c_n·R
chemistry,mechanics,thermo
m³·a³·k⁻³·C⁻¹·c_n·R
C = k₀ · m³·a³·k⁻³·c_n·R
null
0
3
3
12
10.4
-1.4
false
{"mass": "3", "acceleration": "3", "stiffness": "-3", "heat_capacity": "-1", "concentration": "1", "gas_constant": "1"}
6
acceleration,gas_constant,heat_capacity,mass,molar_energy,stiffness
m·a·k·C·E_m·R
chemistry,mechanics,thermo
m²·a²·k⁻¹·C⁻¹·E_m⁻¹·R
k = k₀ · m²·a²·C⁻¹·E_m⁻¹·R
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "heat_capacity": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
acceleration,mass,specific_heat,stiffness,thermal_cond
m·a·k·c·κ
mechanics,thermo
m·a²·k⁻³·c⁻²·κ²
m = k₀ · a⁻²·k³·c²·κ⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "acceleration": "2", "stiffness": "-3", "specific_heat": "-2", "thermal_cond": "2"}
5
acceleration,expansion,mass,specific_heat,stiffness
m·a·k·c·β
mechanics,thermo
m·a²·k⁻¹·c⁻¹·β
m = k₀ · a⁻²·k·c·β⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "stiffness": "-1", "specific_heat": "-1", "expansion": "1"}
6
acceleration,concentration,gas_constant,mass,specific_heat,stiffness
m·a·k·c·c_n·R
chemistry,mechanics,thermo
m²·a³·k⁻³·c⁻¹·c_n·R
c = k₀ · m²·a³·k⁻³·c_n·R
null
0
3
3
11
9.7
-0.7
false
{"mass": "2", "acceleration": "3", "stiffness": "-3", "specific_heat": "-1", "concentration": "1", "gas_constant": "1"}
6
acceleration,gas_constant,mass,molar_energy,specific_heat,stiffness
m·a·k·c·E_m·R
chemistry,mechanics,thermo
m·a²·k⁻¹·c⁻¹·E_m⁻¹·R
m = k₀ · a⁻²·k·c·E_m·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "2", "stiffness": "-1", "specific_heat": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
acceleration,expansion,mass,stiffness,thermal_cond
m·a·k·κ·β
mechanics,thermo
m·a²·k·κ⁻²·β²
m = k₀ · a⁻²·k⁻¹·κ²·β⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "stiffness": "1", "thermal_cond": "-2", "expansion": "2"}
6
acceleration,amount,gas_constant,mass,stiffness,thermal_cond
m·a·k·κ·n·R
chemistry,mechanics,thermo
m³·a²·k⁻³·κ²·n⁻²·R⁻²
a = k₀ · m⁻³ᐟ²·k³ᐟ²·κ⁻¹·n·R
null
0
3
3
14
11.8
-2.8
false
{"mass": "3", "acceleration": "2", "stiffness": "-3", "thermal_cond": "2", "amount": "-2", "gas_constant": "-2"}
6
acceleration,gas_constant,mass,molar_mass,stiffness,thermal_cond
m·a·k·κ·M_m·R
chemistry,mechanics,thermo
m·a²·k⁻³·κ²·M_m²·R⁻²
m = k₀ · a⁻²·k³·κ⁻²·M_m⁻²·R²
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "acceleration": "2", "stiffness": "-3", "thermal_cond": "2", "molar_mass": "2", "gas_constant": "-2"}
6
acceleration,concentration,gas_constant,mass,stiffness,thermal_cond
m·a·k·κ·c_n·R
chemistry,mechanics,thermo
m³·a⁴·k⁻³·κ⁻²·c_n²·R²
