This section specifies the standard units and scales each field uses to quantify its observables so that measurements can be compared, combined, and interpreted consistently. These include base physical units (meters, seconds, kilograms), derived units (pascals, watts, electronvolts, tesla), domain-specific technical units (barns, gray, sievert, decibels, parsecs, ppm, IC₅₀, hPa), and dimensionless quantities (Reynolds number, Mach number, heritability, diversity indices, network centrality scores). In the template, this row defines the quantitative “language” of a domain—how it turns raw signals into numbers that are commensurable across experiments, instruments, scales, and subfields.
Science Analysis Template
Below are the results of cycles 1 & 2 of The Science Project
Units are the formal standards that convert observation into evidence. They specify how a quantity is measured, stabilized, and rendered comparable across observations, observers, and contexts. Without units, observations remain descriptive; with units, they become evaluable.
A unit is not a label. It is a conventional mapping between a conceptual quantity and a repeatable measurement procedure. This mapping is what allows an observation to enter the evidence layer.
Function of Units
Within the SAT framework, units perform four irreducible functions:
- Stabilization — ensure repeated observations refer to the same kind of quantity.
- Comparability — allow observations across time, space, and observers to be evaluated against one another.
- Aggregation — enable observations to be combined into totals, averages, distributions, or trajectories.
- Transmission — preserve semantic meaning as observations move between agents and institutions.
If any function fails, evidence degrades into impression or narrative.
Conceptual Boundaries
Units must be distinguished from related concepts:
- Variables identify what is observed; units define how it is quantified.
- Scales order values; units anchor magnitude.
- Indicators / proxies approximate latent quantities; units define the measured quantity itself.
- Dimensions describe abstract types (time, length, value); units are concrete instantiations.
Confusing these categories produces structural evidence errors.
Validity Conditions
For a unit to function within the Evidence Layer, it must satisfy most of the following:
- Operational definability — tied to a repeatable procedure.
- Stability — meaning does not drift without explicit redefinition.
- Resolution — sufficient granularity for the discipline’s claims.
- Characterizable error — uncertainty can be bounded or described.
- Inter-observer consistency — different observers obtain compatible results under similar conditions.
Variation across disciplines is expected and informative.
Structural Types of Units
Across sciences, units cluster into a small number of forms:
- Fundamental units — defined independently. exists on its own
- Derived units — constructed from combinations of other units. built from others
- Count units — discrete tallies of entities or events. tallies things
- Ordinal units — ranked but not metrically spaced. ranks things
- Index units — normalized or composite measures anchored to a baseline. compares to a baseline
- Threshold units — categorical cutoffs tied to rule activation. triggers a category or rule
Every discipline relies on at least one of these structures.
Fundamental units
Units that are defined independently of all other units.
They do not rely on combinations, normalization, ranking, counting, or rules to exist.
They are the base measurement standards imported into a science.
If you remove every other unit, these still make sense.
A fundamental unit must:
- Be defined independently of the science
- Not rely on combinations, normalization, ranking, counting, or rules
- Remain meaningful if all other units are removed
- Be imported, not constructed within Interaction
Derived units
Units that are constructed from combinations of other units through arithmetic or formal operations.
They do not exist unless their component units exist.
Change the definition of an underlying unit → the derived unit changes.
A derived unit must:
- Be constructed from combinations of other units
- Not exist unless component units exist
- Change if an underlying unit definition changes
- Not be:
- a count unit
- an index unit
- a threshold unit
- a pure probability (unless explicitly constructed)
- a rate that collapses into method without care
Count units
Units that represent discrete tallies of entities or events.
They answer “how many,” not “how much,” not “how intense,” not “how ranked.”
They are additive over identical entities but carry no internal magnitude beyond integer steps.
A count unit must be:
- A raw tally
- Of entities or events
- With no embedded classification
- With no embedded rule
- With no embedded outcome
- With no embedded role
- Usable without knowing what the thing “means”
If the noun itself already implies what kind of thing it is (role, success, intent), it is not a unit — it is a classified observable.
Ordinal units
Units that express order or ranking without meaningful distance between values.
They answer “which comes before/after,” not “how much more.”
Differences between ranks are not metrically interpretable.
An ordinal unit must:
- Encode order only
- Have no meaningful distance
- Be definable at a single observation / elicitation, not across a process
- Not require:
- aggregation across events
- narrative sequencing
- role semantics
- Be a unit, not a description of a process unfolding over time
Index units
Units that are normalized or composite measures anchored to a reference baseline.
They combine multiple quantities or observations into a single comparative scale.
Their absolute value has no standalone meaning outside the baseline definition.
Index units are:
- normalized or composite measures
- explicitly anchored to a reference baseline
- whose absolute value has no standalone meaning
- constructed from other units
- not just “rates with a fancy name”
If an item sneaks in rate-ness, method, or implicit baselines, it’s out.
Threshold units
Units that represent categorical cutoffs tied to rule activation.
They convert continuous or complex inputs into discrete states (e.g., pass/fail, eligible/ineligible).
Crossing the threshold matters; distance from it usually does not.
A threshold unit must be:
- A binary categorical outcome
- Produced by crossing a specific, named cutoff
- Where the cutoff is intrinsic to the unit (not inferred)
- Independent of analyst interpretation
- Not reducible to another threshold already on the list
the Unit Descriptor Table
The table below provides a universal descriptor schema for units within the SAT Evidence Layer. Rather than defining units by discipline or measurement technology, it describes them by their evidentiary behavior—how they function as standards that convert observation into evidence.
Each row represents a specific unit. Each column captures a distinct property that determines how that unit can be used, combined, transformed, and interpreted within scientific reasoning.
This schema applies across all sciences. Differences between disciplines appear in how the columns are populated, not in whether the columns apply.
Column Explanations
Unit Type
The structural role the unit plays in measurement. Examples include:
- fundamental
- derived
- count
- ordinal
- index
- threshold
Unit type does not replace the remaining columns; it explains why certain constraints appear in them. Type determines the shape of evidentiary behavior, not the behavior itself.
Measurement Structure
Describes the internal mathematical or logical structure of the unit, including whether it is:
- discrete or continuous
- additive or non-additive
- linear or nonlinear
- bounded or unbounded
Measurement structure governs which operations are meaningful and which inferences are valid.
Reference Dependence
Specifies what anchors the unit’s meaning. A unit may be:
- absolute (tied to a fixed reference)
- relative (defined against another quantity)
- normalized (anchored to a baseline)
- contextual or institutional (defined by rules or conventions)
All units depend on a reference; this column makes that dependence explicit.
Transformability
Identifies which mathematical or logical transformations preserve meaning. This includes:
- permissible operations (addition, ratios, differences, growth rates)
- valid conversions versus redefinitions
- invariance properties
Invalid transformations are a primary source of empirical error and model failure.
Temporal Behavior
Describes how the unit relates to time. Units may be:
- instantaneous or cumulative
- stock or flow
- time-indexed or timeless
- lag-sensitive or lag-invariant
Temporal behavior determines how units can be compared, aggregated, or modeled dynamically.
Error Profile
Characterizes how uncertainty enters measurement. This may include:
- random or systematic error
- resolution limits
- observer or classification error
- procedural or institutional revision
Even non-empirical units admit error in the form of definitional ambiguity or logical invalidity.
Aggregation Compatibility
Specifies whether and how multiple observations can be combined. This includes:
- validity of summation or averaging
- population versus individual aggregation
- constraints on cross-context aggregation
- scale dependence
Many scientific failures arise from aggregating units that are structurally incompatible.
Interpretive Load
Describes how much meaning the unit carries beyond raw measurement. Units may be:
- minimally interpretive (purely quantitative)
- convention-loaded
- institutionally defined
- normatively embedded
This column distinguishes quantitative measurement from evaluative classification.
