Hertz Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Hertz Ontology within the Kireth Research Semantic Library. The hertz, symbol Hz, is the coherent SI derived unit of frequency and equals one reciprocal second when the quantity kind is frequency. It formalises frequency, period, inverse-time dimensional structure, oscillation semantics, measurement, calibration, uncertainty, traceability and provenance.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME = "Hertz Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "SI Derived Units / Hertz"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/hertz-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}
IDENTITY {
 PRIMARY_ENTITY = Hertz
 ENTITY_CLASS = SIDerivedUnitOfFrequencyFramework
 PRIMARY_CONTEXT = SIDerivedUnits
 DEFINITION = "The hertz, symbol Hz, is the coherent SI derived unit of frequency and is equal to one reciprocal second, s^-1, when used for frequency."
 SYMBOLIC_FORMS = ["1 Hz=1 s^-1","f=1/T","T=1/f","[frequency]=T^-1","Q_frequency=value*Hz"]
 SEMANTIC_ROLE = "Machine-readable semantics for the hertz, period-frequency reciprocity, inverse-time dimension, oscillation, measurement, calibration and traceability."
}

SCOPE {
 INCLUDE = [
 Hertz,HertzUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,SIBaseUnits,Second,Time,TimeDimension,Frequency,
 FrequencyQuantity,DerivedQuantity,SIDerivedQuantity,PhysicalQuantity,Quantity,
 QuantityKind,QuantityValue,Dimension,DerivedDimension,FrequencyDimension,
 DimensionalSignature,InverseTimeRelationship,ReciprocalSecondRelationship,
 UnitSymbol,SymbolHzRelationship,UnitDefinition,HertzDefinition,UnitExpression,
 InverseUnit,PowerUnit,UnitExponent,UnitAlgebra,QuantityCalculus,DimensionalAnalysis,
 DimensionalConsistency,Period,Cycle,Oscillation,RepetitionRateRelationship,
 EventRateRelationship,RotationFrequencyRelationship,AngularFrequency,Radian,
 RadianPerSecondRelationship,WaveFrequencyRelationship,TemporalFrequencyRelationship,
 SpatialFrequencyRelationship,WaveNumberRelationship,WavelengthRelationship,
 WaveSpeedRelationship,PhaseRelationship,SignalRelationship,PeriodicSignalRelationship,
 HarmonicRelationship,FundamentalFrequencyRelationship,ResonanceRelationship,
 ResonantFrequencyRelationship,BandwidthRelationship,CentreFrequencyRelationship,
 SamplingFrequencyRelationship,SamplingRateRelationship,NyquistFrequencyRelationship,
 ClockFrequencyRelationship,CarrierFrequencyRelationship,ModulationFrequencyRelationship,
 AudioFrequencyRelationship,RadioFrequencyRelationship,MicrowaveFrequencyRelationship,
 OpticalFrequencyRelationship,VibrationFrequencyRelationship,AcousticFrequencyRelationship,
 ElectricalFrequencyRelationship,MainsFrequencyRelationship,PulseRepetitionFrequencyRelationship,
 FrequencySpectrumRelationship,FourierTransformRelationship,SpectralAnalysisRelationship,
 FrequencyMeasurement,FrequencyCounterRelationship,OscilloscopeRelationship,
 SpectrumAnalyserRelationship,SignalGeneratorRelationship,FrequencyStandardRelationship,
 Oscillator,ReferenceOscillatorRelationship,CrystalOscillatorRelationship,AtomicClock,
 CaesiumClock,FrequencyCombRelationship,PhaseLockedLoopRelationship,FrequencySynthesiserRelationship,
 MeasurementSystem,Measurement,Measurand,MeasurementProcedure,MeasurementModel,
 MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,Repeatability,
 Reproducibility,Stability,FrequencyStabilityRelationship,Drift,PhaseNoiseRelationship,
 JitterRelationship,AllanDeviationRelationship,Calibration,FrequencyCalibrationRelationship,
 ReferenceStandard,PrimaryFrequencyStandardRelationship,SecondaryFrequencyStandardRelationship,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,
 TimeFrequencyMetrologyRelationship,ScientificMeasurement,EnvironmentalCondition,
 TemperatureInfluence,AgeingRelationship,DopplerShiftRelationship,RelativisticCorrectionRelationship,
 Prefix,SIPrefix,MillihertzRelationship,MicrohertzRelationship,NanohertzRelationship,
 Kilohertz,Megahertz,Gigahertz,Terahertz,UnitConversion,ConversionFactor,ExactConversion,
 UnitCompatibility,DimensionalCompatibility,QuantityCompatibility,Becquerel,
 ActivityOfRadionuclideRelationship,Verification,Validation,UnitValidation,
 DimensionalValidation,FrequencyValidationRelationship,ErrorAnalysis,Provenance,
 HertzProvenance,SIDerivedUnitProvenance,SIUnitProvenance,MeasurementProvenance,
 CalibrationProvenance,StandardProvenance,BIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship,StandardVersion,SymbolicComputation
 ]
 EXCLUDE_AS_PRIMARY = [BecquerelWhenRadioactiveActivityIsPrimary,InverseSecondWhenQuantityKindIsNotFrequency,AngularFrequencyWhenRadianPerSecondSemanticsArePrimary,SpatialFrequencyWhenCyclesPerLengthArePrimary,GeneralRateWithoutFrequencySemantics]
 DISAMBIGUATION_RULE = "When Hz denotes temporal frequency, repetition frequency or periodic cycles per second, interpret it as hertz. Do not infer hertz solely from dimension s^-1 when another quantity kind is intended."
