IndisputableMonolith.Chemistry.VanDerWaals
Fit-free chemistry scaffold for noble-gas Van der Waals trends in Recognition Science. It records noble-gas Z values, boiling-point data, polarizability and London-dispersion proxies, a Lennard-Jones potential with an approximate minimum, and the He→Rn boiling-point chain. Auditors checking residual attractions after noble-gas shell closure would cite it. Most content is definitions plus elementary numeric inequalities.
claimNoble-gas atomic numbers and boiling points; polarizability and London-dispersion proxies; Lennard-Jones potential $V_{\mathrm{LJ}}(r)$ with approximate minimizing distance; and the ordering $T_b(\mathrm{He})<T_b(\mathrm{Ne})<T_b(\mathrm{Ar})<T_b(\mathrm{Kr})<T_b(\mathrm{Xe})<T_b(\mathrm{Rn})$.
background
Recognition Science chemistry sits on the Periodic Table engine: an octave / eight-tick map with $\varphi$-tier rails, fixed $s/p/d/f$ block offsets, and an eight-window neutrality predicate that marks noble-gas shell closures as "rests." No per-element tuning is allowed; the API is deliberately zero-parameter so downstream predictions stay falsifiable.
After a closed shell, residual cohesion is Van der Waals attraction, dominated for noble gases by London dispersion. This module packages the minimal objects needed to state that residual: a noble-gas list, boiling-point anchors, scalar proxies for polarizability and dispersion strength, and a standard Lennard-Jones pair potential whose minimum sets a characteristic length.
Constants enter only through the shared RS tick $\tau_0=1$; the chemistry layer does not rebind $c$, $\hbar$, or $G$ here.
proof idea
Primarily a definition module. Noble-gas sets, boiling-point tables, polarizability/dispersion proxies, and the Lennard-Jones form are introduced as data or closed-form defs. The proved content is a short chain of elementary comparisons: each consecutive noble-gas boiling-point inequality (He–Ne, Ne–Ar, Ar–Kr, Kr–Xe, Xe–Rn) is a direct numeric check. The LJ minimum lemma is an approximate algebraic location of the potential well, not a deep existence proof.
why it matters in Recognition Science
Closes the residual-force side of noble-gas "rests" from the Periodic Table engine: once eight-window neutrality marks a closed shell, this module supplies the language for weak cohesion that still rises with size and polarizability. That matches the qualitative He→Rn boiling-point ladder without dataset binding.
No downstream theorems currently import it (leaf scaffold). It is the natural hook for later chemistry falsifiers: predicted ordering or scaling of dispersion proxies against $\varphi$-tier rails, or LJ length scales tied to the eight-tick octave. It does not yet touch mass-ladder rungs or the $\alpha$ band; those remain separate RS landmarks.
scope and limits
- Does not derive boiling points from $\varphi$-ladder or first-principles RS dynamics.
- Does not claim quantitative match to experimental $T_b$ beyond the stated ordering.
- Does not model multipole, induction, or many-body corrections beyond London proxies.
- Does not bind Lennard-Jones parameters to measured $\sigma$ or $\varepsilon$ datasets.
- Does not treat molecular (non-noble) Van der Waals complexes.
depends on (2)
declarations in this module (16)
-
def
nobleGases -
def
nobleGasBoilingPoint -
def
polarizabilityProxy -
def
londonDispersionProxy -
def
lennardJonesPotential -
def
ljMinimumDistance -
theorem
lj_minimum_approx -
theorem
noble_gas_bp_increases_he_ne -
theorem
noble_gas_bp_increases_ne_ar -
theorem
noble_gas_bp_increases_ar_kr -
theorem
noble_gas_bp_increases_kr_xe -
theorem
noble_gas_bp_increases_xe_rn -
theorem
noble_gas_bp_full_ordering -
theorem
london_decreases_with_distance -
def
ljRatioPhiConnection -
theorem
lj_phi_connection_approx