Boundary Conditions
Defines the conditions under which the unit ceases to be valid. This includes:
- domain limits
- regime changes
- contextual invalidation
- breakdown of assumptions
No unit is universally valid. Explicit boundary conditions are a requirement for evidentiary integrity.
| Element | ||||
|---|---|---|---|---|
| Scope Category | 2.2 Measurement Systems | |||
| Sub-Item | Units | |||
| Science Name Link | Branch Name Link | Field Name Link | Definition | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. |
| Natural Sciences | Physics | Classical Physics | Classical Mechanics | Standard classical units: meters (length), seconds (time), kilograms (mass), newtons (force), joules (energy). These define the quantitative framework of Classical Mechanics. |
| Natural Sciences | Physics | Classical Physics | Classical Electromagnetism | Standard EM units: volts (V), amperes (A), ohms (Ω), coulombs (C), tesla (T), henry (H), farad (F), watts (W). These quantify fields, charge, current, impedance, flux, and EM energy. |
| Natural Sciences | Physics | Classical Physics | Classical Thermodynamics | Standard thermodynamic units: kelvin (K), pascal (Pa), joule (J), mole (mol), cubic meters (m³), specific heat units (J/kg·K), and energy/work units (J). |
| Natural Sciences | Physics | Classical Physics | Statistical Mechanics (Classical) | Standard thermodynamic and mechanical units: kelvin (K), pascal (Pa), joule (J), mole (mol), volume units, and statistical quantities like variance and correlation amplitudes. |
| Natural Sciences | Physics | Classical Physics | Optics (Classical Wave Theory) | Optical units such as meters (wavelength), hertz (frequency), watts (power), photons/sec (intensity proxy), degrees or radians (phase), dB (optical loss), and refractive index (dimensionless). |
| Natural Sciences | Physics | Classical Physics | Acoustics | Pascals (sound pressure), decibels (SPL), hertz (frequency), meters (wavelength and distance), seconds (time), watts/m² (intensity), and impedance units (Pa·s/m). |
| Natural Sciences | Physics | Classical Physics | Continuum Mechanics | Standard units such as meters (displacement), seconds (time), pascals (stress or pressure), kilograms per cubic meter (density), meters per second (velocity), and inverse seconds (strain rate). |
| Natural Sciences | Physics | Classical Physics | Classical Field Theory | Standard units such as meters (distance), seconds (time), volts per meter (field strength), tesla (magnetic field), joules per cubic meter (energy density), and newtons per coulomb (force per charge). |
| Natural Sciences | Physics | Classical Physics | Pre-Relativistic Frameworks | Classical units such as meters (distance), seconds (time), kilograms (mass), newtons (force), joules (energy), pascals (pressure), and pre-standardized electromagnetic units used before modern SI conventions. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Mechanics | Units commonly include electronvolts (energy), nanometers or angstroms (length scale), seconds and femtoseconds (time), hertz (frequency), spin quantum numbers (dimensionless), and volts or amps for device-level measurements. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Relativistic Quantum Mechanics | Common units include electronvolts (energy), giga-electronvolts or tera-electronvolts (relativistic particle energies), meters or femtometers (length scale), seconds or picoseconds (time), and magnetic field units in tesla. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Special Relativity | Standard units such as seconds, meters, meters per second, joules, electronvolts, and dimensionless Lorentz factors used for consistent relativistic measurements. |
| Natural Sciences | Physics | Modern & Fundamental Physics | General Relativity | Common units include meters (distance), seconds (time), kilograms (mass), joules (energy), strain units for gravitational waves, and astronomical units for large-scale measurements. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Field Theory (QFT) | Common units include electronvolts for energy, inverse length for momentum scales, picoseconds for decay times, meters for detector geometry, and dimensionless coupling constants for interaction strengths. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Particle Physics (High-Energy Physics) | Common units include electronvolts (eV, keV, MeV, GeV, TeV), meters for detector geometry, seconds or nanoseconds for decay times, and dimensionless ratios for branching fractions and mixing angles. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Nuclear Physics | Units include electronvolts or mega-electronvolts (energy), seconds or years (half-life), barns (cross-section), meters (detector geometry), and counts per second for radiation intensity. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Statistical Physics | Common units include kelvin and millikelvin for temperature, joules or electronvolts for energy, meters for trap geometry or lattice spacing, and dimensionless occupation numbers for state populations. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Optics | Units include photons per second, nanometers for wavelength, hertz for frequency, seconds for coherence and decay times, decibels for squeezing levels, and meters for cavity dimensions or optical path length. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Information Science | Units include qubits, bits per second for communication rates, fidelity percentages, nanoseconds for gate times, hertz for control pulses, error rates per operation, and dimensionless entanglement metrics. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Symmetry & Group Theory | Units depend on the physical system being examined, including electronvolts (energy), spin quantum numbers, angular momentum units, charge values, and dimensionless group or representation labels. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Gauge Theory | Standard units include electron volts for energy, meters for position, seconds for time, inverse femtobarns for luminosity, and counts or rates for detection events. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | String Theory | Uses standard physics units such as meters, seconds, electron volts, and cosmological units when comparing predictions to observational data. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Differential Geometry in Physics | Uses standard units such as meters for distance, seconds for time, and derived units such as curvature per unit area or acceleration to express geometric effects. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Statistical Field Theory | Uses standard physical units such as meters, seconds, temperature units, energy units, and dimensionless quantities used to express critical exponents and scaling relations. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Mathematical Foundations of Quantum Mechanics | Uses standard units such as meters, seconds, energy units, and probability values to express measurement outcomes and operator expectations. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | General Mathematical Physics | Uses all standard physics units including meters, seconds, mass units, energy units, and dimensionless parameters used in mathematical analysis. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Solid-State Physics | Uses meters, seconds, volts, amperes, ohms, electron volts, teslas, kelvins, and other quantities for transport, optical, thermal, and magnetic measurements. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Semiconductor Physics | Common units include volts, amperes, ohms, meters, seconds, electron volts, kelvins, carrier density per cubic centimeter, and mobility in square centimeters per volt-second. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Magnetism & Spin Physics | Uses units such as teslas, amperes per meter, seconds, electron volts, meters, kelvins, magnetization per volume, and frequency units for spin resonance. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Superconductivity | Common units include ohms, amperes, volts, meters, seconds, kelvins, teslas, and flux units used for quantized magnetic measurements. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Soft Matter Physics | Uses meters, seconds, pascals, newtons, degrees, volume fractions, viscosity in pascal-seconds, elastic modulus in pascals, and characteristic times in seconds. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Nanomaterials & Nanostructures | Common units include nanometers, electron volts, volts, amperes, seconds, kelvins, surface area per mass units, and counts or intensity units for optical and electron measurements. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Strongly Correlated Electron Systems | Uses ohms, amperes, volts, meters, seconds, electron volts, kelvins, teslas, and counts or intensity units for scattering, spectroscopy, or magnetic measurements. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Topological Matter | Uses volts, amperes, ohms, meters, seconds, kelvins, teslas, electron volts, and momentum or energy units used in spectroscopy or scattering. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Materials Science (Physical Perspective) | Uses meters, seconds, pascals, newtons, joules, watts, kelvins, volts, ohms, electron volts, and other standardized physical units for mechanical, thermal, electronic, and optical measurements. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Stellar Astrophysics | Uses meters, seconds, watts, electron volts, kelvins, solar mass units, solar luminosity units, magnitudes, and velocities in kilometers per second. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Galactic Astrophysics | Uses parsecs, kiloparsecs, years, meters, seconds, watts, magnitudes, kelvins, kilometers per second, and integrated flux units for spectroscopy and radio observations. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Extragalactic Astrophysics | Uses parsecs, megaparsecs, gigaparsecs, years, seconds, magnitudes, redshift values, flux units, kelvins, kilometers per second, and luminosity units. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Cosmology | Uses parsecs, megaparsecs, gigaparsecs, years, seconds, kelvins, redshift values, flux units, magnitudes, and energy density fractions. |
| Natural Sciences | Physics | Astrophysics & Cosmology | High-Energy Astrophysics | Uses electron volts, kiloelectron volts, megaelectron volts, teraelectron volts, seconds, flux units, counts per second, kilometers per second, and magnetic field units. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Gravitational Astrophysics | Uses meters, seconds, astronomical units, years, kelvins, watts, magnitudes, kilometers per second, flux units, and mass or radius expressed in Earth or Jupiter units. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Planetary Science & Exoplanets | Uses meters, seconds, astronomical units, Earth or Jupiter mass units, Earth or Jupiter radius units, kelvins, magnitudes, flux units, orbital period in days or years, and velocities in kilometers per second. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrochemistry & Interstellar Medium Physics | Uses meters, seconds, kelvins, flux units, optical depth, column density, wavelength or frequency units, velocity in kilometers per second, and abundance ratios relative to hydrogen. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrobiology | Uses meters, seconds, kelvins, atmospheric mixing ratios, flux units, magnitudes, mass or radius expressed in Earth units, and isotopic ratio units. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fluid Dynamics | Uses meters, seconds, pascals, newtons, meters per second, density units, Reynolds number, Mach number, and energy or heat flux units. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Hydrodynamics (Ideal Fluids) | Uses meters, seconds, teslas, amperes per square meter, pascals, meters per second, density units, temperatures in kelvins, and nondimensional numbers such as magnetic Reynolds number. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Magnetohydrodynamics (MHD) | Uses meters, seconds, teslas, amperes per square meter, pascals, meters per second, kelvins, density units, and nondimensional quantities such as magnetic Reynolds number and plasma beta. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Plasma Physics (General) | Uses meters, seconds, teslas, volts per meter, amperes per square meter, kelvins, density units, energy in electron volts, frequency in hertz, and nondimensional plasma parameters such as Debye length or plasma beta. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Space & Astrophysical Plasmas | Uses meters, seconds, teslas, volts per meter, amperes per square meter, density units, kelvins, electron volts, kilometers per second, and nondimensional parameters such as plasma beta or Mach number. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fusion Plasma Physics | Uses meters, seconds, teslas, volts per meter, amperes, kelvins or electron volts for temperature, particles per cubic meter, watts for power, and neutron counts per second for fusion output. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Computational Fluid & Plasma Physics | Uses meters, seconds, pascals, teslas, volts per meter, density units, kelvins, electron volts, nondimensional units (Reynolds number, Mach number, plasma beta), and code-dependent normalized units. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Non-Newtonian & Complex Fluids | Uses pascals, seconds, meters, shear rate in 1 per second, viscosity in pascal seconds, stress in pascals, strain, strain rate, particle concentration in volume fraction, and temperature in kelvins. |
| Natural Sciences | Physics | Plasma & Fluid Physics | High-Energy-Density Physics (HEDP) | Uses meters, seconds, pascals, kelvins, electron volts, watts, joules, centimeters per microsecond for shock speed, neutron counts, x ray photon counts, and nondimensional parameters such as optical depth and compression ratio. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Biophysics | Uses meters, seconds, newtons, pascals, volts, millivolts, amperes, hertz, molar concentration, diffusion coefficients, elasticity units, probability, and fluorescence intensity counts. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Medical Physics | Uses gray (dose), sievert (effective dose), becquerel (activity), electron volt (energy), hertz, meters, seconds, amperes, volts, counts per second, attenuation coefficients, and HU units in CT. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Geophysics | Uses meters, seconds, pascals, newtons, teslas, siemens per meter, watts per square meter, hertz, kilometers, microgals (gravity), nanoteslas (magnetics), and millimeters for GPS displacement. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Optics & Photonics | Uses meters, seconds, hertz, joules, watts, photons per second, degrees (polarization angle), dB, refractive index units, radiance units, and spectral intensity units. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Computational Physics | Uses meters, seconds, kilograms, joules, pascals, hertz, electron volts, nondimensional numbers, grid units, timestep counts, iteration counts, and code dependent normalized units. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Engineering Physics | Uses meters, seconds, newtons, pascals, degrees Celsius, watts, volts, amperes, hertz, decibels, lumens, teslas, siemens, joules, and nondimensional engineering coefficients such as efficiency or gain. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Chemical Physics | Uses meters, seconds, hertz, joules, kelvins, pascals, electron volts, wavenumbers, concentration units (mol per liter), reaction rate units, intensity counts, and cross-section units. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Environmental & Climate Physics | Uses kelvins, pascals, meters per second, watts per square meter, parts per million, meters, seconds, millimeters of precipitation, salinity units, humidity percent, and radiance units. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Applied Materials Physics | Uses meters, seconds, pascals, kelvins, ohms, siemens per meter, watts per meter kelvin, electron volts, teslas, amperes, lumens, nanometers, and concentration units such as atomic percent. |
| Natural Sciences | Chemistry | Physical Chemistry | Quantum Chemistry | Electronvolts, wavenumbers, hartrees, angstroms, femtoseconds, Debye, atomic units (a.u.). |
| Natural Sciences | Chemistry | Physical Chemistry | Statistical Mechanics | Kelvin, joules, pascals, volumes, particle numbers, correlation lengths, relaxation times, entropy and information measures. |
| Natural Sciences | Chemistry | Physical Chemistry | Thermodynamics | Kelvin, joules, calories, pascals, liters, moles, enthalpy units, entropy units (J/K). |
| Natural Sciences | Chemistry | Physical Chemistry | Kinetics & Reaction Dynamics | Seconds, molarity, pressure, temperature, rate constants (s⁻¹, M⁻¹ s⁻¹), energy units (kJ/mol), cross-sections, molecular flux units. |
| Natural Sciences | Chemistry | Physical Chemistry | Spectroscopy | Wavelength (nm), frequency (Hz), wavenumber (cm⁻¹), intensity (a.u.), chemical shift (ppm), energy (eV), time (fs–s), magnetic field (T). |
| Natural Sciences | Chemistry | Physical Chemistry | Electrochemistry | Volts, amperes, ohms, siemens, coulombs, molarity, pH, chemical activity units, impedance (Ω·cm²), diffusion coefficients (cm²/s). |
