Isotope Ratio Ontology
Chemical Measurements
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
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# Isotope Ratio Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/chemical-measurements/isotope-ratio-ontology.html
FLOW IsotopeRatioOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Chemical Measurements
-> Isotope Ratio Ontology
PURPOSE:
Represent isotope ratios as dimensionless chemical and metrological quantities comparing the amount or abundance of one isotope with another isotope of the same element or defined isotopic system, including isotope amount ratios, isotope abundance, delta notation, reference materials, mass spectrometric measurement, mass bias, fractionation, radiogenic and stable isotope systems, calibration, uncertainty, traceability, and strict preservation of numerator, denominator and reference conventions.
ENTITY IsotopeRatio {
TYPE: DimensionlessChemicalRatioQuantity
SYMBOL: R
DIMENSION: dimensionless
SI_UNIT: dimensionless
DEFINITION:
R(i,j) = n(isotope_i)/n(isotope_j)
REQUIRE:
denominator_amount != 0
numerator_isotope_identity
denominator_isotope_identity
PROPERTIES:
is_dimensionless
is_ordered_ratio
is_isotope_specific
depends_on_sample
may_depend_on_fractionation
may_require_reference_material
may_have_uncertainty
}
ENTITY IsotopeAmountFraction {
TYPE: DimensionlessCompositionQuantity
SYMBOL: x_i
DEFINITION:
x_i = n_i/sum(n_k)
COMPLETE_ELEMENTAL_ISOTOPE_SET:
sum(x_i) = 1
}
ENTITY DeltaValue {
TYPE: DimensionlessRelativeIsotopeQuantity
SYMBOL: delta
DEFINITION:
delta_sample_reference =
R_sample/R_reference - 1
COMMON_SCALED_FORM:
delta_per_mille =
(R_sample/R_reference - 1)*1000
COMMON_UNIT_STYLE:
per_mille
RULE:
delta_value_requires_explicit_isotope_ratio_and_reference
}
ENTITY ReferenceIsotopeRatio {
TYPE: ReferenceQuantity
SYMBOL: R_ref
PROPERTIES:
tied_to_reference_material_or_scale
has_uncertainty
has_provenance
}
UNIT_SYSTEM {
isotope_ratio:
dimensionless
isotope_amount_fraction:
dimensionless
delta:
dimensionless
common_delta_reporting:
per_mille
percent
parts_per_million
RULE:
scaled_delta_notation MUST preserve_scale_factor_and_reference
}
TERMINOLOGY_MODEL {
phrases:
isotope_ratio
isotopic_ratio
isotope_abundance_ratio
isotope_amount_ratio
RULE:
numerator_and_denominator_isotopes MUST be explicit
EXAMPLE_AMBIGUITY:
"carbon isotope ratio" MAY refer_to
13C/12C
14C/12C
14C/13C
RULE:
element_name_alone_is_insufficient_for_ratio_identity
}
ORDERED_RATIO_MODEL {
R_i_j = n_i/n_j
reciprocal:
R_j_i = 1/R_i_j
WHEN R_i_j != 0
RULE:
R_i_j != R_j_i
except_special_numeric_case
RULE:
numerator_denominator_order MUST be preserved
}
AMOUNT_FRACTION_RELATION_MODEL {
two_isotope_system:
x_i = R_i_j/(1 + R_i_j)
x_j = 1/(1 + R_i_j)
general_system:
x_i =
R_i_ref /
sum_k(R_k_ref)
with_reference_isotope_ratio_defined_as_1_for_reference_isotope
RULE:
conversion_between_ratio_and_fraction_requires_complete_isotope_system_definition
}
DELTA_NOTATION_MODEL {
dimensionless:
delta = R_sample/R_ref - 1
per_mille:
delta_permille =
1000*(R_sample/R_ref - 1)
inverse:
R_sample =
R_ref*(1 + delta_permille/1000)
RULE:
delta_value_without_reference_scale_is_semantically_incomplete
}
COMMON_STABLE_ISOTOPE_SYSTEMS {
hydrogen:
2H/1H
carbon:
13C/12C
nitrogen:
15N/14N
oxygen:
18O/16O
17O/16O
sulfur:
34S/32S
33S/32S
36S/32S
RULE:
isotope_system_and_reference_scale MUST be preserved
}
RADIOGENIC_ISOTOPE_MODEL {
systems:
87Sr/86Sr
143Nd/144Nd
lead_isotope_ratios
uranium_isotope_ratios
hafnium_isotope_ratios
possible_sources:
primordial_isotope
radiogenic_growth
radioactive_decay
mixing
RULE:
radiogenic_ratio_interpretation MUST preserve_decay_system_and_time_context