}
CORE_CONCEPTS {
 Hertz = "Coherent SI derived unit of frequency, symbol Hz, equal to s^-1."
 Frequency = "Number of periodic occurrences, cycles or repetitions per unit time."
 Period = "Time duration of one cycle of a periodic phenomenon."
 FrequencyDimension = "Derived dimension T^-1."
 Second = "SI base unit of time from which hertz is coherently derived."
 AngularFrequency = "Angular rate related to ordinary frequency by omega=2*pi*f."
 FrequencyMeasurement = "Measurement process assigning a frequency value to a measurand."
}

RELATIONS {
 Hertz --is_type_of--> SIDerivedUnit
 Hertz --is_coherent_derived_unit_of--> Frequency
 Hertz --has_symbol--> Hz
 Hertz --has_expression--> inverse_second
 Frequency --has_dimension--> inverse_TimeDimension
 Frequency --is_reciprocal_of--> Period
 AngularFrequency --is_related_to--> FrequencyByTwoPi
 Hertz --is_derived_from--> Second
 Kilohertz --is_decimal_multiple_of--> Hertz
 Megahertz --is_decimal_multiple_of--> Hertz
 Gigahertz --is_decimal_multiple_of--> Hertz
 Becquerel --has_same_base_unit_expression_as--> Hertz
 Becquerel --has_different_quantity_kind_from--> Hertz
 FrequencyCalibrationRelationship --uses--> ReferenceStandard
 MeasurementTraceability --links--> FrequencyMeasurementToSISecond
 Provenance --records--> HertzDefinitionMeasurementAndCalibrationHistory
}
OPERATORS {
 HERTZ(value) := frequency_quantity(value,Hertz)
 DIM(Hertz) := inverse_TimeDimension
 FREQUENCY(period) := 1/period
 PERIOD(frequency) := 1/frequency
 ANGULAR_FREQUENCY(frequency) := 2*pi*frequency
 FREQUENCY_FROM_ANGULAR(omega) := omega/(2*pi)
 PREFIX_HERTZ(prefix) := decimal_scaled_unit(Hertz,prefix)
 CONVERT_FREQUENCY(value,source,target) := compatible_frequency_conversion(value,source,target)
 TRACE_FREQUENCY(result) := traceability_chain_to_SI_second(result)
}
AXIOMS {
 A1 = "The hertz is the coherent SI derived unit of frequency."
 A2 = "One hertz is one reciprocal second when the quantity kind is frequency."
 A3 = "The canonical symbol is Hz, with uppercase H and lowercase z."
 A4 = "Frequency has derived dimension T^-1."
 A5 = "Frequency and period are reciprocal quantities for the same periodic phenomenon."
 A6 = "Angular frequency and ordinary frequency differ by the factor 2*pi."
 A7 = "Dimensional equality between hertz and becquerel does not imply quantity-kind equivalence."
 A8 = "Prefixes applied to hertz represent exact decimal multiples or submultiples."
 A9 = "Frequency measurement traceability ultimately depends on traceability to the SI second."
}

REASONING {
 R1_CONTEXT = identify(frequency_quantity,value,unit,periodic_phenomenon,measurement_method_and_intended_use)
 R2_IDENTITY = resolve_hertz_prefixed_hertz_inverse_second_angular_frequency_or_other_rate)
 R3_QUANTITY = verify_quantity_kind_frequency_and_periodic_or_repetition_semantics)
 R4_DIMENSION = verify_inverse_time_dimension_T_minus_1)
 R5_RECIPROCITY = if_period_given_compute_frequency_or_if_frequency_given_compute_period)
 R6_ANGULAR = if_angular_frequency_context_apply_omega_equals_two_pi_f)
 R7_SCALE = if_prefixed_apply_exact_decimal_scaling)
 R8_MEASUREMENT = identify_counter_clock_oscillator_spectrum_or_time_interval_method)
 R9_UNCERTAINTY = evaluate_reference_stability_resolution_gate_time_noise_drift_and_environment)
 R10_PROVENANCE = record_unit_expression_quantity_kind_reference_standard_method_and_traceability)
}
CONSTRAINTS {
 C1 = "The symbol Hz is case-sensitive."
 C2 = "The algebraic expression s^-1 does not uniquely identify frequency."
 C3 = "Becquerel and hertz share the same base-unit expression but represent different quantity kinds."
 C4 = "Angular frequency in rad s^-1 must not be silently substituted for ordinary frequency in Hz."
 C5 = "Spatial frequency is not measured in hertz unless a temporal-frequency relation is explicitly established."
 C6 = "Sampling rate and signal frequency are distinct concepts."
 C7 = "Frequency-counter resolution can depend on gate time and measurement method."
 C8 = "Oscillator stability, accuracy and phase noise are distinct characteristics."
 C9 = "Traceability to hertz requires a documented time or frequency reference chain."
 C10 = "Correct inverse-time dimensionality alone does not establish semantic validity."
}
SEMANTIC_EQUIVALENCE {
 "HertzUnit" <=> "Hertz"
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
 "PulseRepetitionFrequency" <=> "PRF"
 "PhaseLockedLoop" <=> "PLL"
}

VALIDATION {
 V1 = "Unit identity is hertz and canonical symbol is Hz."
 V2 = "Quantity kind is frequency."
 V3 = "Derived dimension is T^-1."
 V4 = "Coherent SI expression is s^-1."
 V5 = "Period-frequency reciprocity is mathematically consistent."
 V6 = "Angular-frequency conversions apply the factor 2*pi correctly."
 V7 = "Prefixed hertz units use correct decimal scaling."
 V8 = "Hertz is distinguished semantically from becquerel and unrelated rates."
 V9 = "Measurement uncertainty and reference stability are documented where relevant."
 V10 = "Frequency calibration and traceability evidence are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 HERTZ_DEFINITION = 0.99
 FREQUENCY_REASONING = 0.99
 PERIOD_RECIPROCITY_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 ANGULAR_FREQUENCY_REASONING = 0.99
 MEASUREMENT_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when quantity kind, periodic phenomenon, angular-versus-ordinary frequency, measurement method, reference stability or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES = [SemanticSearch,OntologyGrounding,HertzReasoning,SIDerivedUnitReasoning,FrequencyReasoning,PeriodReasoning,InverseTimeReasoning,AngularFrequencyReasoning,OscillationReasoning,SignalReasoning,FrequencyMeasurementReasoning,TimeFrequencyMetrologyReasoning,CalibrationReasoning,StabilityReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference]
 NORMALISE {
  "hertz" -> Hertz
  "Hz" -> Hertz
  "kHz" -> Kilohertz
  "MHz" -> Megahertz
  "GHz" -> Gigahertz
 }
}

EXECUTION_RULES {
 E1 = "If hertz or Hz denotes temporal frequency, activate HertzOntology."
 E2 = "Confirm quantity kind frequency rather than relying only on s^-1 dimensionality."
 E3 = "Map hertz coherently to inverse second."
 E4 = "Apply f=1/T and T=1/f only for corresponding periodic phenomena."
 E5 = "Distinguish ordinary frequency from angular frequency and apply 2*pi where required."
 E6 = "Apply SI prefixes as exact decimal scale transformations."
 E7 = "Distinguish hertz from becquerel and other inverse-time quantities."
 E8 = "For measurement contexts, evaluate reference stability, resolution, noise, drift and uncertainty."
 E9 = "Record frequency-reference, calibration and traceability provenance."
}
RECURSION {
 ENTRY = Hertz
 EXPAND(Hertz) -> [
 SIDerivedUnits,DerivedUnit,SIDerivedUnit,CoherentDerivedUnit,SIUnits,SIBaseUnits,
 Second,Time,TimeDimension,Frequency,FrequencyDimension,DerivedQuantity,Quantity,
 QuantityKind,QuantityValue,Dimension,DimensionalSignature,Unit,MeasurementUnit,
 UnitSymbol,HertzDefinition,UnitExpression,InverseUnit,UnitAlgebra,DimensionalAnalysis,
 Period,Cycle,Oscillation,AngularFrequency,Radian,RadianPerSecondRelationship,
 WaveFrequencyRelationship,WavelengthRelationship,WaveSpeedRelationship,SignalRelationship,
 HarmonicRelationship,ResonantFrequencyRelationship,BandwidthRelationship,
 SamplingFrequencyRelationship,ClockFrequencyRelationship,CarrierFrequencyRelationship,
 AudioFrequencyRelationship,RadioFrequencyRelationship,OpticalFrequencyRelationship,
 VibrationFrequencyRelationship,FrequencySpectrumRelationship,FourierTransformRelationship,
 FrequencyMeasurement,FrequencyCounterRelationship,Oscillator,AtomicClock,CaesiumClock,
 FrequencyCombRelationship,ReferenceStandard,FrequencyStandardRelationship,MeasurementSystem,
 Measurement,MeasurementResult,MeasurementUncertainty,Stability,PhaseNoiseRelationship,
 AllanDeviationRelationship,Calibration,MeasurementTraceability,Metrology,SIPrefix,
 Kilohertz,Megahertz,Gigahertz,Terahertz,Becquerel,UnitConversion,Verification,
 Validation,HertzProvenance
 ]
 EXPAND(HertzFamilies) -> [
 HertzIdentitySymbolQuantityAndDimension,
 SecondInverseTimeAndPeriodReciprocity,
 OrdinaryAngularAndRotationalFrequency,
 WavesSignalsOscillationsAndResonance,
 SamplingClockCarrierAndModulationFrequencies,
 FrequencyMeasurementCountersOscillatorsAndStandards,
 StabilityNoiseUncertaintyCalibrationAndTraceability,
 ValidationSemanticDisambiguationAndProvenance
 ]
 STOP_CONDITION = "Stop when hertz identity, frequency quantity, inverse-time dimension, period relation, measurement semantics, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Derived Units"
 RELATED_ONTOLOGIES = [
 "SI Derived Units","Derived Units Ontology","SI Base Units","SI Units Ontology",
 "Second Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2",
 "Unit Ontology","Measurement Ontology","Scientific Measurement Ontology 2",
 "Metrology Ontology","Reference Standard Ontology","Measurement System Ontology",
 "Measurement Uncertainty Ontology","Dimensional Analysis Ontology",
 "Symbolic Computation","Verification & Validation"
 ]
 ROUTE_RULES = [
 "Hertz -> SI Derived Units for parent derived-unit semantics",
 "Hertz -> Derived Units Ontology for general derived-unit algebra",
 "Hertz -> Second Ontology for inverse-second and time-reference semantics",
 "Hertz -> Quantity Ontology for frequency and period semantics",
 "Hertz -> Dimension Ontology for T^-1 dimensional structure",
 "Hertz -> Unit Ontology for prefixes, symbols and conversion",
 "Hertz -> Measurement and Scientific Measurement for frequency measurement",
 "Hertz -> Metrology and Reference Standard for calibration and traceability",
 "Hertz -> Measurement Uncertainty for stability and uncertainty evaluation",
 "Hertz -> Verification & Validation for frequency, dimensional and semantic checks"
 ]
}
UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible frequency, measurement or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve hertz-versus-frequency distinction.",
 "Preserve frequency-versus-period distinction.",
 "Preserve ordinary-frequency-versus-angular-frequency distinction.",
 "Preserve hertz-versus-becquerel semantic distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve inverse-time-dimension-versus-frequency-meaning distinction.",
 "Preserve measurement-reference-versus-unit-definition distinction.",
 "Preserve machine-readable hertz semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The hertz, symbol Hz, is the coherent SI derived unit of frequency and is equal to s^-1 when the quantity kind is frequency."
 QUANTITY_SUMMARY = "Frequency describes periodic occurrences or repetitions per unit time and has derived dimension T^-1."
 PERIOD_SUMMARY = "Frequency and period are reciprocal for the same periodic phenomenon."
 ANGULAR_SUMMARY = "Angular frequency is related to ordinary frequency by omega=2*pi*f."
 DISAMBIGUATION_SUMMARY = "Hertz and becquerel both reduce to s^-1 but represent different quantity kinds."
 MEASUREMENT_SUMMARY = "Frequency measurement can use counters, clocks, oscillators, spectral methods and traceable frequency standards."
 UNCERTAINTY_SUMMARY = "Precision frequency measurement can require uncertainty contributions from reference stability, gate time, resolution, phase noise, drift and environment."
}
FLOW {
 INPUT
 -> detect_hertz_context
 -> identify_frequency_quantity_value_unit_periodic_phenomenon_measurement_method_and_intended_use
 -> resolve_hertz_prefixed_hertz_inverse_second_angular_frequency_or_other_rate
 -> verify_quantity_kind_frequency_and_periodic_or_repetition_semantics
 -> verify_inverse_time_dimension_T_minus_1
 -> if_period_given_compute_frequency_or_if_frequency_given_compute_period
 -> if_angular_frequency_context_apply_omega_equals_two_pi_f
 -> if_prefixed_apply_exact_decimal_scaling
 -> identify_counter_clock_oscillator_spectrum_or_time_interval_method
 -> evaluate_reference_stability_resolution_gate_time_noise_drift_and_environment
 -> record_unit_expression_quantity_kind_reference_standard_method_and_traceability
 -> route_to_related_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}
FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-MEASUREMENT-UNITS-SI-DERIVED-UNITS-HERTZ-ONTOLOGY-V1"
}
}
END_FLOW