κ = k₀ · m³ᐟ²·a²·k⁻³ᐟ²·c_n·R
null
0
3
4
16
13.7
-4.7
false
{"mass": "3", "acceleration": "4", "stiffness": "-3", "thermal_cond": "-2", "concentration": "2", "gas_constant": "2"}
6
acceleration,gas_constant,mass,molar_energy,stiffness,thermal_cond
m·a·k·κ·E_m·R
chemistry,mechanics,thermo
m·a²·k·κ⁻²·E_m⁻²·R²
m = k₀ · a⁻²·k⁻¹·κ²·E_m²·R⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "acceleration": "2", "stiffness": "1", "thermal_cond": "-2", "molar_energy": "-2", "gas_constant": "2"}
6
acceleration,cat_activity,gas_constant,mass,stiffness,thermal_cond
m·a·k·κ·R·z
chemistry,mechanics,thermo
m·a·k⁻¹·κ·R⁻¹·z⁻¹
m = k₀ · a⁻¹·k·κ⁻¹·R·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "acceleration": "1", "stiffness": "-1", "thermal_cond": "1", "gas_constant": "-1", "cat_activity": "-1"}
6
acceleration,avogadro,gas_constant,mass,stiffness,thermal_cond
m·a·k·κ·R·N_A
chemistry,constants,mechanics,thermo
m³·a²·k⁻³·κ²·R⁻²·N_A²
a = k₀ · m⁻³ᐟ²·k³ᐟ²·κ⁻¹·R·N_A⁻¹
null
1
4
3
14
12.4
-3.9
false
{"mass": "3", "acceleration": "2", "stiffness": "-3", "thermal_cond": "2", "gas_constant": "-2", "avogadro": "2"}
5
acceleration,boltzmann,mass,stiffness,thermal_cond
m·a·k·κ·k_B
constants,mechanics,thermo
m³·a²·k⁻³·κ²·k_B⁻²
a = k₀ · m⁻³ᐟ²·k³ᐟ²·κ⁻¹·k_B
null
1
3
3
12
10.1
-1.1
false
{"mass": "3", "acceleration": "2", "stiffness": "-3", "thermal_cond": "2", "boltzmann": "-2"}
4
acceleration,mass,stiffness,thermal_diff
m·a·k·α
mechanics,thermo
m³·a⁴·k⁻³·α⁻²
α = k₀ · m³ᐟ²·a²·k⁻³ᐟ²
null
0
2
4
12
9.7
-0.2
false
{"mass": "3", "acceleration": "4", "stiffness": "-3", "thermal_diff": "-2"}
6
acceleration,amount,expansion,gas_constant,mass,stiffness
m·a·k·β·n·R
chemistry,mechanics,thermo
m²·a²·k⁻¹·β·n⁻¹·R⁻¹
k = k₀ · m²·a²·β·n⁻¹·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "expansion": "1", "amount": "-1", "gas_constant": "-1"}
6
acceleration,expansion,gas_constant,mass,molar_mass,stiffness
m·a·k·β·M_m·R
chemistry,mechanics,thermo
m·a²·k⁻¹·β·M_m·R⁻¹
m = k₀ · a⁻²·k·β⁻¹·M_m⁻¹·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "2", "stiffness": "-1", "expansion": "1", "molar_mass": "1", "gas_constant": "-1"}
6
acceleration,concentration,expansion,gas_constant,mass,stiffness
m·a·k·β·c_n·R
chemistry,mechanics,thermo
m·a·k⁻²·β⁻¹·c_n·R
m = k₀ · a⁻¹·k²·β·c_n⁻¹·R⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "1", "stiffness": "-2", "expansion": "-1", "concentration": "1", "gas_constant": "1"}
6
acceleration,cat_activity,expansion,gas_constant,mass,stiffness
m·a·k·β·R·z
chemistry,mechanics,thermo
m³·a⁴·k⁻¹·β²·R⁻²·z⁻²
k = k₀ · m³·a⁴·β²·R⁻²·z⁻²
null
0
3
4
14
12.3