| Natural Sciences | Chemistry | Physical Chemistry | Surface & Interface Science | Surface energy (J/m²), coverage (monolayers, %), contact angle (degrees), current density (A/cm²), potential (V), thickness (nm), frequency shifts (Hz). |
| Natural Sciences | Chemistry | Physical Chemistry | Colloid & Solution Chemistry | Molarity, pH, ionic strength, turbidity units (NTU), particle size (nm–µm), viscosity (Pa·s), conductivity (S/m), osmotic pressure (Pa), zeta potential (mV). |
| Natural Sciences | Chemistry | Physical Chemistry | Chemical Physics | Wavelength (nm), frequency (Hz), wavenumber (cm⁻¹), energy (eV, kJ/mol), time (fs–s), cross-section (cm²), temperature (K), momentum units, scattering angles (degrees). |
| Natural Sciences | Chemistry | Organic Chemistry | Structural & Mechanistic Organic Chemistry | Molarity, equivalents, temperature (°C/K), rate constants (s⁻¹, M⁻¹ s⁻¹), yields (%), stereomeric ratios, chemical shift (ppm), wavelength (nm), mass (m/z), energy (kJ/mol). |
| Natural Sciences | Chemistry | Organic Chemistry | Stereochemistry & Conformational Analysis | Degrees of rotation (α), ppm (NMR), J-coupling (Hz), population ratios, energy differences (kcal/mol or kJ/mol), wavelength (nm), absorbance (a.u.). |
| Natural Sciences | Chemistry | Organic Chemistry | Synthetic Organic Chemistry | Molarity, equivalents, °C/K, time (s–h), yield (%), optical rotation (°), R_f values, retention times, mass-to-charge (m/z), IR frequencies (cm⁻¹), NMR ppm. |
| Natural Sciences | Chemistry | Organic Chemistry | Physical Organic Chemistry | Rate constants (s⁻¹, M⁻¹ s⁻¹), equilibrium constants (K), activation energies (kJ/mol), isotope ratios, substituent constants (σ), pKa values, ΔG‡, ΔH‡, ΔS‡, solvent parameters. |
| Natural Sciences | Chemistry | Organic Chemistry | Organometallic Organic Chemistry | Redox potential (V), turnover frequency (TOF), turnover number (TON), rate constants (s⁻¹), bond lengths (Å), chemical shifts (ppm), IR stretching frequencies (cm⁻¹), pressure (bar). |
| Natural Sciences | Chemistry | Organic Chemistry | Polymer Chemistry (Carbon-based) | Molecular weight (g/mol), dispersity (Đ), conversion (%), concentration (M), temperature (°C/K), viscosity (Pa·s), diffusion coefficients, T_g/T_m (°C), NMR ppm, scattering intensity. |
| Natural Sciences | Chemistry | Organic Chemistry | Bioorganic Chemistry | Rate constants (s⁻¹, M⁻¹ s⁻¹), binding constants (Kd), Michaelis–Menten parameters (Km, kcat), pKa, ΔG/ΔH/ΔS, absorbance (a.u.), wavelength (nm), chemical shift (ppm), mass (m/z). |
| Natural Sciences | Chemistry | Organic Chemistry | Natural Products Chemistry | Chemical shift (ppm), m/z, retention time (min), optical rotation (°), concentration (mg/mL or µM), bioactivity values (IC₅₀/EC₅₀), UV absorbance (a.u.), isotopic ratios, pH, temperature. |
| Natural Sciences | Chemistry | Organic Chemistry | Medicinal Chemistry | IC₅₀/EC₅₀, Ki/Kd, % inhibition, logP/logD, clearance (mL/min/kg), half-life (h), bioavailability (%), binding occupancy (%), metabolic rate (min⁻¹), concentration (nM–µM). |
| Natural Sciences | Chemistry | Inorganic Chemistry | Main-Group Chemistry | Charge (e⁻), oxidation state (integer), bond lengths (Å), vibrational frequencies (cm⁻¹), potentials (V), concentration (M), temperature (°C/K), pressure (atm), conductivity (S/m). |
| Natural Sciences | Chemistry | Inorganic Chemistry | Transition-Metal Chemistry | Oxidation state, electron count, magnetic moment (μB), redox potential (V), rate constants (s⁻¹), bond lengths (Å), spectral bands (cm⁻¹, nm), conductivity (S/m), concentration (M). |
| Natural Sciences | Chemistry | Inorganic Chemistry | f-Block Chemistry | Oxidation state, magnetic moment (μB), redox potential (V), bond lengths (Å), absorption/emission wavelengths (nm), mass (m/z), concentration (M), radiation counts (cpm), temperature (K). |
| Natural Sciences | Chemistry | Inorganic Chemistry | Coordination Chemistry | Absorbance (a.u.), wavelengths (nm), redox potentials (V), magnetic moments (μB), bond lengths (Å), rate constants (s⁻¹), stability constants (Kf), conductivity (S/m), concentration (M). |
| Natural Sciences | Chemistry | Inorganic Chemistry | Solid-State Chemistry | Lattice parameters (Å), temperature (K/°C), pressure (GPa), conductivity (S/m), magnetic moment (μB), bandgap (eV), diffraction intensity (a.u.), heat capacity (J/mol·K), density (g/cm³). |
| Natural Sciences | Chemistry | Analytical Chemistry | Qualitative Analysis | Wavelength (nm), frequency (cm⁻¹ or MHz), mass-to-charge (m/z), retention time (min), pH units, relative intensity (a.u.), conductivity (S/m), qualitative presence/absence indicators. |
| Natural Sciences | Chemistry | Analytical Chemistry | Quantitative Analysis | Concentration (M, ppm, ppb), absorbance (a.u.), peak area (counts), mass (g/mg/µg), volume (L/mL/µL), charge (C), potential (V), current (A), time (s), temperature (°C/K), pH units. |
| Natural Sciences | Chemistry | Analytical Chemistry | Separation Science | Time (min, s), voltage (V), current (A), flow rate (mL/min), pressure (bar/psi), wavelength (nm), conductivity (S/m), mass-to-charge (m/z), partition coefficients (dimensionless), viscosity (cP). |
| Natural Sciences | Chemistry | Analytical Chemistry | Instrumental Analysis | Absorbance (a.u.), wavelength (nm), frequency (Hz or cm⁻¹), m/z, retention time (min), potential (V), current (A), temperature (°C/K), signal intensity (counts), mass/volume units, time (s). |
| Natural Sciences | Chemistry | Biochemistry | Structural Biochemistry | Distance (Å), chemical shift (ppm), electron density (a.u.), scattering intensity (a.u.), wavelength (nm), temperature (°C/K), pH units, fluorescence intensity, FRET efficiencies, time (ms–min). |
| Natural Sciences | Chemistry | Biochemistry | Enzymology | Concentration (M), rate (M/s), velocity (v₀), catalytic constants (kcat, Km), inhibition constants (Ki), fluorescence intensity (a.u.), absorbance (a.u.), ΔH/ΔCp (cal/mol), pH, time (ms–min). |
| Natural Sciences | Chemistry | Biochemistry | Metabolism & Bioenergetics | Concentration (µM–mM), flux rate (pmol/min/cell or mmol/g/h), redox ratio (NAD⁺/NADH), oxygen consumption rate (pmol O₂/s), membrane potential (mV), Gibbs free energy (kJ/mol), isotopic enrichment (%), pH, temperature. |
| Natural Sciences | Chemistry | Biochemistry | Molecular Biology & Gene Expression | Transcript counts (TPM, RPKM, CPM), protein abundance (a.u. or copies/cell), fluorescence intensity, ChIP enrichment (fold-change), ribosome footprints (reads), methylation (percentage), binding affinities (Kd), time (s–hr). |
| Natural Sciences | Chemistry | Biochemistry | Cellular Biochemistry | Fluorescence intensity (a.u.), ion concentration (nM–mM), membrane potential (mV), pH units, metabolite levels (µM–mM), vesicle trafficking rate (events/s), redox ratio (NADH/NAD⁺), time (ms–hr). |
| Natural Sciences | Chemistry | Biochemistry | Membrane Biochemistry | Fluorescence (a.u.), diffusion coefficients (µm²/s), membrane potential (mV), ion concentrations (nM–mM), lipid composition (%), curvature metrics (1/nm), conductance (pS), vesicle size (nm–µm), time (ms–min). |
| Natural Sciences | Chemistry | Biochemistry | Protein Chemistry | Absorbance (a.u.), fluorescence intensity (a.u.), CD ellipticity (mdeg), mass-to-charge (m/z), concentration (µM–mM), melting temperature (°C), kinetic rates (s⁻¹), binding affinity (Kd), RMSD (Å), peptide coverage (%). |
| Natural Sciences | Chemistry | Biochemistry | Biochemical Genetics | Concentration (µM–mM), enzyme activity (µmol/min/mg), kinetic constants (Km, kcat), flux rates, allele frequency (%), metabolite fold-change, expression counts (TPM/RPKM), protein abundance (copies/cell), variant frequency, redox ratios. |
| Natural Sciences | Earth & Space Sciences | Geology | Mineralogy & Crystallography | Lattice parameters (Å), angles (°), refractive index, density (g/cm³), hardness (Mohs scale), Raman/IR frequencies (cm⁻¹), magnetic susceptibility, electrical conductivity (S/m), temperature (°C), pressure (GPa). |
| Natural Sciences | Earth & Space Sciences | Geology | Petrology | Mineral proportions (%), grain size (µm–mm), chemical compositions (wt%, ppm), density (g/cm³), P–T estimates (°C, GPa), isotopic ratios, modal proportions (%), melt fraction (%), reaction progress (%), orientation angles (°). |
| Natural Sciences | Earth & Space Sciences | Geology | Structural Geology & Tectonics | Orientation (strike/dip), plunge/trend, displacement (m–km), strain (%), stress (MPa), shear strain (γ), GPS velocity (mm/yr), seismic velocity (km/s), crustal thickness (km), depth (m–km), time (Ma). |
| Natural Sciences | Earth & Space Sciences | Geology | Sedimentology & Stratigraphy | Grain size (µm–mm), bed thickness (cm–m), flow velocity proxies, porosity (%), permeability (mD–D), sedimentation rate (mm/yr to m/kyr), stratigraphic thickness (m), seismic time/depth, fossil/assemblage abundance counts, isotopic ratios. |
| Natural Sciences | Earth & Space Sciences | Geology | Geomorphology | Elevation (m), slope (°), curvature, discharge (m³/s), sediment flux (kg/s or t/yr), erosion rate (mm/yr), uplift rate (mm/yr), velocity (m/s), grain size (µm–mm), roughness indices, thickness (m), time (s–Ma). |
| Natural Sciences | Earth & Space Sciences | Geology | Geophysics | Time (s), velocity (km/s), acceleration (m/s²), gravity (mGal), magnetic field (nT), resistivity (Ω·m), heat flow (mW/m²), displacement (mm–cm), temperature (°C), pressure (GPa), geoid height (m). |
| Natural Sciences | Earth & Space Sciences | Geology | Geochemistry | Concentration (ppm, ppb, wt%), isotope ratios (e.g., ⁸⁷Sr/⁸⁶Sr), pH, Eh (mV), ionic strength, speciation percentages, partial pressures (atm), thermodynamic constants (K), activity coefficients, fluxes (mol/m²/s). |
| Natural Sciences | Earth & Space Sciences | Geology | Paleontology | Size (mm–m), counts/abundance, diversity indices, isotopic ratios (δ¹³C, δ¹⁸O, δ³⁴S), geochemical concentrations (ppm, wt%), stratigraphic thickness (m), age (Ma), sedimentation rate (mm/yr), morphological measurements (mm). |
| Natural Sciences | Earth & Space Sciences | Geology | Hydrogeology | Hydraulic head (m), pressure (kPa), hydraulic conductivity (m/s), transmissivity (m²/s), flow rate (L/s or m³/day), concentration (mg/L, µg/L, ppm), isotopic ratios, temperature (°C), electrical conductivity (µS/cm), salinity (ppt). |
| Natural Sciences | Earth & Space Sciences | Geology | Economic & Applied Geology | Concentration (ppm, ppb, wt%), grade (% or g/t), porosity (%), permeability (mD–D), flow rate (m³/day), pressure (kPa–MPa), temperature (°C), seismic velocity (m/s), density (g/cc), magnetic susceptibility, resistivity (Ω·m). |
| Natural Sciences | Earth & Space Sciences | Meteorology | Dynamic Meteorology | Uses SI units such as meters, seconds, Pascals, Kelvin, meters per second, kilograms per cubic meter; also meteorological conventions like hPa, knots, geopotential meters, and potential temperature (K). |
| Natural Sciences | Earth & Space Sciences | Meteorology | Thermodynamic Meteorology | Uses Kelvin, Celsius, Pascals, hPa, grams per kilogram (mixing ratio), Joules per kilogram (CAPE, CIN, enthalpy), watts per square meter (radiation), and meters for cloud-base heights. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Cloud Physics & Microphysics | Micrometers (particle size), grams per cubic meter (water content), per liter or per cubic centimeter (number concentration), meters per second (fall speed), Kelvin, Pascals, and watts per square meter (radiation). |
| Natural Sciences | Earth & Space Sciences | Meteorology | Synoptic & Mesoscale Meteorology | Pascals/hPa, Kelvin/°C, meters per second (winds), geopotential meters, reflectivity (dBZ), brightness temperature (K), mixing ratio (g/kg), and vertical velocity (Pa/s or m/s). |
| Natural Sciences | Earth & Space Sciences | Meteorology | Atmospheric Physics & Chemistry | Mole fractions (ppm, ppb, ppt), micrograms per cubic meter (aerosols), meters (optical path), watts per square meter (radiation), Dobson Units (ozone), Kelvin, Pascals, and spectral units (nm, μm). |
| Natural Sciences | Earth & Space Sciences | Meteorology | Climatology & Climate Dynamics | Kelvin/°C, millimeters (precipitation), watts per square meter (radiation), ppm/ppb (GHGs), meters (sea level), Joules (ocean heat content), and isotopic ratios (paleoclimate proxies). |
| Natural Sciences | Earth & Space Sciences | Oceanography | Physical Oceanography | Temperature (°C), salinity (psu), velocity (m/s), sea-surface height (cm), density (kg/m³), pressure (dbar), heat flux (W/m²), salt flux (kg/m²/s), wave height/period (m, s), turbulence dissipation (W/kg), ice thickness (m). |
| Natural Sciences | Earth & Space Sciences | Oceanography | Chemical Oceanography | Concentration (µM, nM, mg/L, µg/L), pH, alkalinity (µmol/kg), partial pressures (µatm), redox potential (mV), isotopic ratios (δ¹³C, δ¹⁵N), absorption units, fluorescence units, saturation indices (Ω). |
| Natural Sciences | Earth & Space Sciences | Oceanography | Biological Oceanography | Biomass (mg C/m³), chlorophyll-a (mg/m³), abundance (cells/L), productivity (mg C/m²/day), grazing rate (day⁻¹), nutrient uptake rate (µM/day), fluorescence units, optical backscatter, oxygen (µM), microbial gene counts. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Geological Oceanography | Thickness (m), accumulation rate (cm/kyr), grain size (µm–mm), porosity (%), density (g/cc), temperature (°C), heat flow (mW/m²), magnetic intensity (nT), seismic velocity (m/s), sedimentation age (ka–Ma), spreading rate (mm/yr). |
| Natural Sciences | Biology | Molecular Biology | Nucleic Acid Biology | Quantifications using base units (nucleotides, base pairs), concentration (nM, µM), reaction rates (s⁻¹), sequencing depth (reads), fluorescence intensity, Ct values, coverage percentages, and fold-change measures. |
| Natural Sciences | Biology | Molecular Biology | Gene Regulation & Epigenetics | Quantifications expressed in normalized read counts, fragments per kilobase (FPKM/TPM), ChIP enrichment scores, methylation percentages, accessibility indices, contact-frequency units, fluorescence intensity, and fold-change expression values. |
| Natural Sciences | Biology | Molecular Biology | Protein Biology | Mass (kDa), concentration (nM–µM), catalytic rates (kcat, Km), binding affinity (Kd), fluorescence intensity, circular-dichroism ellipticity, structural-resolution units (Å), and spectral absorbance. |
| Natural Sciences | Biology | Molecular Biology | Molecular Complexes & Information Flow | Stoichiometric ratios, binding affinities (Kd), assembly rates (s⁻¹), interaction frequencies, structural resolution (Å), fluorescence intensities, localization coordinates, and information-transfer rates. |
| Natural Sciences | Biology | Molecular Biology | Molecular Methods & Technologies | Fluorescence intensity units, absorbance (A.U.), sequencing read counts, mass/charge (m/z), reaction rates (s⁻¹), concentration (nM–µM), imaging resolution (nm), and calibration-standard units. |
| Natural Sciences | Biology | Cell Biology | Cell Structure & Organelles | Measurements in nanometers (structure), micrometers (organelle size/location), seconds–minutes (dynamic events), fluorescence intensity (protein abundance), pH units, ionic concentrations, and molecular counts. |
| Natural Sciences | Biology | Cell Biology | Cellular Dynamics & Trafficking | Nanometers/µm (distance), ms–s (time), µm/s (velocity), steps/s (motor rates), fluorescence intensity (cargo load), pH units (endosomal identity), concentration values, and probability densities for diffusion and binding events. |
| Natural Sciences | Biology | Cell Biology | Cell Signaling & Communication | Concentration (nM–µM), fluorescence intensity units, phosphorylation percentage, ion concentration (nM–mM), membrane potential (mV), kinetic rates (s⁻¹), diffusion coefficients (µm²/s), gene-expression fold change. |
| Natural Sciences | Biology | Cell Biology | Cell Cycle, Fate & Death | Concentration (nM–µM), fluorescence intensity, phosphorylation percentage, DNA-damage foci counts, cell-cycle phase durations (minutes–hours), caspase activity units, chromatin-modification levels, gene-expression fold change. |
| Natural Sciences | Biology | Cell Biology | Cell Interactions & Microenvironment | Force (pN–nN), stiffness (Pa–kPa), ligand density (molecules/µm²), concentration (nM–µM), distance (µm), time (ms–hours), traction stress (Pa), ECM-porosity (%) signals, flow rates (µm/s). |
| Natural Sciences | Biology | Cell Biology | Cell Morphology & Motility | µm, nm (shape/morphology), seconds–minutes (motility events), µm/s (migration speed), pN–nN (traction force), curvature units, fluorescence intensity (cytoskeletal density), step-size distributions for motor activity. |
| Natural Sciences | Biology | Genetics & Evolution | Classical & Transmission Genetics | Ratios (3:1, 9:3:3:1), percentages, recombination frequency (% RF), map units (centiMorgans), genotype counts, allele frequencies, probability values. |
| Natural Sciences | Biology | Genetics & Evolution | Population Genetics | Allele-frequency values (0–1), genotype proportions, selection coefficients (s, h), mutation rates (per generation), migration rates (m), inbreeding coefficient (F), LD values (D, r²), effective population size (Ne). |
| Natural Sciences | Biology | Genetics & Evolution | Quantitative Genetics | Trait units (cm, g, counts, scores), variance units, covariance values, correlation coefficients, heritability estimates (h², H²), selection differential (S), response to selection (R), additive genetic variance (VA), dominance variance (VD). |
| Natural Sciences | Biology | Genetics & Evolution | Genomic Evolution & Comparative Genomics | Sequence identity (%), substitution rates (per site per generation), dN/dS ratios, GC content (%), copy-number counts, synteny block lengths, branch lengths in substitutions/site, genome-size (bp), TE frequency. |
| Natural Sciences | Biology | Genetics & Evolution | Phylogenetics & Systematics | Sequence identity (%), substitutions per site, branch lengths, morphological character counts, bootstrap percentages, posterior probabilities, divergence times (MYA), taxonomic ranks. |
| Natural Sciences | Biology | Genetics & Evolution | Macroevolution & Speciation Theory | Speciation/extinction rate parameters (λ, μ), divergence time (Mya), morphological disparity units, range size metrics, reproductive isolation indices, branch-length units, diversification-rate shifts, geographic distance measures. |
| Natural Sciences | Biology | Physiology | Cellular & Tissue Physiology | mV (membrane potential), pA/pF (ionic current densities), µm (cell/tissue dimensions), Pa (pressure), nN–µN (force), molarity, fluorescence intensity, and time units from ms to hours. |
| Natural Sciences | Biology | Physiology | Neurophysiology | mV (voltage), pA/nA (current), Hz (firing rate), µM (neurotransmitter), fluorescence intensity units, ms (timing), and µm (morphological scale). |
| Natural Sciences | Biology | Physiology | Endocrine & Regulatory Physiology | pg/mL or ng/mL (hormones), molarity for second messengers, metabolic units (mg/dL glucose), receptor density units (fmol/mg tissue), secretion rates, and time (s–hours). |
| Natural Sciences | Biology | Physiology | Cardiovascular & Respiratory Physiology | mmHg (pressure), L/min (flow/ventilation), bpm (heart rate), L (lung volumes), SpO₂ (%), PaO₂/PaCO₂ (mmHg), cardiac output (L/min), and compliance/resistance units. |
| Natural Sciences | Biology | Physiology | Metabolic & Energetic Physiology | VO₂ and VCO₂ (mL/min or L/min), energy expenditure (kcal/day or Watts), glucose (mg/dL), lactate (mmol/L), substrate-oxidation rates, temperature (°C), and hormone/metabolite concentrations. |
| Natural Sciences | Biology | Physiology | Renal, Fluid & Homeostatic Physiology | mEq/L (electrolytes), mOsm/kg (osmolarity), mL/min (urine flow, clearance), pH units, mmHg (blood pressure contributors), L (fluid volumes), and ng/mL or pg/mL (hormones). |
| Natural Sciences | Biology | Developmental Biology | Cell Fate & Lineage Specification | Gene-expression levels, fluorescence intensity, chromatin-accessibility units, signaling-activity scores, lineage trace frequencies, potency metrics, spatial position (µm), temporal resolution (minutes–hours). |
| Natural Sciences | Biology | Developmental Biology | Pattern Formation & Embryonic Axes | Concentration units for morphogens, fluorescence intensity, distance along embryonic axes (µm), oscillation phase/time, gradient steepness, positional identity scores, segmentation period, signal-to-noise ratios. |
| Natural Sciences | Biology | Developmental Biology | Morphogenesis & Tissue-Level Mechanics | Microns (cell shape/geometry), microns/min (tissue flow velocities), Pascals (pressure), Newtons or piconewtons (force), strain (% deformation), curvature (1/µm), elasticity/viscosity parameters, fluorescence intensity for mechanical reporters. |
| Natural Sciences | Biology | Developmental Biology | Organogenesis & Multi-Tissue Assembly | Microns (tissue geometry), µm/min (tissue flow), branching frequency, lumen diameter, ECM density units, signaling intensity levels, pressure units (Pa) for lumenal expansion, adhesion or stiffness measurements, volumetric growth rates. |
| Natural Sciences | Biology | Developmental Biology | Growth, Timing, Regeneration & Life-Cycle Transitions | Microns/mm (size, growth), %/hour (proliferation), hormone concentration (ng/mL or nM), regeneration index (% restored), timing units (hours/days to transitions), circadian phase (degrees or hours), wound size (µm²), stem-cell activation markers (fluorescence intensity). |
| Natural Sciences | Biology | Developmental Biology | Evolutionary Development (Evo–Devo) | Expression levels (counts/FPKM/TPM), enhancer activity intensity, spatial coordinates (µm) for expression domains, embryonic-stage timing (hours/days), morphometric distances, phylogenetic branch lengths, regulatory motif scores. |
| Natural Sciences | Biology | Ecology | Organismal Ecology | Distance (m), time (s), temperature (°C), metabolic rate (mL O₂/hr), energy units (kJ), heart rate (bpm), hydration level (%), luminance (lux), humidity (%), and movement velocity (m/s). |
| Natural Sciences | Biology | Ecology | Population Ecology | Number of individuals, density (individuals per area/volume), growth rate (r, λ), survival probability, fecundity per female, recruitment rate, migration probability, and time in days, seasons, or years. |
| Natural Sciences | Biology | Ecology | Community Ecology | Counts of individuals, abundance per area, biomass, diversity metrics (Shannon, Simpson), interaction coefficients, trophic-flow units (energy or biomass flux), and spatial metrics (m², km²). |
| Natural Sciences | Biology | Ecology | Ecosystem Ecology | Biomass (g/m²), productivity (g C/m²/yr), nutrient concentration (mg/L or ppm), flux rates (g C/m²/day), stoichiometric ratios (C:N:P), energy units (kJ), and environmental units (temperature, moisture). |
| Natural Sciences | Biology | Ecology | Landscape & Spatial Ecology | Spatial units (m, km), area (m²–km²), connectivity indices, edge density, patch metrics, dispersal distances, landscape heterogeneity indices, and spatial autocorrelation coefficients. |
| Natural Sciences | Biology | Ecology | Global Ecology & Earth-System Interactions | PPM (atmospheric gases), W/m² (radiative flux), g C/m²/yr (productivity), °C (temperature), mm/yr (precipitation), Pg C/yr (carbon fluxes), km² (biome extent), δ¹³C/δ¹⁵N (isotopes), and sea-level units. |
| Formal Sciences | Logic | Proof Theory | Proof Calculi | Proof length, proof depth, number of rule applications, branching factor, derivation height, complexity class (e.g., P, NP, PSPACE). |
| Formal Sciences | Logic | Proof Theory | Structural Proof Theory | Proof height, proof width, number of cut occurrences, count of structural-rule applications, normalization length, permutation depth, complexity class of derivability. |
| Formal Sciences | Logic | Proof Theory | Proof Theory of Non-Classical Logics | Proof height, resource counts, modality depth, label-propagation steps, relevance-preservation checks, cut-rank, number of accessibility transitions, valuation degrees in many-valued systems. |
| Formal Sciences | Logic | Proof Theory | Ordinal & Strength Analysis | Ordinal height, order type, induction level, reflection rank, recursion-growth class, proof-length bounds parameterized by ordinal size, fast-growing hierarchy indices (e.g., F_α). |
| Formal Sciences | Logic | Proof Theory | Proof Complexity | Length (number of steps), size (total symbol count), width (maximum clause width), space (memory footprint of active clauses), depth (height of proof tree/DAG), degree (Polynomial Calculus), rank (Nullstellensatz), and asymptotic growth with respect to input size n. |
| Formal Sciences | Logic | Proof Theory | Automated & Interactive Reasoning | Time (ms/s), memory usage, number of solver steps, proof length, search depth, number of tactics executed, number of constraints generated, model size, backtracking count, branching factor, number of rewrite operations. |
| Formal Sciences | Logic | Model Theory | Structures, Languages & Interpretations | Logical units: arity, quantifier rank, formula complexity, cardinality of language, size of domains, degree of definability. |
| Formal Sciences | Logic | Model Theory | Satisfaction & Definability Theory | Logical units: quantifier rank, arity, formula length, domain cardinality, complexity of definability, size of signature. |
| Formal Sciences | Logic | Model Theory | Quantifier Theory & Model Completeness | Quantifier rank, alternation depth, formula length, domain cardinality, signature size, definability complexity, degree of Skolemization. |
| Formal Sciences | Logic | Model Theory | Classification Theory | Rank values (RM, U), cardinalities measuring saturation, multiplicity of types, forking depth, dividing chains, independence dimensions, definability degrees. |
| Formal Sciences | Logic | Model Theory | Tame / O-Minimal Model Theory | Dimensions, number of cells, sizes of definable partitions, quantifier complexity, lengths of definable chains. |
| Formal Sciences | Logic | Set Theory | Axiomatic Foundations & Cumulative Hierarchy | Ordinals, cardinals, rank values, cumulative levels ( V_\alpha ), transfinite lengths, combinatorial cardinal characteristics. |