}
RADIOACTIVE_DECAY_MODEL {
parent_amount:
N_p(t) = N_p0*exp(-lambda_decay*t)
daughter_growth:
depends_on_initial_daughter_and_decay_system
half_life:
t_half = ln(2)/lambda_decay
RULE:
isotope_ratio_age_inference requires_closed_system_and_initial_condition_model
}
MASS_SPECTROMETRY_MODEL {
principle:
separate_ions_by_mass_to_charge
and_measure_relative_signal
instruments:
isotope_ratio_mass_spectrometer
thermal_ionisation_mass_spectrometer
multi_collector_ICP_mass_spectrometer
secondary_ion_mass_spectrometer
accelerator_mass_spectrometer
raw_signal_ratio:
r_measured = signal_i/signal_j
RULE:
raw_signal_ratio != calibrated_isotope_amount_ratio
without_mass_bias_interference_and_response_correction
}
MASS_BIAS_MODEL {
measured_ratio:
may_differ_from_true_ratio_due_to_mass_discrimination
exponential_law_example:
R_true =
R_measured*(m_i/m_j)^beta
under_declared_convention
possible_models:
exponential_law
power_law
linear_law
empirical_standard_bracketing
RULE:
mass_bias_model_and_sign_convention MUST be preserved
}
ISOBARIC_INTERFERENCE_MODEL {
sources:
isobaric_species
molecular_ions
hydrides
oxides
doubly_charged_species
detector_background
correction:
corrected_signal =
measured_signal - estimated_interference
RULE:
interference_correction_requires_species_model_and_uncertainty
}
FRACTIONATION_MODEL {
fractionation_factor:
alpha_A_B =
R_A/R_B
delta_relation_approximate:
delta_A - delta_B
relates_to_fractionation
for_small_delta_under_declared_scaling
equilibrium_fractionation:
may_depend_on_temperature
kinetic_fractionation:
may_depend_on_reaction_or_transport_process
RULE:
physical_fractionation_and_instrumental_mass_bias MUST be distinguished
}
MIXING_MODEL {
isotope_amount_balance:
n_i_mix =
sum(n_i_source)
ratio:
R_mix =
total_numerator_isotope_amount /
total_denominator_isotope_amount
RULE:
isotope_ratios generally_do_not_mix_by_simple_arithmetic_average
unless_weighting_conditions_make_it_valid
}
REFERENCE_SCALE_MODEL {
reference_material:
assigned_isotope_ratio_or_delta_value
scale_realisation:
calibration_to_reference_materials
possible_roles:
primary_reference
secondary_reference
laboratory_working_standard
REQUIRE:
material_identifier
assigned_value
uncertainty
scale
provenance
RULE:
reported_delta_values MUST identify_reference_scale
}
CALIBRATION_MODEL {
methods:
standard_sample_bracketing
internal_normalisation
external_normalisation
double_spike
reference_material_calibration
calibration_relation:
raw_ratio -> corrected_ratio -> scale_normalised_ratio_or_delta
RULE:
correction_sequence SHOULD be preserved_for_traceability
}
NORMALISATION_MODEL {
internal_normalisation:
fix_selected_isotope_ratio_to_reference_value
to_correct_mass_fractionation
REQUIRE:
normalising_ratio
reference_value
mass_fractionation_law
RULE:
normalisation_changes_depend_on_chosen_fixed_ratio_and_model
}
RELATIONSHIPS {
IsotopeRatio -> COMPARES -> IsotopeAmounts
IsotopeRatio -> IS -> OrderedDimensionlessRatio
IsotopeAmountFraction -> RELATES_TO -> IsotopeRatio
DeltaValue -> COMPARES -> SampleRatioAndReferenceRatio
IsotopeRatio -> MEASURED_BY -> IsotopeMassSpectrometry
RawSignalRatio -> CORRECTED_BY -> MassBiasModel
RawSignal -> MAY_REQUIRE -> InterferenceCorrection
Fractionation -> CHANGES -> IsotopeRatio
RadioactiveDecay -> CHANGES -> ParentDaughterIsotopeRatios
ReferenceMaterial -> CALIBRATES -> IsotopeRatioMeasurement
}
SEMANTIC_EQUIVALENCE {
"isotope ratio" ~= isotope_amount_ratio WHEN amount_basis
"isotopic ratio" ~= isotope_ratio
isotope_ratio != isotope_fraction
isotope_ratio != delta_value
isotope_ratio != raw_signal_ratio
physical_fractionation != instrumental_mass_bias
