Redshift Ontology
Astronomical Measurements
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Redshift Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/astronomical-measurements/redshift-ontology.html
FLOW RedshiftOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Redshift Ontology
PURPOSE:
Represent astronomical redshift as a dimensionless measure of the fractional displacement of observed spectral wavelength or frequency relative to a defined rest-frame value, including wavelength and frequency formulations, blueshift, Doppler and relativistic interpretations, cosmological redshift, gravitational redshift, peculiar velocity, spectroscopic and photometric estimation, spectral-line identification, reference frames, cosmological distance inference, calibration, uncertainty, provenance, and strict distinctions between redshift, radial velocity, recession velocity and astronomical distance.
ENTITY Redshift {
TYPE: DimensionlessSpectralShiftQuantity
SYMBOL: z
DIMENSION: dimensionless
DEFINITION:
redshift :=
fractional_change_between_observed_and_rest_spectral_coordinate
under_declared_wavelength_or_frequency_convention
WAVELENGTH_FORM:
z =
(lambda_obs-lambda_rest)/lambda_rest
EQUIVALENT:
1+z =
lambda_obs/lambda_rest
PROPERTIES:
is_dimensionless
may_be_positive_zero_or_negative
depends_on_rest_frame
may_have_multiple_physical_contributions
may_have_uncertainty
}
ENTITY Blueshift {
TYPE: NegativeRedshiftContext
CONDITION:
z < 0
INTERPRETATION:
observed_wavelength_shorter_than_rest_wavelength
under_wavelength_definition
}
ENTITY CosmologicalRedshift {
TYPE: Redshift
INTERPRETATION:
spectral_shift_associated_with_cosmic_expansion
under_declared_cosmological_model
}
ENTITY DopplerRedshift {
TYPE: Redshift
INTERPRETATION:
spectral_shift_due_to_relative_motion
under_declared_reference_frame_and_relativistic_model
}
UNIT_SYSTEM {
redshift:
dimensionless
unit_symbol: 1
wavelength:
metre
nanometre
angstrom
frequency:
hertz
megahertz
gigahertz
velocity_when_derived:
m/s
km/s
RULE:
redshift MUST NOT be assigned_velocity_or_distance_units
}
WAVELENGTH_MODEL {
definition:
z =
(lambda_obs-lambda_0)/lambda_0
inverse:
lambda_obs =
lambda_0*(1+z)
rest:
lambda_0 =
lambda_obs/(1+z)
WHEN z != -1
RULE:
observed_and_rest_wavelengths MUST use_compatible_medium_and_units
}
FREQUENCY_MODEL {
wavelength_frequency:
c =
lambda*nu
in_vacuum
redshift_frequency_relation:
1+z =
nu_rest/nu_obs
equivalent:
z =
nu_rest/nu_obs - 1
RULE:
frequency_shift_sign_is_inverse_to_wavelength_shift
}
SCALE_FACTOR_MODEL {
cosmological_relation:
1+z =
a(t_obs)/a(t_emit)
common_present_epoch_normalisation:
a(t_obs) = 1
then:
a(t_emit) =
1/(1+z)
RULE:
relation_applies_to_cosmological_redshift_under_FLRW_like_expansion_context
}
LOW_VELOCITY_DOPPLER_MODEL {
approximation:
z approximately_equals
v_r/c
CONDITIONS:
abs(v_r) << c
Doppler_motion_dominates
declared_sign_convention
RULE:
cz_is_velocity_approximation_not_general_identity
}
RELATIVISTIC_DOPPLER_MODEL {
purely_radial_special_relativistic_motion:
1+z =
sqrt((1+beta)/(1-beta))
WHERE:
beta =
v_r/c
inverse:
beta =
((1+z)^2-1)/
((1+z)^2+1)
RULE:
relativistic_Doppler_velocity_requires_motion_interpretation
and_is_not_cosmological_recession_velocity_in_general
}
PECULIAR_VELOCITY_MODEL {
observed_redshift:
combines_cosmological_and_peculiar_components
multiplicative_relation:
(1+z_obs) =
(1+z_cos)*(1+z_pec)
under_suitable_line_of_sight_factorisation
low_velocity_peculiar:
z_pec approximately_equals v_pec/c
RULE:
redshift_components SHOULD be_combined_multiplicatively_not_simply_added_at_high_precision
}
GRAVITATIONAL_REDSHIFT_MODEL {
weak_field:
z_grav approximately_equals
delta_Phi/c^2
strong_field:
requires_metric_specific_relation
RULE:
gravitational_redshift_depends_on_gravitational_potential_or_spacetime_metric
}
TOTAL_REDSHIFT_MODEL {
possible_components:
cosmological
Doppler
gravitational
local_source_motion
observer_motion
generic_multiplicative:
1+z_total =
product(1+z_i)
when_component_factorisation_is_valid
RULE:
physical_decomposition_requires_model_and_reference_frames
}
REFERENCE_FRAME_MODEL {
possible_frames:
topocentric
geocentric
heliocentric
barycentric
local_standard_of_rest
cosmic_microwave_background
RULE:
measured_spectral_shift SHOULD preserve_reference_frame
}
BARYCENTRIC_CORRECTION_MODEL {
purpose:
remove_observer_motion_due_to_Earth_rotation_and_orbit
relative_to_selected_barycentric_reference
corrected_spectral_coordinate:
derived_using_observer_velocity_and_time
REQUIRE:
observatory_position
observation_time
target_coordinates
ephemeris
RULE:
correction_convention_and_sign MUST be preserved
}
SPECTRAL_LINE_MODEL {
rest_line:
known_transition_wavelength_or_frequency
observed_line:
measured_centroid
redshift:
inferred_from_rest_and_observed_positions
REQUIRE:
line_identification
laboratory_rest_value
wavelength_calibration
line_profile_model
RULE:
incorrect_line_identification_can_produce_incorrect_redshift
}
MULTILINE_MODEL {
measurements:
z_1, z_2, ..., z_n
combined:
weighted_or_model_based_estimate
REQUIRE:
line_quality
uncertainty
blend_handling
RULE:
aggregation_method MUST be preserved
}
CROSS_CORRELATION_MODEL {
observed_spectrum:
S_obs
template:
S_template
redshift_estimate:
shift_maximising_declared_correlation_or_likelihood
RULE:
template_identity_resolution_and_preprocessing MUST be preserved
}
TEMPLATE_FITTING_MODEL {
model:
observed_spectrum approximately_equals
shifted_and_scaled_template
inferred:
z
possible_parameters:
continuum
extinction
velocity_dispersion
line_strengths
RULE:
redshift_is_model_parameter_with_fit_uncertainty
}
PHOTOMETRIC_REDSHIFT_MODEL {
input:
broadband_fluxes_or_colours
inference:
z_phot =
f(photometry, templates_or_machine_model, prior)
RULE:
photometric_redshift != spectroscopic_redshift
and_requires_model_version_and_probability_information_when_available
}
SPECTROSCOPIC_REDSHIFT_MODEL {
input:
resolved_spectral_features
output:
z_spec
RULE:
spectral_resolution_signal_to_noise_and_line_identification affect_precision
}
REDSHIFT_UNCERTAINTY_MODEL {
possible_sources:
wavelength_calibration
line_centroid
spectral_resolution
signal_to_noise
template_mismatch
line_blending
reference_frame
observer_motion
model_degeneracy
result:
z =
best_estimate +/- uncertainty
}
VELOCITY_CONVENTION_MODEL {
possible_reportings:
cz
optical_velocity
radio_velocity
relativistic_velocity
RULE:
velocity_convention MUST be identified
and_none_should_be_assumed_identical_to_redshift
}
RADIO_VELOCITY_MODEL {
commonly_based_on:
frequency_shift
RULE:
radio_velocity_and_optical_velocity_conventions_can_differ_materially_at_large_shift
}
OPTICAL_VELOCITY_MODEL {
commonly_based_on:
wavelength_redshift
generic_low_z:
v_opt approximately_equals c*z
RULE:
optical_velocity_is_conventional_derived_quantity
}
COSMOLOGICAL_DISTANCE_MODEL {
redshift:
observable_input
distance_types:
comoving_distance
luminosity_distance
