module module high

`IndisputableMonolith.Chemistry.IonicBond`

The IonicBond module defines Recognition Science predicates and energy proxies for ionic bonding, centered on alkali-halogen pairs that combine low ionization energy with high electron affinity. Researchers building parameter-free bond-type classifiers in the φ-ladder framework would cite these definitions. The module consists of element-class predicates, an electronegativity-difference threshold, and lattice-energy proxies assembled from upstream scaling results.

claimLet $Z$ range over atomic numbers. Define alkaliMetalZ and halogenZ as the sets {3,11,19,37,55,87} and {9,17,35,53,85} respectively. Then isIonicBond$(Z_1,Z_2)$ holds when one element belongs to alkaliMetalZ, the other to halogenZ, and the electronegativity difference exceeds ionicThreshold, with latticeEnergyProxy$(Z_1,Z_2)$ given by the Madelung sum for the corresponding crystal structure.

background

The module sits inside the Recognition Science chemistry layer that maps the eight-tick octave of PeriodicTable onto element blocks. Upstream IonizationEnergy supplies the sawtooth I₁(Z) pattern forced by φ-rail scaling φ^{2n} plus position-to-closure factors. ElectronAffinity predicts high values for halogens (one electron short of closure) and low values for alkali metals (one past closure). Electronegativity combines these via the classical √(IE × EA) form modulated by distance to next closure, exactly as stated in its doc-comment.

proof idea

This is a definition module, no proofs. It imports the five upstream modules, declares the concrete Z-sets alkaliMetalZ and halogenZ, lifts the isAlkaliMetal and isHalogen predicates, computes electronegativityDifference from the imported EN function, introduces the fixed ionicThreshold, and assembles isIonicBond together with the three Madelung lattice proxies.

why it matters in Recognition Science

The module supplies the ionic-bond classification that feeds lattice-energy calculations (madelungNaCl, madelungCsCl, madelungZnS) and closes the CH-00x chemistry series. It directly implements the low-ionization-energy property of alkali metals stated in the module doc-comment and connects to the eight-tick octave (T7) and φ-ladder scaling (T6) of the UnifiedForcingChain. It touches the open question of deriving bond-type thresholds without empirical fitting.

scope and limits

Does not compute numerical lattice energies from first principles.
Does not treat covalent or metallic bonding criteria.
Does not incorporate relativistic corrections for heavy elements.
Does not validate predictions against measured bond lengths or dissociation energies.

depends on (5)

Lean names referenced from this declaration's body.

IndisputableMonolith.Chemistry.ElectronAffinity module_import
IndisputableMonolith.Chemistry.Electronegativity module_import
IndisputableMonolith.Chemistry.IonizationEnergy module_import
IndisputableMonolith.Chemistry.PeriodicTable module_import
IndisputableMonolith.Constants module_import

declarations in this module (19)

def alkaliMetalZ L39
def halogenZ L42
def isAlkaliMetal L45
def isHalogen L48
def electronegativityDifference L58
def ionicThreshold L77
def isIonicBond L80
theorem alkali_halogen_ionic L95
def latticeEnergyProxy L127
def madelungNaCl L133
def madelungCsCl L136
def madelungZnS L139
theorem madelung_nacl_pos L142
theorem lattice_energy_increases_with_charge L148
theorem alkali_valence_one L164
theorem halogen_dist_one L170
theorem alkali_halogen_stable_1_1 L177
def bornExponentProxy L184
theorem born_exponent_in_range L188