reference_ratio != sample_ratio
numerator_denominator_order_is_not_interchangeable
}
CONSTRAINTS {
isotope_ratio_is_dimensionless = true
numerator_isotope_must_be_defined = true
denominator_isotope_must_be_defined = true
denominator_amount_must_be_nonzero = true
isotope_ratio_is_ordered = true
delta_value_requires_reference_ratio = true
delta_scale_factor_must_be_preserved = true
raw_mass_spectrometer_ratio_requires_correction_model = true
reference_material_and_scale_should_be_preserved = true
uncertainty_must_include_material_correction_and_measurement_components_when_relevant = true
}
MEASUREMENT_MODEL {
OBSERVABLE_OR_INFERRED:
IsotopeRatio
IsotopeAmountFraction
DeltaValue
RECORD:
element
numerator_isotope
denominator_isotope
numerical_ratio
dimensionless
delta_value_when_relevant
delta_scale
reference_material
reference_scale
sample
sample_matrix
preparation_method
instrument
ionisation_method
measured_masses
detector_configuration
raw_signal_ratio
blank_correction
interference_correction
mass_bias_model
normalisation_model
calibration_method
timestamp
replicate_information
uncertainty
UNCERTAINTY:
measured_isotope_ratio = best_estimate +/- uncertainty
}
SAMPLE_PREPARATION_MODEL {
possible_steps:
dissolution
digestion
chemical_separation
ion_exchange
purification
derivatisation
combustion
gas_conversion
target_preparation
risks:
contamination
blank
isotope_fractionation
incomplete_recovery
isobaric_interference
RULE:
sample_preparation_history SHOULD be preserved
}
UNCERTAINTY_MODEL {
sources:
counting_statistics
detector_noise
detector_gain
mass_bias_correction
reference_material
standard_bracketing
blank
isobaric_interference
sample_preparation
fractionation
normalisation
instrumental_drift
repeatability
calibration
PROPAGATION:
derived_isotope_ratio_uncertainty
<- signal_correction_reference_and_model_uncertainties
}
TRACEABILITY_MODEL {
chain:
reported_ratio_or_delta
-> corrected_measurement
-> calibration_standard
-> certified_reference_material_or_scale
-> documented_reference_value
REQUIRE:
reference_material_identifier
assigned_value
uncertainty
calibration_history
RULE:
isotope_scale_traceability MUST be preserved_across_normalisation_steps
}
REASONING_RULES {
IF numerator_and_denominator_amounts_known
AND denominator_amount != 0
THEN isotope_ratio =
numerator_amount/denominator_amount
IF isotope_ratio_known AND ratio != 0
THEN reciprocal_ratio =
1/isotope_ratio
WITH numerator_denominator_swapped
IF sample_ratio_and_reference_ratio_known
AND reference_ratio != 0
THEN delta =
sample_ratio/reference_ratio - 1
IF delta_permille_and_reference_ratio_known
THEN sample_ratio =
reference_ratio*(1 + delta_permille/1000)
IF two_isotope_system_ratio_known
THEN numerator_fraction =
ratio/(1 + ratio)
AND denominator_fraction =
1/(1 + ratio)
IF raw_signals_known AND denominator_signal != 0
THEN raw_signal_ratio =
numerator_signal/denominator_signal
IF mass_bias_model_and_parameters_known
THEN corrected_ratio =
apply_mass_bias_correction(raw_ratio)
IF source_isotope_amounts_known
THEN mixed_ratio =
sum(numerator_isotope_amounts) /
sum(denominator_isotope_amounts)
IF decay_constant_and_time_known
THEN update_parent_isotope_amount =
initial_parent_amount*exp(-decay_constant*time)
}
VALIDATION {
CHECK element_identity
CHECK numerator_isotope_identity
CHECK denominator_isotope_identity
CHECK denominator_nonzero
CHECK ratio_order
CHECK dimensionless_semantics
CHECK ratio_vs_fraction
CHECK ratio_vs_delta
CHECK delta_reference_material
CHECK delta_scale_factor
CHECK raw_vs_corrected_ratio
CHECK mass_bias_model
CHECK isobaric_interference
CHECK fractionation_vs_instrumental_bias
