IndisputableMonolith.Physics.SuperfluidityHeliumFromJCost
Packages a Recognition-Science account of helium-4 superfluidity driven by the J-cost. Condensed-matter and RS auditors cite the domain cost, the canonical threshold, and the SuperfluidHe4 certificate. The module is mostly definitions plus short positivity and inhabitation lemmas over Cost and Constants.
claimDefine a domain cost $C$ from the Recognition $J$-cost, a canonical threshold $\theta>0$, and a certificate that $^4\mathrm{He}$ meets the RS superfluidity criterion comparing $C$ to $\theta$ in RS-native units ($c=1$, tick $\tau_0$).
background
Recognition Science forces the cost $J(x)=(x+x^{-1})/2-1$ (T5) and builds physics from comparisons of $J$-derived quantities to dimensionless thresholds. This module sits in the physics layer and imports only Constants (RS time quantum $\tau_0=1$ tick) and Cost (the $J$-cost API).
Sibling objects introduce a domain cost for the helium setting, prove it is nonnegative and agrees with its pointwise evaluation, fix a canonical positive threshold, and wrap the comparison into a SuperfluidHe4 certificate type with an inhabitation proof. The intended reading is that superfluid response appears when the $J$-cost of the relevant recognition domain falls on the allowed side of that threshold.
No external condensed-matter axioms are imported: the claim is internal to the RS cost calculus.
proof idea
Definition-heavy module, not a single deep theorem. domainCost is introduced and tied to evaluation by an equality lemma; nonnegativity is inherited from $J\ge 0$. canonicalThreshold is a positive constant (positivity lemma). SuperfluidHe4Cert is a Prop/structure packaging the cost-threshold comparison; cert and cert_inhabited discharge that the helium instance inhabits it. Argument shape: Cost lemmas plus elementary real inequalities, no analytic PDE model of the two-fluid equations.
why it matters in Recognition Science
Gives an RS-native, certificate-style prediction that $^4\mathrm{He}$ is superfluid from $J$-cost alone, rather than from a phenomenological order parameter. Downstream used_by is currently empty, so this is a leaf physics module: it closes a condensed-matter claim inside the monolith instead of feeding a larger forcing step.
It sits downstream of T5 $J$-uniqueness and the Cost library, and uses Constants only for RS units. Auditors checking whether RS produces ordinary-matter phases (not only particle masses and $\alpha$) land here. It does not yet connect to the eight-tick octave, $D=3$, or the mass ladder; those remain separate chain steps.
scope and limits
- Does not derive the two-fluid equations or a critical temperature $T_c$.
- Does not treat $^3\mathrm{He}$, mixtures, or rotating-bucket quantization.
- Does not claim experimental fit beyond the internal cost-threshold certificate.
- Does not connect to alpha, mass rungs, or the T0–T8 forcing chain beyond using $J$.
- Does not model vortices, healing length, or laboratory geometries.