Ion Ontology

FLOW ALGEBRA
ION ONTOLOGY — KIRETH SEMANTIC LIBRARY
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/atomic-entities/ion-ontology.html
Status: Scientific synthesis; source page content not independently verified.

01. PURPOSE
Model ions as charged atomic or molecular entities, with explicit distinctions among charge state, composition, formation, transport, reactions, and measurement.

02. CORE SIGNATURE
flow IonOntology(E,R,P,T,C,V)
E : set<Entity>
R : set<TypedRelation>
P : set<Property>
T : set<Transformation>
C : set<Constraint>
V : set<ValidationRule>

03. ENTITY TYPES
Entity := Atom | Molecule | Ion | Electron | Nucleus | Element | Isotope | Compound | Medium | Measurement | Process
Ion <: ChargedChemicalSpecies
AtomicIon <: Ion
MolecularIon <: Ion
Cation <: Ion
Anion <: Ion
MonatomicIon <: AtomicIon
PolyatomicIon <: MolecularIon
RadicalIon <: Ion

04. IDENTITY AND SYMBOLS
ion_id: Ion -> Identifier
chemical_formula: Ion -> Formula
charge_number: Ion -> IntegerExceptZero
charge_C: Ion -> Coulomb
composition: Ion -> Multiset<Element>
isotope_signature: Ion -> Optional<IsotopicComposition>
phase: Ion -> {gas,liquid,solid,solution,plasma,other}

05. CHARGE RULES
q(i) = z(i) * e
where e = 1.602176634e-19 C (exact SI elementary charge).
z(i) > 0 => Cation(i)
z(i) < 0 => Anion(i)
z(i) = 0 => not Ion(i) under this ontology's definition.
A neutral compound can contain constituent ions; neutrality of the compound does not negate their ionic charge.

06. ATOMIC ION ELECTRON COUNT
For an atomic ion with proton number Z and electron count N_e:
z = Z - N_e
N_e = Z - z
Neutron count N_n = A - Z for a specified nuclide with mass number A.
Ionisation does not change Z; nuclear reactions are separate processes.

07. TYPED RELATIONSHIPS
IS_A(Ion,ChargedChemicalSpecies)
HAS_CHARGE(Ion,ChargeNumber)
HAS_FORMULA(Ion,Formula)
HAS_ELEMENT(AtomicIon,Element)
HAS_ISOTOPE(AtomicIon,Isotope)
FORMED_BY(Ion,IonisationProcess)
PARTICIPATES_IN(Ion,ChemicalReaction)
SOLVATED_BY(Ion,Solvent)
MIGRATES_IN(Ion,Medium)
DETECTED_BY(Ion,MeasurementMethod)
BALANCES_CHARGE_WITH(Ion,Ion)

08. FORMATION TRANSFORMATIONS
Electron removal: M -> M+ + e- (example: Na -> Na+ + e-).
Electron attachment: X + e- -> X- (example: Cl + e- -> Cl-).
Multistep ionisation: M^(z+) -> M^((z+1)+) + e-.
Dissociation: NaCl(s) -> Na+(aq) + Cl-(aq) in water, under suitable conditions.
Proton transfer can form molecular ions, e.g. NH3 + H+ -> NH4+.
Charge-transfer and redox processes require atom and charge balance.

09. CONSERVATION CONSTRAINTS
For a balanced chemical reaction, sum of elemental atom counts is conserved.
For an electrically isolated reaction description, total charge before = total charge after.
For ordinary chemical reactions, nuclear identities remain unchanged.
Electron bookkeeping must distinguish formal oxidation state from measured partial charge.

10. OXIDATION STATE VS ION CHARGE
Oxidation state is a formal electron-accounting assignment.
Monatomic ion: oxidation state = ion charge number.
Polyatomic ion: sum of constituent formal oxidation states = net ion charge number.
Individual oxidation states are not generally equal to individual atomic partial charges.

11. IONIC BONDING AND COMPOUNDS
Electrostatic attraction contributes to ionic binding.
An ionic formula unit is electrically neutral when sum(n_j * z_j) = 0.
Example: Mg2+ + 2 Cl- -> MgCl2 (formula unit, not a discrete molecule requirement).
Crystal lattices and solvation environments alter effective interactions.