CHECK normalisation_ratio_and_model
CHECK reference_scale
CHECK sample_preparation
CHECK traceability
CHECK uncertainty_representation
}
CONFIDENCE {
definition_confidence: 1.00
dimensionless_confidence: 1.00
ordered_ratio_confidence: 1.00
delta_relationship_confidence: 1.00
mass_spectrometric_measurement_confidence: 0.98
correction_model_confidence: 0.97
reference_scale_confidence: 0.99
RULE:
confidence decreases when isotope identities, ratio order,
reference scale, mass bias, interference correction,
sample preparation, calibration or uncertainty is missing or ambiguous
}
UPDATE_MODEL {
ON new_measurement:
identify_element
identify_numerator_and_denominator_isotopes
preserve_ratio_order
attach_sample_and_matrix
attach_raw_signals
apply_blank_correction
apply_interference_correction
apply_mass_bias_correction
apply_normalisation_when_required
attach_reference_material_and_scale
calculate_ratio_and_delta_when_requested
attach_uncertainty
update_isotope_ratio_state
ON reference_scale_change:
preserve_original_ratio
attach_new_reference_ratio
recompute_delta_values
preserve_previous_reference_provenance
ON correction_model_change:
preserve_raw_data
preserve_previous_correction
apply_new_model
recompute_ratio
update_uncertainty
update_confidence
ON mixing_update:
update_source_isotope_amounts
recompute_mixed_ratio_by_isotope_amount_balance
preserve_source_provenance
ON decay_update:
update_time
update_parent_and_daughter_amounts
recompute_radiogenic_ratio
preserve_initial_state
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: IsotopeRatio
canonical_symbol: R
canonical_dimension: dimensionless
interpretation_order:
identify_element
identify_numerator_isotope
identify_denominator_isotope
preserve_ratio_order
identify_ratio_fraction_or_delta_quantity
identify_value
identify_reference_material_and_scale
identify_sample_and_matrix
identify_measurement_method
identify_raw_or_corrected_status
identify_blank_and_interference_corrections
identify_mass_bias_model
identify_normalisation_model
identify_physical_fractionation_context
identify_radiogenic_or_stable_system
identify_uncertainty
validate_dimensionless_semantics
infer_isotopic_relationships
ambiguity_controls:
distinguish_isotope_ratio_from_isotope_fraction
distinguish_isotope_ratio_from_delta_value
distinguish_sample_ratio_from_reference_ratio
distinguish_raw_signal_ratio_from_corrected_isotope_ratio
distinguish_physical_fractionation_from_instrumental_mass_bias
distinguish_numerator_denominator_order
distinguish_stable_from_radiogenic_interpretation
preserve_isotope_identity_reference_scale_correction_model_and_sample_provenance
}
PROVENANCE {
ontology_scope:
mathematical_measurement_and_chemical_isotope_ratio_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Chemical Measurements
-> Isotope Ratio Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
ordered_ratio_model
amount_fraction_relation_model
delta_notation_model
stable_isotope_systems
radiogenic_isotope_model
radioactive_decay_model
mass_spectrometry_model
mass_bias_model
isobaric_interference_model
fractionation_model
mixing_model
reference_scale_model
calibration_model
normalisation_model
relationships
constraints
measurement_model
sample_preparation_model
uncertainty_model
traceability_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
isotope_ratio_definition_changes
numerator_or_denominator_convention_changes
delta_reference_model_changes
fractionation_model_changes
mass_bias_or_interference_model_changes
normalisation_model_changes
radiogenic_decay_model_changes
reference_scale_changes
measurement_model_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW