IndisputableMonolith.Chemistry.IonicBond
Defines ionic bonding in RS chemistry via electronegativity difference and alkali–halogen pair predicates, plus lattice-energy proxies with classical Madelung factors (NaCl, CsCl, ZnS). Chemists and RS auditors use it to classify bonds without per-element fits. Structure is definitional predicates and constants built on IE/EA/EN and the periodic-table engine.
claimIonic character is decided by an electronegativity gap $\Delta\chi(Z_1,Z_2)$ against a fixed threshold, with alkali metals and halogens as the canonical donor/acceptor classes. A lattice-energy proxy combines charge product, Madelung constant $M$ (NaCl, CsCl, or ZnS), and a length scale from the $\varphi$-ladder. Alkali–halogen pairs are predicted ionic under these rules.
background
Recognition Science chemistry sits on the fit-free periodic-table engine: octave/eight-tick shell structure, $\varphi$-tier rails, fixed s/p/d/f block offsets, and noble-gas closures as neutrality rests. No per-element tuning is allowed.
Upstream modules supply the energetic ingredients. Ionization energy follows $\varphi$-rail sawteeth (base $\varphi^{2n}$ by period, rise toward closure, block offsets). Electron affinity peaks for halogens (one short of closure), is near zero or negative for nobles, and is low for alkalis. Electronegativity is the Mulliken-style combination of IE and EA, equivalently distance-to-closure modulated by shell number.
This module turns those scalars into bond-type predicates: alkali and halogen $Z$-sets, $\Delta\chi$, an ionic threshold, and simple Madelung-weighted lattice proxies for the standard cubic structure types.
proof idea
Definition module, not a deep proof stack. It introduces finite $Z$-classifiers for alkalis and halogens, a difference map on electronegativities, a numeric ionic threshold, and the boolean `is ionic' predicate. The alkali–halogen claim is a direct case split on those classifiers. Lattice energy is a proxy formula (charges, Madelung $M$, length), with three named Madelung constants for NaCl, CsCl, and ZnS structure types. Any lemmas are thin wrappers over the imported IE/EA/EN and periodic-table APIs.
why it matters in Recognition Science
Closes the CH-side path from shell geometry and $\varphi$-ladder energetics to a concrete bond-type decision rule used in RS chemistry. It is the natural consumer of the ionization-energy (P0-A2), electron-affinity (CH-006), and electronegativity (CH-008) modules, and of the zero-parameter periodic-table scaffold. Downstream work on salts, lattice stability, and ionic vs covalent falsifiers is expected to import these predicates and Madelung proxies; the present graph shows no formal used-by edges yet. Ties to the eight-tick octave only indirectly, through the shell-closure language of the periodic engine.
scope and limits
- Does not derive Madelung constants from RS first principles; they are classical structure factors.
- Does not claim a full Born–Haber cycle or quantitative lattice energies in eV.
- Does not treat partial ionicity, polarization, or covalent–ionic continuum models.
- Does not bind to experimental datasets; classifiers are scaffold-level.
- Does not prove uniqueness of the ionic threshold from the forcing chain.
depends on (5)
declarations in this module (19)
-
def
alkaliMetalZ -
def
halogenZ -
def
isAlkaliMetal -
def
isHalogen -
def
electronegativityDifference -
def
ionicThreshold -
def
isIonicBond -
theorem
alkali_halogen_ionic -
def
latticeEnergyProxy -
def
madelungNaCl -
def
madelungCsCl -
def
madelungZnS -
theorem
madelung_nacl_pos -
theorem
lattice_energy_increases_with_charge -
theorem
alkali_valence_one -
theorem
halogen_dist_one -
theorem
alkali_halogen_stable_1_1 -
def
bornExponentProxy -
theorem
born_exponent_in_range