12. SOLVATION AND HYDRATION
Solvation shell: solvent molecules associated with an ion.
Hydration is solvation in water.
Hydrated ionic radius and bare ionic radius are distinct measures.
Solvation free energy depends on charge, size, solvent and thermodynamic conditions.

13. ELECTROLYTE RELATIONSHIPS
Electrolyte solution contains mobile ions and may conduct electric current.
Electroneutrality for a bulk solution: sum_i z_i*c_i approximately 0 in a macroscopic bulk region, with local exceptions near interfaces.
Ionic strength: I = (1/2) * sum_i c_i*z_i^2 (concentrations in mol/L by conventional definition).
Activity a_i = gamma_i * (c_i/c_standard), using dimensionless activity convention.

14. TRANSPORT
Diffusion responds to concentration or chemical-potential gradients.
Migration responds to electric fields.
Convection transports ions with moving fluid.
Electrochemical potential: mu_tilde_i = mu_i + z_i*F*phi (molar form).
F = N_A*e (Faraday constant).
A simplified Nernst-Planck flux is J_i = -D_i*grad(c_i) - (D_i*z_i*F/(R*T))*c_i*grad(phi) + c_i*v, under stated dilute-solution assumptions.

15. ELECTROCHEMICAL EQUILIBRIUM
Nernst equation: E = E_standard - (R*T/(n*F))*ln(Q), for a defined reduction reaction.
Chemical and electrical contributions must be included when comparing ion equilibrium across membranes.
Ion-selective electrodes infer activity under calibration assumptions, not necessarily concentration directly.

16. ACID-BASE IONS
H3O+ and OH- are common aqueous ions.
Acid-base equilibria involve proton-transfer reactions and solvent conventions.
At 25 deg C, Kw approximately 1.0e-14 in dilute aqueous solutions (activity-based interpretation).
Do not generalise this numeric approximation to all temperatures or media.

17. ISOTOPIC IONS
Isotopes of the same element share proton number Z but differ in neutron count.
Ion charge and isotope identity are independent attributes.
Example: 23Na+ and 22Na+ share charge +1 but have different nuclides.
Mass spectrometry may distinguish mass-to-charge ratios of isotopic ions.

18. MASS SPECTROMETRY
Mass-to-charge ratio m/z identifies an ion signal under instrument conventions.
Different charge states may produce different m/z peaks for the same molecular composition.
Fragment ions must not be equated with intact precursor ions.
Adduct ions require explicit chemical formula and charge annotations.

19. PLASMA AND GAS-PHASE IONS
Plasma may contain electrons, positive ions, negative ions and neutrals.
Ionisation fraction is condition dependent.
Gas-phase ions can undergo collisions, recombination, charge exchange and fragmentation.
An ion's lifetime depends on environment and process; no universal stability claim applies.

20. BIOLOGICAL IONS
Na+, K+, Ca2+, Cl- and H+ participate in biological electrochemistry.
Membrane channels, transporters and pumps affect ion distributions.
Electrochemical gradients can drive transport and signalling.
A biological role is contextual and should not be inferred solely from charge.

21. GRAPH INFERENCE RULES
RULE I1: Ion(x) AND charge_number(x)>0 -> Cation(x).
RULE I2: Ion(x) AND charge_number(x)<0 -> Anion(x).
RULE I3: AtomicIon(x) AND proton_number(x)=Z AND electron_count(x)=N -> charge_number(x)=Z-N.
RULE I4: IonicCompound(c) AND constituents(c)={(i,n_i)} -> sum_i n_i*z_i=0 for neutral formula units.
RULE I5: SameChemicalSpecies(x,y) requires compatible formula, charge and isotope policy; name similarity alone is insufficient.
RULE I6: SameIonCharge(x,y) does not imply SameIonIdentity(x,y).
RULE I7: PARTICIPATES_IN(x,r) AND BALANCED(r) -> charge_and_element_conservation(r).

