module module moderate

`IndisputableMonolith.Physics.Superfluidity`

The Physics.Superfluidity module defines the Bose-Einstein occupation number at temperature T along with related quantities such as BEC temperature, lambda point, and quantized vortices. Researchers modeling quantum fluids or critical phenomena inside the Recognition Science framework would cite these objects. The module consists of direct definitions and simple positivity statements built on the imported J-cost core.

claimThe Bose-Einstein occupation number is $n(T) = 1/(e^{J(T)} - 1)$ together with the derived BEC temperature $T_{BEC}$, lambda point $T_λ$, and vortex quantum $h/m$.

background

The module sits inside the Recognition Science derivation of physics from the single functional equation and imports the J-cost core that supplies the J function (J(x) = (x + x^{-1})/2 - 1) and the Recognition Composition Law. It therefore inherits the phi-ladder mass formula, the eight-tick octave, and the native units in which c = 1, ħ = ϕ^{-5}. The sibling declarations introduce the occupation number, its positivity, the BEC temperature, the lambda point for ^{4}He, and the quantized circulation of vortices.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the concrete objects needed to connect the J-cost formalism to observed superfluid phenomena such as the lambda transition and vortex quantization. It therefore feeds any later derivation of critical exponents or hydrodynamic equations inside the Recognition Science chain. No downstream theorems are listed yet, indicating the module is still at the interface stage between the cost core and full fluid dynamics.

scope and limits

Does not derive the full Gross-Pitaevskii or hydrodynamic equations.
Does not prove the value of the critical exponent beyond the listed rs_critical_exponent declaration.
Does not address finite-temperature corrections beyond the basic occupation number.
Does not treat fermionic superfluidity or pairing mechanisms.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost.JcostCore module_import

declarations in this module (19)

def be_occupation L23
theorem be_occupation_positive L27
def bec_temperature L37
theorem bec_temperature_positive L41
def lambda_point L51
theorem lambda_point_lt_bec L55
def lambda_point_He4 L73
theorem lambda_He4_in_range L76
def vortex_quantum L84
theorem vortex_quantum_positive L87
theorem vortex_quantized L92
def rs_critical_exponent L99
lemma golden_ratio_gt_one L103
theorem rs_critical_exponent_positive L110
def superfluid_fraction L117
theorem superfluid_fraction_at_zero L121
theorem superfluid_fraction_at_lambda L127
theorem superfluid_fraction_between L133
theorem he3_b_phase_global_minimum L149