| Formal Sciences | Logic | Set Theory | Constructibility & Inner Models | Ordinal height, fine-structure levels, definability complexity, admissibility levels, projecta, sharps indicators (e.g., existence of (0^\sharp)). |
| Formal Sciences | Logic | Set Theory | Large Cardinal Theory | Critical point values, ranks of large cardinals, extender lengths, Mitchell order, consistency strength levels, degrees of indescribability, closure ordinals. |
| Formal Sciences | Logic | Set Theory | Forcing & Independence Theory | Cardinal characteristics, chain conditions (ccc, properness), closure degrees, Boolean truth values, ranks of names, lengths of forcing iterations, complexity of posets. |
| Formal Sciences | Logic | Set Theory | Descriptive Set Theory | Borel rank, projective level, Wadge degree, tree rank, norm lengths, scale complexity, descriptive complexity. |
| Formal Sciences | Logic | Computability Theory | Models of Computation & Recursive Function Theory | Number of computation steps, recursion depth, number of reductions, tape movement count, register updates, size of encoding, oracle call count, quantifier alternation depth (in definability analyses). |
| Formal Sciences | Logic | Computability Theory | Recursively Enumerable (r.e.) Sets & Degrees | Enumeration stages, injury counts, requirement-satisfaction counts, oracle-query counts, reducibility-step counts, approximation depth, rate of convergence, functional evaluation steps. |
| Formal Sciences | Logic | Computability Theory | Reducibility & Degrees of Unsolvability | Reduction steps, oracle-query counts, stage index of approximation, number of requirement satisfactions, injury counts (if priority used), jump level reached, complexity of encoding. |
| Formal Sciences | Logic | Computability Theory | Arithmetical & Analytical Hierarchies | Quantifier depth, alternation count, arithmetical or analytical level (n in Σₙ, Πₙ), jump level (0′, 0″, etc.), oracle complexity, reduction-step counts, coding lengths for sets/functions. |
| Formal Sciences | Mathematics | Algebra | Group Theory | Group order; element order; index of subgroup; dimension (for Lie groups); number of generators; length of relation words; degree of permutation representation; matrix size in linear representations. |
| Formal Sciences | Mathematics | Algebra | Ring Theory | Degree of polynomial; norm/valuation (in valuation rings); dimension (Krull dimension); index of ideal; multiplicative order (in some finite rings); determinant/trace (for matrix rings); characteristic; size of generating sets. |
| Formal Sciences | Mathematics | Algebra | Field Theory | Extension degree; characteristic; valuation magnitude; ramification index; discriminant size; residue degree; order of automorphism groups; polynomial degree; norm and trace values; embedding count. |
| Formal Sciences | Mathematics | Algebra | Module Theory | Rank (if meaningful); minimal number of generators; length of composition series; dimension over a field; torsion order; homological dimensions (projective/injective/flat); matrix size in module presentations; Betti numbers. |
| Formal Sciences | Mathematics | Algebra | Linear Algebra | Vector norms; matrix norms; determinant magnitude; rank value; condition number; eigenvalue magnitude; angle between vectors; projection coefficients; singular values; numerical error bounds. |
| Formal Sciences | Mathematics | Algebra | Representation Theory | Dimension of representation; character values; multiplicities of irreducible components; rank of weight spaces; highest-weight parameters; matrix entries; norms in unitary representations; Casimir eigenvalues. |
| Formal Sciences | Mathematics | Algebra | Universal Algebra | Arity counts; number of operations; generator-set size; term-tree depth; congruence-class count; size of free algebras; identity-basis size; complexity of term reductions. |
| Formal Sciences | Mathematics | Algebra | Algebraic Combinatorics | Partition sizes; tableau shape parameters; polynomial degrees; eigenvalue magnitudes; multiplicities; generating-function coefficients; rank/dimension; path lengths in posets; Coxeter lengths. |
| Formal Sciences | Mathematics | Mathematical Analysis | Real Analysis | ε–δ tolerances; norms (Lᵖ norms, sup norm); derivative values; integral values; oscillation magnitude; measure of sets; convergence rate indicators; step size in approximations; partition mesh size; error bounds. |
| Formal Sciences | Mathematics | Mathematical Analysis | Complex Analysis | Magnitude ( |
| Formal Sciences | Mathematics | Mathematical Analysis | Functional Analysis | Norm values (‖x‖, ‖T‖); inner products; spectral radii; eigenvalues/eigenfrequencies; approximation error; dual-pairing values ⟨f,x⟩; variation magnitude; modulus of continuity; step size in discretizations; operator resolvent norms. |
| Formal Sciences | Mathematics | Mathematical Analysis | Harmonic Analysis | Frequency (Hz or rad/s equivalents); amplitude; phase; Lᵖ norms; energy (L² norm); convolution magnitude; wavelet-scale parameters; spectral density; multiplier values; oscillation measures. |
| Formal Sciences | Mathematics | Mathematical Analysis | Differential Equations (ODE/PDE) | Amplitude; frequency; time constants; spatial length scales; derivative magnitudes; energy norms (L², H¹); stability exponents (Lyapunov-type); step sizes (Δt, Δx); residual norms; spectral values (eigenvalues). |
| Formal Sciences | Mathematics | Geometry & Topology | Differential Geometry | Curvature values, metric coefficients, lengths, angles, volume, geodesic parameters, tensor components, coordinate derivatives. |
| Formal Sciences | Mathematics | Geometry & Topology | Algebraic Geometry | Degree, dimension, multiplicity, intersection number, cohomological dimension, characteristic of base field, rank of bundles, valuations. |
| Formal Sciences | Mathematics | Geometry & Topology | Metric Geometry | Distances, lengths, radii, diameters, Lipschitz constants, curvature bounds, covering radii, Gromov–Hausdorff distances. |
| Formal Sciences | Mathematics | Geometry & Topology | Point-Set Topology | Cardinality of bases, size of open covers, length of refinement chains, T0–T4 separation level, compactness via finite subcovers. |
| Formal Sciences | Mathematics | Geometry & Topology | Homotopy Theory | Homotopy-group values (\pi_n(X)); connectivity degree; cell dimensions; spectrum indices; lengths/positions in long exact sequences. |
| Formal Sciences | Mathematics | Geometry & Topology | Knot Theory | Crossing number, linking number, genus, braid index, polynomial invariant coefficients, hyperbolic volume, torsion values, Seifert-matrix entries. |
| Formal Sciences | Mathematics | Number Theory | Elementary Number Theory | Integer size, modulus value, prime factor exponents, gcd/lcm values, residue classes, arithmetic-function outputs, Diophantine parameter counts. |
| Formal Sciences | Mathematics | Number Theory | Algebraic Number Theory | Field degree, discriminant, ramification index (e), residue degree (f), valuations (v_p), norm/trace values, class number, unit rank. |
| Formal Sciences | Mathematics | Number Theory | Analytic Number Theory | Values of L(s); magnitudes of sums (\sum_{n\le x} a_n); growth rates; analytic error terms; modulus q; zero ordinates; partial-sum lengths; log-scale growth factors. |
| Formal Sciences | Mathematics | Number Theory | Arithmetic Geometry | Height values; discriminant; conductor; norm and trace from number fields; reduction prime p; valuations; ranks of Mordell–Weil groups; Selmer ranks; local invariants of fibers. |
| Formal Sciences | Mathematics | Number Theory | Modular and Automorphic Forms | Fourier coefficients (a_n); Hecke eigenvalues (\lambda_p); level (N); weight (k); conductor; local Satake parameters; L-function values (L(s)); spectral eigenvalues. |
| Formal Sciences | Mathematics | Number Theory | Transcendental Number Theory | Heights, degrees of algebraic numbers, approximation exponents, lower bounds for linear forms, error-term magnitudes, coefficients of auxiliary polynomials, evaluation points. |
| Social Sciences | Anthropology | Human Evolutionary Anthropology | Millimeters (morphology), ratios (indices), stable isotope δ¹³C/δ¹⁵N values, radiometric ages (ka/Ma), allele frequencies (%), population divergence times (kya), wear-pattern frequencies, artifact typology counts, cranial capacity (cc), biomechanical force estimates. | |
| Social Sciences | Anthropology | Kinship, Descent & Domestic Organization | Household counts; number of kin per ego; descent-depth metrics; marriage rates; residence-type frequencies; property-transfer values; time-use hours; fertility rates; kinship-term frequency; generational spacing (years); co-residence duration. | |