angular_diameter_distance
proper_distance
mapping:
distance =
f(z, cosmological_parameters, distance_definition)
RULE:
redshift != distance
and_distance_type_and_cosmology MUST be declared
}
HUBBLE_LOW_Z_MODEL {
approximation:
d approximately_equals
c*z/H_0
CONDITIONS:
low_redshift
peculiar_velocity_small_relative_to_Hubble_flow
declared_cosmology
RULE:
low_z_Hubble_relation_is_approximation
}
COMOVING_DISTANCE_MODEL {
D_C =
c*integral_0^z(
dz_prime/H(z_prime)
)
RULE:
H(z)_model_and_cosmological_parameters MUST be preserved
}
LUMINOSITY_DISTANCE_MODEL {
flat_or_general_transverse_relation:
D_L =
(1+z)*D_M
RULE:
luminosity_distance_is_not_redshift
}
ANGULAR_DIAMETER_DISTANCE_MODEL {
relation:
D_A =
D_M/(1+z)
distance_duality:
D_L =
(1+z)^2*D_A
under_standard_conditions
RULE:
angular_diameter_and_luminosity_distance_are_distinct
}
LOOKBACK_TIME_MODEL {
t_L =
integral_0^z(
dz_prime/
((1+z_prime)*H(z_prime))
)
RULE:
lookback_time != redshift
and_lookback_time != distance
}
K_CORRECTION_CONTEXT_MODEL {
redshift:
shifts_rest_frame_spectrum_through_observed_bandpasses
photometric_correction:
K(z, spectrum, filters)
RULE:
K_correction_depends_on_redshift_but_is_not_redshift
}
REDSHIFT_SPACE_MODEL {
observed_position:
angular_coordinates_plus_redshift
redshift_space_distance:
may_include_peculiar_velocity_distortions
RULE:
redshift_space_position != true_real_space_position
}
CLUSTER_GALAXY_MODEL {
galaxy_redshifts:
may_be_used_to_estimate_cluster_mean_redshift_and_velocity_dispersion
RULE:
velocity_dispersion_inference_requires_relativistically_consistent_or_declared_approximation
}
NEGATIVE_REDSHIFT_MODEL {
z < 0:
blueshift
possible_causes:
approaching_motion
gravitational_effect
local_kinematics
physical_bound_under_wavelength_definition:
z > -1
RULE:
negative_redshift_is_valid_and_MUST_NOT be_treated_as_missing_value
}
HIGH_REDSHIFT_MODEL {
z_large:
wavelength_stretch_factor = 1+z
consequences:
rest_frame_band_shift
time_dilation
cosmological_distance_model_dependence
observed_time_interval:
delta_t_obs =
(1+z)*delta_t_emit
for_cosmological_time_dilation
RULE:
high_redshift_requires_relativistic_and_cosmological_semantics
}
RELATIONSHIPS {
Redshift -> RELATES -> ObservedAndRestWavelength
Redshift -> RELATES -> ObservedAndRestFrequency
DopplerRedshift -> MAY_RELATE_TO -> RadialMotion
CosmologicalRedshift -> RELATES -> CosmicScaleFactor
GravitationalRedshift -> RELATES -> GravitationalPotential
SpectralLine -> PROVIDES -> RedshiftMeasurement
ReferenceFrame -> QUALIFIES -> Redshift
BarycentricCorrection -> ADJUSTS -> ObserverMotionEffect
PhotometricModel -> ESTIMATES -> PhotometricRedshift
CosmologicalModel -> MAPS -> RedshiftToDistanceAndLookbackTime
}
SEMANTIC_EQUIVALENCE {
"z" ~= redshift WHEN astronomical_spectral_shift_context
"spectroscopic redshift" ~= z_spec
"photometric redshift" ~= z_phot
redshift != radial_velocity
redshift != recession_velocity
redshift != astronomical_distance
redshift != lookback_time
redshift != wavelength
redshift != frequency
photometric_redshift != spectroscopic_redshift
cosmological_redshift != peculiar_velocity
}
CONSTRAINTS {
redshift_is_dimensionless = true
rest_spectral_coordinate_must_be_defined = true
observed_spectral_coordinate_must_be_defined = true
wavelength_or_frequency_convention_must_be_defined = true
reference_frame_should_be_defined = true
redshift_and_velocity_are_not_semantically_equivalent = true
redshift_and_distance_are_not_semantically_equivalent = true
