module module high

`IndisputableMonolith.Chemistry.IonicBond`

This module defines predicates and constants for classifying ionic bonds, centered on alkali metal-halogen pairs using electronegativity differences and lattice energy proxies derived from phi-ladder scaling. Chemists working within Recognition Science would cite it when modeling bond types from the eight-tick periodic structure. The module is a collection of definitions assembled from imported modules on ionization energies, electron affinities, and electronegativities, with no internal proofs.

claimDefines alkaliMetalZ, halogenZ, isAlkaliMetal(Z), isHalogen(Z), electronegativityDifference(Z1,Z2), ionicThreshold, isIonicBond(Z1,Z2), alkali_halogen_ionic, latticeEnergyProxy, and Madelung constants (madelungNaCl, madelungCsCl, madelungZnS) for ionic structures.

background

The module sits in the chemistry domain of Recognition Science. It imports the PeriodicTable engine, which supplies the octave to eight-tick mapping, phi-tier rails, block offsets for s/p/d/f subshells, and neutrality predicate for noble-gas closures. IonizationEnergy supplies the sawtooth pattern with phi-rail scaling phi^{2n} for period n and position factors toward closure. ElectronAffinity encodes the approach-to-closure pattern with high EA for halogens and low EA for alkali metals. Electronegativity follows distToNextClosure^{-1} modulated by shell number, consistent with the Mulliken relation EN ~ sqrt(IE * EA). Constants supplies the base RS time quantum tau_0 = 1 tick.

Sibling definitions translate these into ionic-bond criteria: alkali metals (low IE) paired with halogens (high EA) produce large electronegativity differences that exceed ionicThreshold, triggering isIonicBond and alkali_halogen_ionic. Lattice energy proxies and structure-specific Madelung constants (NaCl, CsCl, ZnS) complete the bond-energy scaffolding.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the ionic-bond classification layer that supports downstream chemical predictions in the Recognition Science framework. It directly implements the CH-006/CH-008 patterns from ElectronAffinity and Electronegativity together with the P0-A2 ionization scaling, feeding the phi-ladder chemistry propositions. No used-by edges are recorded yet, indicating it is an early scaffold for bond-type falsifiers.

scope and limits

Does not compute numerical lattice energies from quantum mechanics.
Does not classify covalent or metallic bonding.
Does not include transition-metal or f-block elements.
Does not derive Madelung constants from electrostatic summation.
Does not predict specific compound formation 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