| Social Sciences | Anthropology | Ritual, Cultural Practice & Symbolic Systems | Frequency of ritual performance; number of participants; duration (minutes/hours/days); symbolic density (coded elements per unit time); gesture counts; narrative units; spatial dimensions of ritual areas; intensity ratings (ethnographer-coded); recurrence intervals (annual, life-cycle). | |
| Social Sciences | Anthropology | Subsistence Systems, Environment & Human Adaptation | Kilocalories; return rates (kcal/hour); biomass; herd size; yield per hectare; mobility distance (km); seasonality indices; biodiversity counts; soil-fertility values; water-volume estimates; isotopic ratios (δ¹³C, δ¹⁵N, δ¹⁸O); artifact frequencies; foraging-effort hours; energy expenditure measures. | |
| Social Sciences | Anthropology | Material Culture, Technology & Archaeological Interpretation | Metric dimensions (mm/cm); mass (g); artifact frequency counts; density per cubic meter of sediment; chemical concentration (ppm); isotopic ratios; hardness values; refit counts; spatial coordinates; radiometric ages (BP, ka); ceramic firing temperatures; residue absorbance values; tool-efficiency measures. | |
| Social Sciences | Anthropology | Ethnographic Method & Comparative Analysis | Frequencies of behaviors; coded thematic categories; duration of observed interactions; counts of social ties; spatial coordinates; narrative units; consensus indices; lexical frequency; time-allocation hours; comparative trait presence/absence; cultural domain salience scores. | |
| Social Sciences | Economics | Choice (Microeconomic Foundations) | Prices; quantities; income/wealth; hours worked; marginal utilities (inferred); elasticities; risk-aversion coefficients; discount factors; willingness-to-pay; marginal rates of substitution; marginal costs. | |
| Social Sciences | Economics | Interaction (Markets, Strategy & Mechanisms) | Prices, quantities, bids, payoffs, utilities (inferred), production costs, profits, wages, transaction counts, welfare metrics, surplus measures, probabilities of strategic types, market shares, match quality scores. | |
| Social Sciences | Economics | Aggregation & Dynamics (Macroeconomic Systems) | Real/nominal dollars; growth rates (%∆); inflation indexes; unemployment %; interest rates (nominal/real); productivity measures (TFP indexes); capital stock units; consumption/investment shares; fiscal/monetary ratios; credit aggregates; volatility metrics. | |
| Social Sciences | Geography (Human) | Spatial Patterns & Spatial Analysis | Coordinate pairs; meters/kilometers; population per area unit; density values; travel time (min); flow magnitudes (counts/time); spatial autocorrelation coefficients (Moran’s I, Geary’s C); clustering indices (Ripley’s K); accessibility scores; network centrality metrics; land-use percentages; raster pixel values. | |
| Social Sciences | Geography (Human) | Mobility, Flows & Connectivity | Flow volume (persons/hour, tons/day, packets/sec); travel time (minutes); travel cost; distance (km); latency (ms); centrality scores; connectivity indices; accessibility scores; path redundancy; mode shares (%); congestion levels; migration rates (per 1,000 population); OD-matrix cell values; network density; temporal frequency of flows. | |
| Social Sciences | Geography (Human) | Human–Environment Interaction & Landscape Modification | Land-cover percentages; NDVI/vegetation indices; soil nutrient concentrations; sediment load (mg/L); water-flow volume (m³/s); erosion rate (mm/yr); carbon emissions or sequestration (tons CO₂e); land-use transition counts; pollutant ppm values; temperature/precipitation metrics; deforestation rate (ha/yr); infrastructure footprint area; biodiversity richness indices. | |
| Social Sciences | Geography (Human) | Place, Territory & Spatial Experience | Frequencies of spatial practices; counts of boundary markers; perception scores; attachment indices; narrative-theme frequencies; spatial familiarity scores; visibility metrics; accessibility levels; density of symbolic elements; ratings of emotional valence; territory-control measures; distance or proximity values; spatial configuration descriptors. | |
| Social Sciences | Linguistics | Phonetics & Phonology | Milliseconds (duration), Hz (pitch, formants), dB (intensity), airflow volume, articulatory displacement units, phonotactic probability scores, tonal step levels, stress prominence ratings. | |
| Social Sciences | Linguistics | Morphology | Token and type frequency; distributional probability; paradigm-slot occupancy; morphological complexity scores; productivity indices; affix-attraction metrics; morphological regularity ratings. | |
| Social Sciences | Linguistics | Syntax | Acceptability ratings, reaction-time units, dependency-length counts, error rates, corpus frequency per million words, node counts in trees, feature-value distributions, branching metrics, constraint-violation scores. | |
| Social Sciences | Linguistics | Semantics | Truth-value outcomes (true/false), acceptability scales, similarity ratings, scalar-implicature rates, entailment validity scores, reaction-time units, ERP/FMRI activation metrics for semantic anomalies. | |
| Social Sciences | Linguistics | Pragmatics | Acceptability ratings; interpretation-choice frequencies; discourse-coherence scores; referent identification accuracy; response latency; scalar-implicature rates; contextual-success measures; eye-tracking fixation counts. | |
| Social Sciences | Political Science | Political Institutions & Formal Political Order | Legislative seats; veto thresholds; constitutional index scores; judicial independence scores; bureaucratic capacity ratings; regime-type indicators (Freedom House, Polity); rule-of-law indexes; centralization metrics; amendment frequency; executive decree counts; party fragmentation indexes. | |
| Social Sciences | Political Science | Political Behavior, Mobilization & Collective Action | Percent turnout; vote shares; protest counts; crowd-size estimates; participation rates; donation amounts; ideological scale scores; identity salience indices; network centrality metrics; grievance indicators; mobilization thresholds; sentiment scores. | |
| Social Sciences | Political Science | Governance, Policy Formation & State Capacity | Regulatory-quality scores; corruption indices; bureaucratic capacity ratings; fiscal extraction ratios; policy-output counts; implementation-compliance percentages; service-delivery metrics (coverage, timeliness, quality); administrative-turnover rates; crisis-response speed; procurement-efficiency scores. | |
| Social Sciences | Political Science | International Relations & Global Order | Military expenditure (USD); troop numbers; GDP/trade volumes; sanctions severity indices; conflict intensity scores; alliance-depth metrics; IO voting similarity indexes; territorial-dispute severity; power-distribution metrics; reputation scores; diplomatic frequency counts. | |
| Social Sciences | Psychology | Cognitive Processes & Mental Architecture | Milliseconds (RT), accuracy scores, memory strength indices, attentional-allocation percentages, confidence ratings, decision thresholds, effect sizes, error magnitudes, eye-movement metrics. | |
| Social Sciences | Psychology | Learning, Conditioning & Behavioral Mechanisms | Response counts, response latency (ms), reinforcement magnitude, reinforcement probability, error rates, learning-rate parameters, associative-strength values, extinction duration, discrimination accuracy percentages. | |
| Social Sciences | Psychology | Emotion, Motivation & Affect Regulation | Arousal indices, valence scales, heart-rate change (bpm), galvanic skin response units, cortisol concentrations, emotion-intensity ratings, reaction-time delays, approach-avoidance distances, regulation-success scores. | |
| Social Sciences | Psychology | Development, Individual Differences & Psychometrics | Standard scores, percentile ranks, factor scores, item difficulty parameters, discrimination parameters, developmental age-equivalent units, reliability coefficients, error variances, growth-model slopes/intercepts. | |
| Social Sciences | Sociology | Social Interaction Mechanisms | Interaction frequency, duration, turn-taking intervals, emotional-intensity ratings, response latency, degree of alignment/misalignment, face-threat severity, norm-salience scores. | |
| Social Sciences | Sociology | Social Structure Mechanisms | Income brackets; wealth quantiles; occupational prestige scores; education levels; mobility rates; inequality indices (Gini, Theil); access scores; rule-enforcement frequencies; demographic proportions. | |
| Social Sciences | Sociology | Social Network & Relational Dynamics | Degree counts; betweenness/closeness/eigenvector scores; tie weights; frequency intervals; diffusion speed; clustering coefficients; reciprocity rates; network density; structural equivalence indices. |