fermiEnergyExponent
plain-language theorem explainer
fermiEnergyExponent records the non-relativistic Fermi energy scaling as the rational constant 2/3. Workers deriving degeneracy pressure in white dwarfs and neutron stars cite this value when relating number density to energy density under the Pauli exclusion constraint. The declaration is a direct one-line rational assignment with no lemmas or tactics.
Claim. The non-relativistic Fermi energy satisfies $E_F ∝ n^{2/3}$, where $n$ is number density; the exponent is the constant $2/3$.
background
Recognition Science derives the Pauli exclusion principle from ledger single-occupancy: fermions are odd-phase entries in the eight-tick cycle, so identical states would violate antisymmetry and force the wave function to zero. Module QFT-004 therefore links this constraint to atomic shells and to degeneracy pressure in compact objects. The upstream pressure definition supplies the effective source term $p = ρ · (W k a) · δ$ used in gravitational calculations.
proof idea
The declaration is a direct definition that assigns the rational value 2/3. No lemmas are invoked and no tactics are executed; the body simply records the conventional non-relativistic exponent for later arithmetic combination.
why it matters
This definition supplies the energy exponent that enters the relation degeneracyPressureExponent = 1 + fermiEnergyExponent, which supports the approximate Chandrasekhar mass limit. It sits inside the QFT-004 derivation of Pauli exclusion from the ledger cycle and feeds the pressure calculations that stabilize white dwarfs and neutron stars.
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