-3.3
false
{"mass": "3", "acceleration": "4", "stiffness": "-1", "expansion": "2", "gas_constant": "-2", "cat_activity": "-2"}
6
acceleration,avogadro,expansion,gas_constant,mass,stiffness
m·a·k·β·R·N_A
chemistry,constants,mechanics,thermo
m²·a²·k⁻¹·β·R⁻¹·N_A
k = k₀ · m²·a²·β·R⁻¹·N_A
null
1
4
2
8
7.7
0.8
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "expansion": "1", "gas_constant": "-1", "avogadro": "1"}
5
acceleration,boltzmann,expansion,mass,stiffness
m·a·k·β·k_B
constants,mechanics,thermo
m²·a²·k⁻¹·β·k_B⁻¹
k = k₀ · m²·a²·β·k_B⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "expansion": "1", "boltzmann": "-1"}
5
acceleration,charge,mass,stiffness,voltage
m·a·k·q·U
em,mechanics
m²·a²·k⁻¹·q⁻¹·U⁻¹
k = k₀ · m²·a²·q⁻¹·U⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "charge": "-1", "voltage": "-1"}
5
acceleration,charge,mass,resistance,stiffness
m·a·k·q·R
em,mechanics
m⁵·a⁴·k⁻³·q⁻⁴·R⁻²
R = k₀ · m⁵ᐟ²·a²·k⁻³ᐟ²·q⁻²
null
0
2
5
18
14.7
-5.2
false
{"mass": "5", "acceleration": "4", "stiffness": "-3", "charge": "-4", "resistance": "-2"}
5
acceleration,capacitance,charge,mass,stiffness
m·a·k·q·C_e
em,mechanics
m²·a²·k⁻¹·q⁻²·C_e
k = k₀ · m²·a²·q⁻²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "charge": "-2", "capacitance": "1"}
5
acceleration,charge,inductance,mass,stiffness
m·a·k·q·L_e
em,mechanics
m³·a²·k⁻²·q⁻²·L_e⁻¹
L_e = k₀ · m³·a²·k⁻²·q⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "3", "acceleration": "2", "stiffness": "-2", "charge": "-2", "inductance": "-1"}
5
acceleration,charge,mag_flux,mass,stiffness
m·a·k·q·Φ
em,mechanics
m⁵·a⁴·k⁻³·q⁻²·Φ⁻²
q = k₀ · m⁵ᐟ²·a²·k⁻³ᐟ²·Φ⁻¹
null
0
2
5
16
13.3
-3.8
false
{"mass": "5", "acceleration": "4", "stiffness": "-3", "charge": "-2", "mag_flux": "-2"}
5
acceleration,charge,mass,permittivity,stiffness
m·a·k·q·ε
em,mechanics
m³·a³·k⁻²·q⁻²·ε
ε = k₀ · m⁻³·a⁻³·k²·q²
null
0
2
3
11
8.8
0.7
false
{"mass": "3", "acceleration": "3", "stiffness": "-2", "charge": "-2", "permittivity": "1"}
5
acceleration,charge,mass,permeability,stiffness
m·a·k·q·μ₀
em,mechanics
m²·a·k⁻¹·q⁻²·μ₀⁻¹
a = k₀ · m⁻²·k·q²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "1", "stiffness": "-1", "charge": "-2", "permeability": "-1"}
5
acceleration,charge,conductivity,mass,stiffness
m·a·k·q·σ
em,mechanics
m⁷·a⁶·k⁻⁵·q⁻⁴·σ²
σ = k₀ · m⁻⁷ᐟ²·a⁻³·k⁵ᐟ²·q²
null
0
2
7
24
19.9
-10.4
false
{"mass": "7", "acceleration": "6", "stiffness": "-5", "charge": "-4", "conductivity": "2"}
5
acceleration,charge,mass,resistivity,stiffness
m·a·k·q·ρ_e
em,mechanics
m⁷·a⁶·k⁻⁵·q⁻⁴·ρ_e⁻²
ρ_e = k₀ · m⁷ᐟ²·a³·k⁻⁵ᐟ²·q⁻²
null
0
2
7
24
19.9
-10.4
false
{"mass": "7", "acceleration": "6", "stiffness": "-5", "charge": "-4", "resistivity": "-2"}
5
acceleration,current,mass,stiffness,voltage
m·a·k·i·U
em,mechanics
m³·a⁴·k⁻¹·i⁻²·U⁻²
k = k₀ · m³·a⁴·i⁻²·U⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "3", "acceleration": "4", "stiffness": "-1", "current": "-2", "voltage": "-2"}
5
acceleration,current,mass,resistance,stiffness
m·a·k·i·R
em,mechanics
m³·a⁴·k⁻¹·i⁻⁴·R⁻²
k = k₀ · m³·a⁴·i⁻⁴·R⁻²
null
0
2
4
14
11.4
-1.9
false
{"mass": "3", "acceleration": "4", "stiffness": "-1", "current": "-4", "resistance": "-2"}
5
acceleration,current,inductance,mass,stiffness
m·a·k·i·L_e
em,mechanics
m²·a²·k⁻¹·i⁻²·L_e⁻¹
k = k₀ · m²·a²·i⁻²·L_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "current": "-2", "inductance": "-1"}
5
acceleration,current,efield,mass,stiffness
m·a·k·i·E_f
em,mechanics
m·a²·k·i⁻²·E_f⁻²
m = k₀ · a⁻²·k⁻¹·i²·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "stiffness": "1", "current": "-2", "efield": "-2"}
5
acceleration,current,mag_flux,mass,stiffness
m·a·k·i·Φ
em,mechanics
m²·a²·k⁻¹·i⁻¹·Φ⁻¹
k = k₀ · m²·a²·i⁻¹·Φ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "current": "-1", "mag_flux": "-1"}
5
acceleration,current,mass,permittivity,stiffness
m·a·k·i·ε
em,mechanics
m²·a³·k⁻¹·i⁻²·ε
k = k₀ · m²·a³·i⁻²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "stiffness": "-1", "current": "-2", "permittivity": "1"}
5
acceleration,conductivity,current,mass,stiffness
m·a·k·i·σ
em,mechanics
m⁵·a⁶·k⁻³·i⁻⁴·σ²
σ = k₀ · m⁻⁵ᐟ²·a⁻³·k³ᐟ²·i²
null
0
2
6
20
16.6
-7.1
false
{"mass": "5", "acceleration": "6", "stiffness": "-3", "current": "-4", "conductivity": "2"}
5
acceleration,current,mass,resistivity,stiffness
m·a·k·i·ρ_e
em,mechanics
m⁵·a⁶·k⁻³·i⁻⁴·ρ_e⁻²
ρ_e = k₀ · m⁵ᐟ²·a³·k⁻³ᐟ²·i⁻²
null
0
2
6
20
16.6
-7.1
false
{"mass": "5", "acceleration": "6", "stiffness": "-3", "current": "-4", "resistivity": "-2"}
5
acceleration,mass,resistance,stiffness,voltage
m·a·k·U·R
em,mechanics
m³·a⁴·k⁻¹·U⁻⁴·R²
k = k₀ · m³·a⁴·U⁻⁴·R²
null
0
2
4
14
11.4
-1.9
false
{"mass": "3", "acceleration": "4", "stiffness": "-1", "voltage": "-4", "resistance": "2"}
5
acceleration,capacitance,mass,stiffness,voltage
m·a·k·U·C_e
em,mechanics
m²·a²·k⁻¹·U⁻²·C_e⁻¹
k = k₀ · m²·a²·U⁻²·C_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "acceleration": "2", "stiffness": "-1", "voltage": "-2", "capacitance": "-1"}
5
acceleration,efield,mass,stiffness,voltage
m·a·k·U·E_f
em,mechanics
m·a·k⁻¹·U⁻¹·E_f
m = k₀ · a⁻¹·k·U·E_f⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "stiffness": "-1", "voltage": "-1", "efield": "1"}
5
acceleration,bfield,mass,stiffness,voltage
m·a·k·U·B
em,mechanics
m³·a⁴·k⁻³·U⁻²·B²
U = k₀ · m³ᐟ²·a²·k⁻³ᐟ²·B
null
0
2
4
14
11.4
-1.9
false
{"mass": "3", "acceleration": "4", "stiffness": "-3", "voltage": "-2", "bfield": "2"}
5
acceleration,mass,permeability,stiffness,voltage
m·a·k·U·μ₀
em,mechanics
m²·a³·k⁻¹·U⁻²·μ₀
k = k₀ · m²·a³·U⁻²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "stiffness": "-1", "voltage": "-2", "permeability": "1"}
5
acceleration,conductivity,mass,stiffness,voltage
m·a·k·U·σ
em,mechanics
m·a²·k·U⁻⁴·σ⁻²
m = k₀ · a⁻²·k⁻¹·U⁴·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "acceleration": "2", "stiffness": "1", "voltage": "-4", "conductivity": "-2"}
5
acceleration,mass,resistivity,stiffness,voltage
m·a·k·U·ρ_e
em,mechanics
m·a²·k·U⁻⁴·ρ_e²
m = k₀ · a⁻²·k⁻¹·U⁴·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "acceleration": "2", "stiffness": "1", "voltage": "-4", "resistivity": "2"}
5
acceleration,elem_charge,mass,stiffness,voltage
m·a·k·U·e
constants,em,mechanics
m²·a²·k⁻¹·U⁻¹·e⁻¹
k = k₀ · m²·a²·U⁻¹·e⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "2", "acceleration": "2", "stiffness": "-1", "voltage": "-1", "elem_charge": "-1"}
5
acceleration,bfield,mass,resistance,stiffness
m·a·k·R·B
em,mechanics
m³·a⁴·k⁻⁵·R⁻²·B⁴
R = k₀ · m³ᐟ²·a²·k⁻⁵ᐟ²·B²
null
0
2
5
18
14.7
-5.2
false
{"mass": "3", "acceleration": "4", "stiffness": "-5", "resistance": "-2", "bfield": "4"}
5
acceleration,mag_flux,mass,resistance,stiffness
m·a·k·R·Φ
em,mechanics
m⁵·a⁴·k⁻³·R²·Φ⁻⁴
R = k₀ · m⁻⁵ᐟ²·a⁻²·k³ᐟ²·Φ²
null
0
2
5
18
14.7
-5.2
false
{"mass": "5", "acceleration": "4", "stiffness": "-3", "resistance": "2", "mag_flux": "-4"}
5
acceleration,mass,permittivity,resistance,stiffness
m·a·k·R·ε
em,mechanics
m·a²·k⁻¹·R²·ε²
m = k₀ · a⁻²·k·R⁻²·ε⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "stiffness": "-1", "resistance": "2", "permittivity": "2"}
5
acceleration,mass,permeability,resistance,stiffness
m·a·k·R·μ₀
em,mechanics
m·a²·k⁻¹·R⁻²·μ₀²
m = k₀ · a⁻²·k·R²·μ₀⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "stiffness": "-1", "resistance": "-2", "permeability": "2"}
5
acceleration,conductivity,mass,resistance,stiffness
m·a·k·R·σ
em,mechanics
m·a·k⁻¹·R·σ
m = k₀ · a⁻¹·k·R⁻¹·σ⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "stiffness": "-1", "resistance": "1", "conductivity": "1"}
5
acceleration,mass,resistance,resistivity,stiffness
m·a·k·R·ρ_e
em,mechanics
m·a·k⁻¹·R·ρ_e⁻¹
m = k₀ · a⁻¹·k·R⁻¹·ρ_e
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "stiffness": "-1", "resistance": "1", "resistivity": "-1"}