IndisputableMonolith.Chemistry.VanDerWaals
Scaffold for noble-gas van der Waals physics in Recognition Science: London dispersion proxies, a Lennard-Jones potential, and monotone boiling-point inequalities along He–Ne–Ar–Kr–Xe–Rn. Chemists and condensed-matter theorists cite it when linking φ-ladder polarizability to macroscopic cohesion without fitted parameters. Structure is definitional proxies plus short comparison lemmas on tabulated boiling points.
claimModule objects: noble-gas set $\{Z\}$; boiling-point map $T_b(Z)$; polarizability proxy $\alpha(Z)$; London dispersion proxy $\propto \alpha_i\alpha_j/r^6$; Lennard-Jones $V_{\mathrm{LJ}}(r)=4\varepsilon\bigl[(\sigma/r)^{12}-(\sigma/r)^6\]$ with approximate minimum $r_{\min}\approx 2^{1/6}\sigma$; and inequalities $T_b(\mathrm{He})<T_b(\mathrm{Ne})<\cdots<T_b(\mathrm{Rn})$.
background
Recognition Science chemistry sits on the Periodic Table engine: an octave ↔ eight-tick map with φ-tier rails, fixed s/p/d/f block offsets, and an eight-window neutrality predicate that marks noble-gas closures as rests. No per-element tuning is allowed; the API is deliberately zero-parameter so downstream predictions remain falsifiable.
This module specializes that scaffold to closed-shell cohesion. Noble gases interact only through induced multipoles. The London dispersion energy scales with polarizability products over $r^6$; polarizability itself is expected to track atomic size on the φ-ladder. A standard Lennard-Jones pair potential packages the short-range Pauli wall and the attractive tail, with minimum near $2^{1/6}\sigma$.
Constants supplies the RS time quantum $\tau_0=1$ tick; chemistry here is still in dimensionless or proxy units pending full unit conversion.
proof idea
Definition-heavy module. It introduces the noble-gas list, boiling-point and polarizability proxies, a London dispersion proxy, and a Lennard-Jones potential with an approximate minimum-distance lemma. The only theorem-shaped content is a chain of elementary inequalities asserting that tabulated noble-gas boiling points strictly increase from He through Rn; each step is a direct numeric comparison, not a derivation from first principles.
why it matters in Recognition Science
Closes the chemistry side of weak intermolecular forces without dataset binding. Upstream PeriodicTable supplies the fit-free noble-gas rests via the eight-window neutrality predicate; this module turns those rests into cohesion observables (dispersion proxies, LJ well, boiling-point order). Downstream use is still open (used_by empty), so the file is a prediction surface: any RS mass or polarizability formula on the φ-ladder can be wired into the London proxy and checked against the monotone $T_b$ chain. Ties to the eight-tick octave (T7) and φ-ladder mass/yardstick structure rather than to the forcing chain’s geometric steps T5–T8 directly.
scope and limits
- Does not derive boiling points from the φ-ladder or J-cost; inequalities are numeric order facts.
- Does not claim a first-principles polarizability formula; only a named proxy.
- Does not calibrate Lennard-Jones ε, σ to experiment or to RS constants.
- Does not treat molecular (non-noble) van der Waals or hydrogen bonding.
- Does not yet connect to used_by parents; prediction surface only.
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