cosmological_distance_requires_cosmological_model = true
photometric_redshift_requires_inference_model = true
uncertainty_should_include_calibration_line_identification_reference_and_model_components = true
}
MEASUREMENT_MODEL {
OBSERVABLE_OR_INFERRED:
Redshift
SpectroscopicRedshift
PhotometricRedshift
DopplerRedshift
CosmologicalRedshift
COMMON_METHODS:
spectral_line_centroid
multi_line_fit
spectral_cross_correlation
template_fitting
photometric_template_fitting
machine_learning_photometric_redshift
RECORD:
celestial_object
object_identifier
redshift_value
redshift_type
rest_wavelength_or_frequency
observed_wavelength_or_frequency
spectral_line_identification
wavelength_or_frequency_unit
observation_time
observatory
instrument
spectral_resolution
reference_frame
barycentric_or_other_velocity_correction
template_or_model
photometric_bands_when_relevant
cosmological_model_when_distance_inferred
quality_flag
uncertainty
provenance
UNCERTAINTY:
measured_or_inferred_redshift =
best_estimate +/- uncertainty
}
CALIBRATION_MODEL {
spectroscopy:
wavelength_or_frequency_calibration
references:
arc_lamps
sky_lines
frequency_standards
calibration_sources
photometric:
photometric_zero_points_and_bandpass_calibration
REQUIRE:
calibration_version
valid_range
uncertainty
RULE:
calibration_model MUST match_measurement_method
}
REASONING_RULES {
IF observed_and_rest_wavelength_known
AND rest_wavelength != 0
THEN redshift =
(observed_wavelength-rest_wavelength)/rest_wavelength
IF redshift_known AND rest_wavelength_known
THEN observed_wavelength =
rest_wavelength*(1+redshift)
IF observed_and_rest_frequency_known
AND observed_frequency != 0
THEN redshift =
rest_frequency/observed_frequency - 1
IF redshift_known
AND purely_radial_special_relativistic_Doppler_context
THEN beta =
((1+redshift)^2-1)/
((1+redshift)^2+1)
IF abs(redshift) << 1
AND low_velocity_Doppler_context
THEN radial_velocity approximately_equals
c*redshift
IF cosmological_redshift_known
AND cosmological_model_known
THEN infer_cosmological_distances_and_lookback_time
preserving_distance_type
IF multiple_valid_line_redshifts_known
THEN combine_redshift_estimates
using_declared_weighting_or_fit_model
IF raw_spectrum_known
THEN calibrate_spectral_axis
identify_features
apply_reference_frame_correction
BEFORE final_redshift_inference
}
VALIDATION {
CHECK redshift_dimensionless
CHECK rest_spectral_coordinate
CHECK observed_spectral_coordinate
CHECK wavelength_vs_frequency_definition
CHECK line_identification
CHECK spectral_calibration
CHECK reference_frame
CHECK barycentric_correction
CHECK redshift_vs_velocity
CHECK redshift_vs_distance
CHECK Doppler_vs_cosmological_interpretation
CHECK photometric_vs_spectroscopic_redshift
CHECK cosmological_model_when_distance_inferred
CHECK negative_redshift_validity
CHECK quality_flag
CHECK uncertainty_representation
}
CONFIDENCE {
definition_confidence: 1.00
wavelength_relationship_confidence: 1.00
frequency_relationship_confidence: 1.00
relativistic_Doppler_confidence: 1.00
spectroscopic_measurement_confidence: 0.99
photometric_redshift_confidence: 0.94
cosmological_mapping_confidence: 0.96
measurement_context_confidence: 0.98
RULE:
confidence decreases when rest feature, line identification,
spectral calibration, reference frame, redshift type,
inference model, cosmology or uncertainty is missing or ambiguous
}
UPDATE_MODEL {
ON new_spectral_measurement:
identify_celestial_object
