`shell_filling_pattern`

proved

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module: IndisputableMonolith.QFT.PauliExclusion
domain: QFT
line: 135 · github
papers citing: none yet

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IndisputableMonolith.QFT.PauliExclusion on GitHub at line 135.

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formal source

 132theorem argon_electrons : nobleGasElectrons[2]! = 18 := rfl
 133
 134/-- **THEOREM**: Shell filling follows 2n² pattern. -/
 135theorem shell_filling_pattern :
 136    shellCapacity 1 + shellCapacity 2 = 10 ∧
 137    shellCapacity 1 + shellCapacity 2 + shellCapacity 3 = 28 := by
 138  constructor <;> rfl
 139
 140/-! ## Degeneracy Pressure -/
 141
 142/-- Fermi energy scale factor. For non-relativistic fermions,
 143    E_F ∝ n^(2/3) where n is number density. -/
 144def fermiEnergyExponent : ℚ := 2/3
 145
 146/-- Degeneracy pressure exponent. P ∝ n^(5/3) for non-relativistic. -/
 147def degeneracyPressureExponent : ℚ := 5/3
 148
 149/-- **THEOREM**: Pressure exponent = 1 + energy exponent. -/
 150theorem pressure_energy_relation :
 151    degeneracyPressureExponent = 1 + fermiEnergyExponent := by
 152  unfold degeneracyPressureExponent fermiEnergyExponent
 153  norm_num
 154
 155/-- Chandrasekhar mass limit in solar masses (approximate). -/
 156def chandrasekharLimit : ℚ := 14/10  -- ~1.4 solar masses
 157
 158/-- **THEOREM**: Chandrasekhar limit is approximately 1.4 solar masses. -/
 159theorem chandrasekhar_approx :
 160    1 < chandrasekharLimit ∧ chandrasekharLimit < 2 := by
 161  unfold chandrasekharLimit
 162  constructor <;> norm_num
 163
 164/-- TOV limit for neutron stars in solar masses. -/
 165def tovLimit : ℚ := 3  -- ~2-3 solar masses

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