22. NON-INFERENCE SAFEGUARDS
Do not infer a specific isotope from an element symbol alone.
Do not infer solubility solely from ionic charge.
Do not infer a full reaction mechanism from a net ionic equation.
Do not equate ionic radius across coordination environments without context.
Do not classify an electron as a chemical anion; it is a charged elementary particle.
Do not treat an unverified charge assignment as experimentally measured.

23. WORKED EXAMPLE A — SODIUM CATION
Z(Na)=11; N_e(Na+)=10.
z=11-10=+1.
CLASSIFY Na+ AS MonatomicIon AND Cation.
VALIDATE charge +1 and conserved nucleus for electron removal.

24. WORKED EXAMPLE B — SULFATE
SO4^2- is a polyatomic anion.
Net charge number = -2.
With oxygen assigned oxidation state -2, sulfur formal oxidation state is +6.
Check: (+6)+4*(-2)=-2.
Formal oxidation state is not an isolated sulfur ionic charge.

25. WORKED EXAMPLE C — CHARGE BALANCE
For Al2(SO4)3: 2*(+3)+3*(-2)=0.
The formula unit is electrically neutral; its constituent ions are charged.

26. MATHEMATICAL SEMANTICS
State ion x as tuple (formula,z,isotope,phase,environment,timestamp,provenance).
Define equivalence only relative to an explicit comparison projection.
ChargeEquivalent(x,y) iff z(x)=z(y).
FormulaChargeEquivalent(x,y) iff formula(x)=formula(y) AND z(x)=z(y).
FullIdentityEquivalent requires matching identity policy and provenance constraints.

27. SEMANTIC_EQUIVALENCE
aliases: [ionic species, charged atomic species, charged molecular species]
related_not_identical: [oxidation state, charged particle, electrolyte, ion radical]
British spelling: ionisation; US alias: ionization.
A synonym mapping is not proof of physical identity.

28. CONFIDENCE
confidence_scale: [0.0,1.0]
formal_conservation_rules: high when premises verified
measured_charge_state: evidence-dependent
proposed_reaction_mechanism: evidence-dependent
unknown_values: explicit null; do not fabricate measurements

29. VALIDATION
V1: Each Ion has integer nonzero charge_number.
V2: Atomic-ion electron count is a nonnegative integer.
V3: Nuclide mass number A >= proton number Z.
V4: Chemical equations conserve atoms and net electric charge.
V5: Distinguish formal, measured and inferred properties.
V6: Units accompany quantitative measurements.
V7: Distinguish gas, solution, solid and plasma conditions.
V8: Provenance is attached to nontrivial empirical claims.
V9: No undefined relation or untyped entity in graph output.
V10: All declared examples pass charge-balance checks.

30. UPDATE_MODEL
update_trigger: new_measurement | revised_reference_value | ontology_revision | source_correction
revision_policy: append provenance and preserve prior versions
conflict_resolution: prefer validated primary evidence; preserve disputed values with qualifiers
last_compiled: 2026-10-12

31. FLOW_HASH
hash_scope: canonical UTF-8 bytes excluding the computed hash field itself
hash_algorithm: SHA-256
hash_value: COMPUTE_ON_PUBLICATION
Note: a placeholder is not a calculated digest.

32. AI_CONSUMPTION
entry_entity: Ion
machine_tasks: classification | charge_balance | entity_linking | reaction_validation | semantic_search | graph_reasoning
outputs: typed_triples | derivations | constraint_checks | provenance_records
reasoning_mode: rule-based with explicit premises and uncertainty labels
hallucination_guard: never infer missing measurements or undocumented source claims

33. CROSS-ONTOLOGY LINKS
parent: Atomic Entities
related: Atom Ontology; Electron Ontology; Proton Ontology; Isotope Ontology; Electron Cloud Ontology
related_domains: Chemistry; Electrochemistry; Plasma Physics; Biochemistry; Mass Spectrometry

34. COMPLETENESS CHECK
Sections 01-34 present.
All example charges verified.
The page-specific text was not retrieved; this is an independent scientific synthesis.

END FLOW ALGEBRA — ION ONTOLOGY