identify_rest_and_observed_feature
calibrate_wavelength_or_frequency_axis
attach_reference_frame
apply_observer_motion_correction_when_required
compute_line_redshift
attach_quality_flag
attach_uncertainty
update_redshift_state
ON multiline_update:
preserve_individual_line_measurements
update_line_quality_and_blend_status
recompute_combined_redshift
preserve_aggregation_or_fit_method
ON photometric_update:
preserve_input_photometry
attach_photometric_model_and_prior
compute_redshift_probability_distribution
preserve_model_version
update_quality_and_uncertainty
ON reference_frame_revision:
preserve_original_redshift
update_observer_motion_correction
recompute_frame_corrected_redshift
preserve_source_and_target_frames
ON cosmology_revision:
preserve_observed_redshift
update_cosmological_parameters
recompute_derived_distance_and_lookback_time_quantities
preserve_distance_types
update_provenance
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Redshift
canonical_symbol: z
canonical_dimension: dimensionless
interpretation_order:
identify_celestial_object
identify_redshift_value
identify_spectroscopic_photometric_Doppler_cosmological_or_gravitational_context
identify_rest_and_observed_spectral_coordinates
identify_wavelength_or_frequency_definition
identify_spectral_line_or_template
identify_reference_frame
identify_observer_motion_correction
identify_measurement_or_inference_method
identify_cosmological_model_when_distance_is_derived
identify_quality_flag
identify_uncertainty
validate_dimensionless_semantics
infer_spectral_velocity_and_cosmological_relationships
ambiguity_controls:
distinguish_redshift_from_radial_velocity
distinguish_redshift_from_recession_velocity
distinguish_redshift_from_astronomical_distance
distinguish_redshift_from_lookback_time
distinguish_wavelength_shift_from_frequency_shift_convention
distinguish_photometric_from_spectroscopic_redshift
distinguish_cosmological_redshift_from_peculiar_velocity
distinguish_negative_redshift_from_missing_or_invalid_data
preserve_object_feature_frame_method_model_cosmology_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_and_astronomical_redshift_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Redshift Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
wavelength_model
frequency_model
scale_factor_model
low_velocity_Doppler_model
relativistic_Doppler_model
peculiar_velocity_model
gravitational_redshift_model
total_redshift_model
reference_frame_model
barycentric_correction_model
spectral_line_model
multiline_model
cross_correlation_model
template_fitting_model
photometric_redshift_model
spectroscopic_redshift_model
redshift_uncertainty_model
velocity_convention_model
radio_velocity_model
optical_velocity_model
cosmological_distance_model
Hubble_low_z_model
comoving_distance_model
luminosity_distance_model
angular_diameter_distance_model
lookback_time_model
K_correction_context_model
redshift_space_model
cluster_galaxy_model
negative_redshift_model
high_redshift_model
relationships
constraints
measurement_model
calibration_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
redshift_definition_or_spectral_coordinate_model_changes
Doppler_or_gravitational_model_changes
reference_frame_or_observer_motion_correction_changes
spectroscopic_or_photometric_inference_model_changes
cosmological_distance_model_changes
calibration_model_changes
measurement_model_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW