This section specifies the fundamental attributes that the entities of each field are allowed to have and vary. For every science, it lists the core quantities and traits—mass, charge, temperature, curvature, genotype, fitness, preference, utility, authority, centrality, etc.—that define the state of its basic objects and enter into its laws. These are the properties that can be measured, compared, conserved, transformed, or selected over time. Together with Entities, this row fixes the internal “state space” of each discipline: once you know what kinds of things exist and which properties they can bear, you know what it means for a system in that field to change, remain stable, interact, or be explained at all.
Science Analysis Template
Below are the results of cycles 1 & 2 of The Science Project
THE SEVEN UNIVERSAL PROPERTY-CATEGORIES
These seven categories describe the full space of admissible properties in any scientific domain. Every item in the table is an instance of one or more of these categories. Nothing in any science falls outside them. They are the “coordinate system” of ontology.
- Magnitude → “How much?”
- Structure → “How arranged?”
- Dynamics → “How does it change?”
- Interaction → “What influences what?”
- Constraint → “What is allowed?”
- Information → “What is known or encoded?”
- Evaluation → “What is better or worse?”
1. Magnitude
Formal Definition
A magnitude property assigns a quantitative value to an entity or configuration, representing “how much” of some dimension exists.
Functional Role
Magnitudes establish scale, intensity, or quantity. They let a science measure, compare, and compute differences or gradients.
Examples Across Sciences
- Physics: mass, energy, charge, velocity
- Chemistry: concentration, bond energy
- Biology: metabolic rate, fitness value
- Economics: income, consumption level
- Sociology: inequality level, group size
- Formal sciences: cardinality, length of proof, complexity class
Why It’s Universal
You cannot analyze behavior, change, or structure without amount. Magnitude is the foundational axis of all state-description.
Ontological Implication
What a science treats as real is what it can quantify.
Value Types
Magnitude observables fall into a small set of forms. Treat these as mutually exclusive Value Types.
A. Level (state level at a time)
A quantity at a specific timepoint.
- Examples: population at t, money stock at t, capital stock at t
B. Period-total (integral over a window)
A quantity accumulated over an interval.
- Examples: total output in Q1, total consumption in 2024, total births in a year
C. Rate (per unit time)
A quantity normalized by time.
- Examples: inflation per year, job creation per month, migration per day
D. Density / Intensity (per unit of something else)
A quantity normalized by population, area, capital, etc.
- Examples: GDP per capita, energy per square mile, cases per 100k
E. Index / normalized magnitude (dimensionless)
A scaled magnitude relative to a baseline.
- Examples: CPI index, output index (2015=100)
2. Structure
Formal Definition
A structural property describes the arrangement, form, organization, or pattern of elements within a system.
Functional Role
Structure explains constraints, affordances, and invariants. It encodes shape, relationships, and configuration.
Examples Across Sciences
- Physics: lattice structure, field geometry
- Chemistry: molecular geometry, symmetry group
- Biology: DNA sequence, tissue architecture
- Linguistics: syntactic trees, morphological patterns
- Society: network topology, institutional architecture
- Math: algebraic structure, topological space
Why It’s Universal
Systems behave differently based on how parts are arranged. Without structure, magnitude is meaningless.
Ontological Implication
Entities are recognized by the relational patterns that persist when other features vary.
3. Dynamics
Formal Definition
A dynamic property describes change over time—rates, processes, trajectories, or temporal evolution.
Functional Role
Dynamics generate predictions. They encode how a system moves, grows, decays, oscillates, or stabilizes.
Examples Across Sciences
- Physics: velocity, acceleration, decay rate
- Biology: growth rate, mutation rate, flux
- Ecology: turnover rate, nutrient cycling
- Economics: inflation inertia, adjustment speed
- Politics: regime stability, mobilization rate
- Formal sciences: convergence rate, recurrence, algorithmic runtime
Why It’s Universal
Without dynamics, a science cannot explain why or how anything happens.
Ontological Implication
Only variables that can evolve or drive evolution become part of a domain’s causal ontology.
4. Interaction
Formal Definition
An interaction property captures how components influence one another—forces, couplings, incentives, communication, or feedback.
Functional Role
Interaction binds systems. It enables causal networks, strategic behavior, correlations, and propagation of effects.
Examples Across Sciences
- Physics: gravitational force, electromagnetic coupling
- Chemistry: reaction pathways, bonding affinities
- Biology: signaling strength, predation pressure
- Economics: strategic complementarities, externalities
- Sociology: tie strength, influence, reciprocity
- Math: operator action, correlation structure
Why It’s Universal
No system exists in isolation. Interaction produces structure, organizes dynamics, and generates emergent behavior.
Ontological Implication
A science’s worldview is defined by the kinds of interactions it recognizes and models.
5. Constraint
Formal Definition
A constraint property limits what a system can do—boundaries, capacities, permissible states, conservation rules, feasibility regions.
Functional Role
Constraints determine the shape of the possibility space. They define what the system cannot violate.
Examples Across Sciences
- Physics: conservation laws, stability regions, energy barriers
- Biology: carrying capacity, developmental constraints
- Ecology: resource limits, habitat constraints
- Economics: budget constraints, institutional veto points
- Sociology: role expectations, norms, legal frameworks
- Mathematics: admissibility, well-posedness, domain restrictions
Why It’s Universal
Without constraints, prediction collapses. All explanatory systems need a defined boundary of feasible behavior.
Ontological Implication
A scientific ontology is as much about forbidden states as permitted ones.
6. Information
Formal Definition
An information property concerns uncertainty, complexity, signal content, noise, definability, or descriptive resolution.
Functional Role
Information governs prediction accuracy, strategic behavior, inference, learning, and communication.
Examples Across Sciences
- Physics: entropy, coherence, noise
- Biology: genetic information, signal fidelity
- Economics: beliefs, expectations, information quality
- Psychology: memory strength, perception accuracy
- Sociology: communication density, clarity of norms
- Formal sciences: complexity classes, definability, descriptive depth
Why It’s Universal
Every science must address what can be known, encoded, predicted, or communicated.
Ontological Implication
Many entities are defined by the information they carry rather than their material composition.
7. Evaluation
Formal Definition
An evaluative property assigns a value, quality, desirability, or normative ranking to states or outcomes.
Functional Role
Evaluation orients optimization, adaptation, selection, and decision-making—either biologically or institutionally.
Examples Across Sciences
- Biology: fitness, reproductive success
- Ecology: resilience, stability
- Economics: welfare, efficiency
- Politics: legitimacy, governance quality
- Sociology: cohesion, fairness
- Engineering: optimality, cost
- Math/logic: minimality, optimality, proof elegance
Why It’s Universal
All systems—natural, social, or formal—imply criteria that distinguish better from worse configurations.
Ontological Implication
A science’s hidden worldview is encoded in what it treats as improvement, stability, efficiency, or fitness.
| Element | ||||
|---|---|---|---|---|
| Scope Category | ||||
| Sub-Item | Properties | |||
| Science Name Link | Branch Name Link | Field Name Link | Definition | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). |
| Natural Sciences | Physics | Classical Physics | Classical Mechanics | Core properties include mass, position, velocity, acceleration, momentum, energy, angular momentum, and forces. These quantities fully describe a system’s physical state. |
| Natural Sciences | Physics | Classical Physics | Classical Electromagnetism | Charge magnitude and sign, field strength and direction, permittivity, permeability, conductivity, potential, flux, wave frequency and wavelength, and energy/momentum densities (e.g., Poynting vector). |
| Natural Sciences | Physics | Classical Physics | Classical Thermodynamics | State variables including temperature, pressure, volume, internal energy, entropy, enthalpy, Gibbs and Helmholtz free energies, heat capacity, chemical potential. |
| Natural Sciences | Physics | Classical Physics | Statistical Mechanics (Classical) | Particle positions, momenta, energies, interactions (potentials), volume, temperature, pressure, entropy, distribution functions, and ensemble-averaged quantities. |
| Natural Sciences | Physics | Classical Physics | Optics (Classical Wave Theory) | Wavelength, frequency, amplitude, phase, polarization, refractive index, coherence length, intensity, propagation direction, and material optical constants. |
| Natural Sciences | Physics | Classical Physics | Acoustics | Sound speed, density, compressibility, bulk modulus, pressure amplitude, frequency, wavelength, phase, intensity, impedance, and attenuation coefficients. |
| Natural Sciences | Physics | Classical Physics | Continuum Mechanics | Density, velocity, pressure, temperature, deformation, stress, strain, viscosity, elasticity, compressibility, stiffness, and other material parameters describing how the continuum responds to applied forces. |
| Natural Sciences | Physics | Classical Physics | Classical Field Theory | Field strength, field direction, potential, energy density, momentum density, sources, boundary values, coupling constants, propagation speed, and continuity or differentiability of field values. |
| Natural Sciences | Physics | Classical Physics | Pre-Relativistic Frameworks | Mass, position, velocity, acceleration, force, potential energy, absolute time, absolute spatial coordinates, classical field strength, mechanical momentum, and classical wave speed through a medium or ether. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Mechanics | Quantized energy levels, probability distributions, spin values, quantum numbers, expectation values, coherence, phase, superposition, uncertainty relations, and transition amplitudes. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Relativistic Quantum Mechanics | Rest mass, relativistic energy, momentum, spin, charge, probability currents, and relativistic invariants such as proper time and invariant mass. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Special Relativity | Rest mass, energy, momentum, velocity, spacetime interval, proper time, simultaneity structure, Lorentz invariance, and the invariant speed of light. |
| Natural Sciences | Physics | Modern & Fundamental Physics | General Relativity | Curvature, metric structure, proper time, geodesic deviation, gravitational redshift, event horizons, stress-energy components, and invariants such as scalar curvature. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Field Theory (QFT) | Mass, charge, spin, coupling strengths, quantum numbers, field amplitudes, symmetry properties, decay rates, interaction probabilities, and vacuum expectation values. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Particle Physics (High-Energy Physics) | Mass, charge, spin, color charge, weak isospin, hypercharge, decay rates, lifetimes, coupling strengths, and conserved quantum numbers such as baryon and lepton number. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Nuclear Physics | Mass number, atomic number, binding energy, spin, parity, magnetic moments, nuclear energy levels, decay half-lives, cross-sections, and reaction probabilities. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Statistical Physics | Quantum statistics (Bose-Einstein or Fermi-Dirac), chemical potential, entropy, heat capacity, coherence, superfluid fraction, correlation lengths, degeneracy pressure, emergent quasiparticle properties, and phase coherence. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Optics | Photon number, phase, coherence, polarization, frequency, intensity at the quantum scale, quantum noise characteristics, entanglement strength, Rabi frequencies, and cavity quality factors. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Information Science | Coherence time, gate fidelity, entanglement measures, error rates, quantum channel capacity, quantum state purity, measurement probabilities, noise characteristics, and logical-qubit robustness. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Symmetry & Group Theory | Group structure, dimensionality, commutation relations, representation type, invariance properties, conserved charges, eigenvalue spectra, and algebraic structure of generators. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Gauge Theory | Gauge charges, coupling strengths, representation labels, particle masses, field strength values, and gauge redundancy. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | String Theory | Tension of strings, allowed vibration modes, dimensionality of objects, coupling strengths, geometric properties of compact dimensions, conserved charges, and supersymmetry-related attributes in some versions. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Differential Geometry in Physics | Smoothness, continuity, curvature values, connection rules, lengths and distances determined by geometric structure, and transformation behavior under coordinate change. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Statistical Field Theory | Correlation lengths, susceptibilities, fluctuation sizes, coupling strengths, noise amplitudes, and coarse-grained field values characterizing system behavior. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Mathematical Foundations of Quantum Mechanics | Linearity, completeness of state spaces, operator domains, spectral properties, probability rules, and transformation behavior under symmetry or measurement operations. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | General Mathematical Physics | Properties include continuity, differentiability, symmetry characteristics, algebraic relations, boundary behavior, stability, and structural features defined by the mathematical model. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Solid-State Physics | Charge, spin, effective mass, band energies, lattice spacing, symmetry properties, conductivity, mobility, and interaction strengths. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Semiconductor Physics | Charge, mobility, effective mass, carrier lifetime, band gap energy, recombination rate, dielectric constant, and optical absorption characteristics. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Magnetism & Spin Physics | Spin magnitude, magnetic moment, exchange strength, anisotropy, magnetization, coercivity, susceptibility, and relaxation times. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Superconductivity | Critical temperature, critical field, coherence length, penetration depth, zero resistance, energy gap, flux quantization, and vortex mobility. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Soft Matter Physics | Viscosity, elasticity, surface tension, bending stiffness, interaction strength, relaxation time, volume fraction, and structural order or disorder. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Nanomaterials & Nanostructures | Size, shape, surface area, surface charge, surface chemistry, confinement effects, optical response, mechanical strength, thermal behavior, and electronic states. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Strongly Correlated Electron Systems | Correlation strength, effective mass, charge order, spin order, energy gap types, coherence scale, susceptibility, and response to temperature or doping. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Topological Matter | Topological invariants, band connectivity, robustness to disorder, edge conduction, chirality, quantized response properties, and protected boundary behavior. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Materials Science (Physical Perspective) | Mechanical strength, elasticity, plasticity, thermal conductivity, electrical conductivity, magnetic response, optical properties, phase stability, and defect energies. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Stellar Astrophysics | Mass, radius, luminosity, temperature, density, composition, magnetic field strength, rotation rate, fusion rate, instability modes, and lifetime. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Galactic Astrophysics | Mass distribution, rotation speed, metallicity, star formation rate, temperature of gas phases, density, velocity dispersion, magnetic field strength, and dark matter content. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Extragalactic Astrophysics | Luminosity, mass, star formation rate, metallicity, redshift, morphology, velocity dispersion, gas content, cluster mass, and activity level of central black holes. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Cosmology | Density, temperature, expansion rate, curvature, composition fractions, fluctuation amplitude, horizon size, growth rate of structure, and redshift. |
| Natural Sciences | Physics | Astrophysics & Cosmology | High-Energy Astrophysics | Energy, luminosity, magnetic field strength, particle spectra, variability timescales, jet power, compact object mass, spin, and radiation hardness. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Gravitational Astrophysics | Mass, radius, density, composition, temperature, albedo, atmospheric pressure, orbital parameters, surface gravity, magnetic field strength, and internal heat flow. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Planetary Science & Exoplanets | Mass, radius, density, temperature, albedo, composition, atmospheric pressure, orbital period, eccentricity, inclination, surface gravity, magnetic field strength, and internal heat flow. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrochemistry & Interstellar Medium Physics | Density, temperature, ionization fraction, molecular abundance, dust composition, extinction, radiation flux, chemical reaction rates, and magnetic field strength. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrobiology | Chemical complexity, metabolic pathways, energy availability, environmental tolerance ranges, atmospheric composition, solvent properties, and surface or subsurface chemical gradients. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fluid Dynamics | Density, viscosity, pressure, velocity, temperature, compressibility, vorticity, and energy content. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Hydrodynamics (Ideal Fluids) | Conductivity, density, pressure, velocity, magnetic field strength, electric current, viscosity, resistivity, temperature, and plasma beta. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Magnetohydrodynamics (MHD) | Density, pressure, conductivity, resistivity, temperature, velocity, magnetic field strength, electric field strength, viscosity, and plasma beta. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Plasma Physics (General) | Charge density, temperature, conductivity, collision frequency, magnetization, electric and magnetic field strength, plasma frequency, gyration frequency, and ionization fraction. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Space & Astrophysical Plasmas | Density, temperature, charge state, magnetic field strength, electric field strength, flow velocity, plasma beta, collision frequency, ionization fraction, and energy distribution. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fusion Plasma Physics | Temperature, density, charge state, confinement time, magnetic field strength, electric field strength, collision frequency, ionization fraction, fusion reaction rate, and transport coefficients. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Computational Fluid & Plasma Physics | Density, velocity, temperature, pressure, electric and magnetic fields, distribution functions, numerical fluxes, stability properties, error levels, and convergence behavior. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Non-Newtonian & Complex Fluids | Viscosity, relaxation time, elasticity, yield stress, shear-thinning index, shear-thickening strength, thixotropic decay rate, particle concentration, microstructure orientation, and strain-dependent modulus. |
| Natural Sciences | Physics | Plasma & Fluid Physics | High-Energy-Density Physics (HEDP) | Pressure, temperature, density, ionization fraction, opacity, conductivity, equation-of-state parameters, radiation energy density, shock strength, and compression ratio. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Biophysics | Charge, mass, binding affinity, diffusion coefficient, elasticity, viscosity, membrane potential, conformational state, energy consumption rate, and reaction kinetics. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Medical Physics | Energy, attenuation coefficient, stopping power, scattering cross section, decay rate, dose, field strength, spatial resolution, contrast, signal to noise ratio, and biological effectiveness. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Geophysics | Density, elasticity, viscosity, temperature, pressure, magnetic susceptibility, electrical conductivity, porosity, permeability, attenuation, seismic velocity, and gravitational potential. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Optics & Photonics | Wavelength, frequency, polarization, phase, intensity, coherence, refractive index, absorption, scattering, dispersion, nonlinear susceptibility, and quantum statistical properties such as photon number distributions. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Computational Physics | Energy, momentum, position, velocity, charge density, field amplitude, coupling constants, interaction potentials, numerical stability bounds, and discretization accuracy. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Engineering Physics | Mass, stiffness, conductivity, permittivity, permeability, strength, thermal capacity, damping, stress, strain, efficiency, frequency response, energy density, and material microstructure. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Chemical Physics | Mass, charge, spin, bond length, bond angle, ionization energy, electron affinity, polarizability, reaction barrier height, diffusion coefficient, dipole moment, and vibrational frequency. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Environmental & Climate Physics | Temperature, pressure, humidity, albedo, emissivity, heat capacity, density, radiative forcing strength, optical depth, salinity, wind speed, turbulence intensity, and greenhouse gas concentration. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Applied Materials Physics | Elastic modulus, hardness, conductivity, resistivity, band gap, magnetization, coercivity, refractive index, thermal conductivity, diffusivity, defect density, fracture toughness, and phase stability. |
| Natural Sciences | Chemistry | Physical Chemistry | Quantum Chemistry | Spin, charge, mass, orbital energies, electron density, symmetry, correlation energy, quantum numbers. |
| Natural Sciences | Chemistry | Physical Chemistry | Statistical Mechanics | Energy, momentum, configuration, degeneracy, probability weights, conserved quantities, statistical correlations. |
| Natural Sciences | Chemistry | Physical Chemistry | Thermodynamics | Temperature, pressure, volume, entropy, energy, enthalpy, free energies, chemical potentials, heat capacities. |
| Natural Sciences | Chemistry | Physical Chemistry | Kinetics & Reaction Dynamics | Activation energy, rate constants, reaction cross-sections, molecular energies, orientation factors, collision frequencies. |
| Natural Sciences | Chemistry | Physical Chemistry | Spectroscopy | Energy levels, frequencies, intensities, linewidths, transition probabilities, symmetry properties, oscillator strengths. |
| Natural Sciences | Chemistry | Physical Chemistry | Electrochemistry | Redox potentials, charge, conductivity, current, overpotential, ionic mobility, diffusion coefficients, electric fields, chemical activities. |
| Natural Sciences | Chemistry | Physical Chemistry | Surface & Interface Science | Surface energy, surface tension, work function, adsorption energy, charge distribution, wettability, electronic states, catalytic activity. |
| Natural Sciences | Chemistry | Physical Chemistry | Colloid & Solution Chemistry | Charge, zeta potential, solubility, ionic strength, polarity, surface tension, particle size, shape, hydrophobicity, dielectric properties. |
| Natural Sciences | Chemistry | Physical Chemistry | Chemical Physics | Energy levels, molecular geometry, charges, spins, dipole moments, force constants, interaction potentials, scattering cross-sections. |
| Natural Sciences | Chemistry | Organic Chemistry | Structural & Mechanistic Organic Chemistry | Electronegativity, bond strength, steric hindrance, electron density, polarity, charge distribution, resonance stabilization, orbital energies. |
| Natural Sciences | Chemistry | Organic Chemistry | Stereochemistry & Conformational Analysis | Chirality, configuration (R/S), conformation (gauche/anti), axial/equatorial preferences, torsional strain, steric hindrance, dipole interactions, stereoelectronic effects. |
| Natural Sciences | Chemistry | Organic Chemistry | Synthetic Organic Chemistry | Reactivity, selectivity, functional-group compatibility, stereochemical stability, oxidation state, acidity/basicity, nucleophilicity/electrophilicity, steric/electronic profiles. |
| Natural Sciences | Chemistry | Organic Chemistry | Physical Organic Chemistry | Acidity/basicity, nucleophilicity/electrophilicity, charge density, resonance stabilization, polarizability, steric demand, bond strengths, solvation energies, activation parameters. |
| Natural Sciences | Chemistry | Organic Chemistry | Organometallic Organic Chemistry | Oxidation state, electron count, coordination number, ligand field strength, bond energies, metal–carbon bond polarity, steric profiles, redox potentials, migratory aptitude. |
| Natural Sciences | Chemistry | Organic Chemistry | Polymer Chemistry (Carbon-based) | Molecular weight, dispersity, chain length, tacticity, crystallinity, glass transition temperature, melting point, chain mobility, polarity, branching density. |
| Natural Sciences | Chemistry | Organic Chemistry | Bioorganic Chemistry | Chirality, stereoelectronic preferences, acidity/basicity, redox characteristics, hydrogen-bonding capacity, hydrophobicity, conformational flexibility, biochemical compatibility/reactivity. |
| Natural Sciences | Chemistry | Organic Chemistry | Natural Products Chemistry | Stereochemical complexity, functional-group density, bioactivity, solubility, oxidation state, hydrogen-bonding patterns, conformational constraints, stability in biological environments. |
| Natural Sciences | Chemistry | Organic Chemistry | Medicinal Chemistry | Affinity, potency, selectivity, lipophilicity, solubility, permeability, metabolic stability, toxicity, stereochemistry, conformational preferences, redox characteristics. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Main-Group Chemistry | Electronegativity, oxidation state, valence electron count, acidity/basicity, polarity, Lewis acidity, hybridization tendencies, cluster electron counts, bonding preferences. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Transition-Metal Chemistry | Oxidation state, spin state, ligand field strength, magnetic moment, covalency/ionicity, electron count, backbonding ability, redox potential, coordination number, geometrical preferences. |
| Natural Sciences | Chemistry | Inorganic Chemistry | f-Block Chemistry | Oxidation states, ionic radii trends (lanthanide contraction), magnetic moments, spectroscopic transitions (Laporte-forbidden f–f), covalency (more pronounced in actinides), redox potentials, coordination numbers. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Coordination Chemistry | Coordination number, denticity, ligand field strength, electron count, spin state, stability constants, redox potentials, geometry, covalency/ionicity, Jahn–Teller distortion propensity. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Solid-State Chemistry | Bandgap, lattice energy, coordination environment, symmetry, conductivity, magnetism, hardness, thermal stability, defect concentration, dielectric properties, vibrational modes. |
| Natural Sciences | Chemistry | Analytical Chemistry | Qualitative Analysis | Spectral fingerprints, chemical reactivity, solubility, color/precipitate formation, redox behavior, functional-group presence, ion–ligand interactions, mass/charge patterns. |
| Natural Sciences | Chemistry | Analytical Chemistry | Quantitative Analysis | Concentration, absorbance, signal intensity, slope/sensitivity, linearity, precision, accuracy, bias, limit of detection (LOD), limit of quantification (LOQ), uncertainty, matrix effects. |
| Natural Sciences | Chemistry | Analytical Chemistry | Separation Science | Polarity, charge, hydrophobicity/hydrophilicity, size, mass, diffusion coefficients, partition coefficients (K), electrophoretic mobility, affinity, volatility, adsorption strength. |
| Natural Sciences | Chemistry | Analytical Chemistry | Instrumental Analysis | Absorbance, emission intensity, mass/charge ratio, retention time, signal intensity, resolution, noise level, selectivity, response factor, sensitivity, dynamic range, drift characteristics. |
| Natural Sciences | Chemistry | Biochemistry | Structural Biochemistry | Charge distribution, hydrophobicity, stereochemistry, secondary-structure propensity, conformational stability, flexibility/rigidity, binding affinity, surface topology, molecular shape. |
| Natural Sciences | Chemistry | Biochemistry | Enzymology | Catalytic efficiency (kcat/Km), binding affinity, turnover rate, specificity, allosteric responsiveness, thermodynamic stability, protonation states, redox states, conformational dynamics. |
| Natural Sciences | Chemistry | Biochemistry | Metabolism & Bioenergetics | Gibbs free energy (ΔG), redox potential, flux rate, phosphorylation potential, concentration gradients, proton motive force (PMF), binding affinity, catalytic efficiency, thermodynamic coupling strength. |
| Natural Sciences | Chemistry | Biochemistry | Molecular Biology & Gene Expression | Base-pair identity, sequence-specific binding affinity, transcription rate, translation efficiency, epigenetic modification state, chromatin accessibility, RNA stability, codon usage bias, regulatory strength. |
| Natural Sciences | Chemistry | Biochemistry | Cellular Biochemistry | Concentration, localization, turnover rate, binding affinity, membrane potential, pH of compartments, redox state, metabolite flux, viscosity, crowding, ionic strength, macromolecular interactions, structural stability. |
| Natural Sciences | Chemistry | Biochemistry | Membrane Biochemistry | Fluidity, curvature, charge asymmetry, thickness, permeability, lateral diffusion, phase behavior, lipid composition, protein insertion topology, membrane potential, elastic modulus, domain formation propensity. |
| Natural Sciences | Chemistry | Biochemistry | Protein Chemistry | Charge, hydrophobicity, pKa values, stereochemistry, stability (ΔG_fold), solubility, reactivity, redox state, conformational flexibility, aggregation propensity, binding affinity, modification state. |
| Natural Sciences | Chemistry | Biochemistry | Biochemical Genetics | Catalytic efficiency, binding affinity, enzyme stability, PTM susceptibility, metabolite abundance, allele penetrance, expressivity, biochemical flux, mutation severity, genotype–phenotype strength. |
| Natural Sciences | Earth & Space Sciences | Geology | Mineralogy & Crystallography | Hardness, cleavage, color, luster, refractive index, density, crystal symmetry, lattice parameters, bond strength, optical behavior, electrical conductivity, magnetic properties, thermal expansion. |
| Natural Sciences | Earth & Space Sciences | Geology | Petrology | Mineral proportions, grain size, texture, fabric, modal composition, bulk chemistry, density, porosity, permeability, degree of metamorphism, melt fraction, volatile content, reaction progress, reactivity. |
| Natural Sciences | Earth & Space Sciences | Geology | Structural Geology & Tectonics | Stress, strain, viscosity, strength, rheology, displacement, slip rate, orientation, symmetry, anisotropy, cohesion/friction, strain rate, competency, ductility/brittleness, mechanical layering. |
| Natural Sciences | Earth & Space Sciences | Geology | Sedimentology & Stratigraphy | Grain size, sorting, roundness, porosity, permeability, composition, cohesion, bed thickness, lamination, sediment flux, flow velocity, facies attributes, accommodation, subsidence rate, sedimentation rate. |
| Natural Sciences | Earth & Space Sciences | Geology | Geomorphology | Slope, curvature, roughness, shear stress, sediment flux, erodibility, cohesion, porosity, permeability, discharge, uplift rate, precipitation rate, grain size, channel width/depth, flow velocity, ice thickness, soil strength. |
| Natural Sciences | Earth & Space Sciences | Geology | Geophysics | Seismic velocity, density, magnetization, electrical resistivity, thermal conductivity, heat production, attenuation (Q), anisotropy, viscosity, strain rate, wave amplitude, acceleration, gravity anomalies. |
| Natural Sciences | Earth & Space Sciences | Geology | Geochemistry | Concentration, activity, pH, Eh, ionic strength, solubility, diffusivity, partition coefficients, isotope ratios, binding energies, redox state, thermodynamic potentials (G, μ), equilibrium constants, reaction rates. |
| Natural Sciences | Earth & Space Sciences | Geology | Paleontology | Morphology, size, ornamentation, phylogenetic characters, preservational state, chemical composition, isotopic signatures, abundance, diversity, ecological traits, functional attributes, stratigraphic position. |
| Natural Sciences | Earth & Space Sciences | Geology | Hydrogeology | Hydraulic conductivity, transmissivity, storativity, porosity, permeability, head, gradient, recharge rate, discharge rate, groundwater velocity, saturation, specific yield, dispersion coefficients, water quality parameters. |
| Natural Sciences | Earth & Space Sciences | Geology | Economic & Applied Geology | Grade, tonnage, concentration, permeability, porosity, fracture density, reservoir quality, thermal gradient, alteration style, mineral associations, metal tenor, ore textures, fluid composition, pressure, temperature. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Dynamic Meteorology | Attributes include velocity, density, temperature, pressure, vorticity, stability parameters, moisture content, and buoyancy. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Thermodynamic Meteorology | Temperature, potential temperature, moisture content, specific humidity, mixing ratio, heat capacity, latent heat, buoyancy, lapse rates, saturation properties, and radiative emissivity. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Cloud Physics & Microphysics | Size, mass, shape, density, phase, fall speed, charge, hygroscopicity, refractive index, nucleation efficiency, freezing/melting properties, and collision–coalescence tendencies. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Synoptic & Mesoscale Meteorology | Temperature gradients, pressure fields, humidity distributions, vorticity, divergence, vertical velocity, wind shear, CAPE/CIN, frontal slope, baroclinicity, stability indices, and mesoscale forcing parameters. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Atmospheric Physics & Chemistry | Chemical concentration, absorption cross-sections, refractive index, radiative flux, energy states, reaction rates, lifetime, optical depth, scattering properties, and thermodynamic variables such as temperature and pressure. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Climatology & Climate Dynamics | Global temperature, radiative forcing, ocean heat content, albedo, greenhouse-gas concentrations, climate sensitivity, heat transport, humidity distributions, circulation indices, and multi-scale variability metrics. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Physical Oceanography | Temperature, salinity, density, velocity, shear, turbulence intensity, buoyancy, heat content, salt content, mixed-layer depth, pressure, sea-surface height, viscosity, diffusivity. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Chemical Oceanography | Concentration, activity, pH, alkalinity, redox potential, solubility, complexation strength, residence time, saturation state, isotope ratios, speciation fractions, ligand-binding constants. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Biological Oceanography | Biomass, growth rate, productivity, respiration, nutrient uptake, stoichiometry, grazing rate, diversity, size spectra, metabolic rate, elemental composition (C:N:P ratios), physiological traits, motility, mortality. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Geological Oceanography | Grain size, composition, sorting, mineralogy, sedimentation rate, accumulation rate, porosity, density, magnetic properties, chemical composition, isotope ratios, thermal gradients, tectonic stress. |
| Natural Sciences | Biology | Molecular Biology | Nucleic Acid Biology | Sequence identity, base-pairing specificity, chemical reactivity, helical form (A/B/Z), methylation status, folding potential, thermodynamic stability, susceptibility to damage, and capacity to encode information. |
| Natural Sciences | Biology | Molecular Biology | Gene Regulation & Epigenetics | Binding affinity, transcriptional activity, chromatin accessibility, methylation levels, histone-modification states, nucleosome positioning, cooperative factor binding, and regulatory plasticity across conditions or cell types. |
| Natural Sciences | Biology | Molecular Biology | Protein Biology | Sequence identity, charge distribution, hydrophobicity, folding stability, catalytic activity, binding affinity, conformational flexibility, allosteric behavior, dynamic transitions, and PTM states. |
| Natural Sciences | Biology | Molecular Biology | Molecular Complexes & Information Flow | Stoichiometry, assembly state, interaction strength, conformational flexibility, information throughput, catalytic capacity, modularity, spatial localization, allosteric coupling, and signal-to-noise fidelity. |
| Natural Sciences | Biology | Molecular Biology | Molecular Methods & Technologies | Sensitivity, specificity, resolution, throughput, fidelity, reaction kinetics, probe intensity, enzymatic efficiency, labeling accuracy, signal-to-noise ratio, and compatibility with biological samples. |
| Natural Sciences | Biology | Cell Biology | Cell Structure & Organelles | Morphology, membrane composition, protein content, lumenal environment, polarity, mechanical stiffness, pH gradients, ion conditions, dynamic remodeling capacity. |
| Natural Sciences | Biology | Cell Biology | Cellular Dynamics & Trafficking | Directionality, velocity, processivity, diffusion coefficients, binding affinities, membrane curvature, fusion competence, compartment identity markers, energy dependence, pH or ion properties of trafficking compartments. |
| Natural Sciences | Biology | Cell Biology | Cell Signaling & Communication | Binding affinity, signal strength, amplification potential, phosphorylation state, activation thresholds, diffusion rates, residence times, conformational states, cooperativity, spatial localization, and feedback sensitivity. |
| Natural Sciences | Biology | Cell Biology | Cell Cycle, Fate & Death | Proliferative capacity, checkpoint sensitivity, differentiation potential, chromatin accessibility, metabolic state, DNA integrity, damage load, apoptotic threshold, mitochondrial outer-membrane permeabilization sensitivity, lineage-specific transcriptional signatures. |
| Natural Sciences | Biology | Cell Biology | Cell Interactions & Microenvironment | Adhesion strength, matrix stiffness, ligand density, mechanical compliance, spatial gradients, ECM composition, tension, porosity, receptor expression levels, niche-factor concentration, diffusion profiles, remodeling rates. |
| Natural Sciences | Biology | Cell Biology | Cell Morphology & Motility | Polymerization rate, depolymerization rate, filament stiffness, adhesion strength, contractility, cortical tension, membrane elasticity, polarity state, diffusion coefficients of regulators, protrusion velocity, traction force. |
| Natural Sciences | Biology | Genetics & Evolution | Classical & Transmission Genetics | Allelic state, dominance, segregation ratio, recombination frequency, penetrance, expressivity, linkage distance. |
| Natural Sciences | Biology | Genetics & Evolution | Population Genetics | Allele and genotype frequencies, fitness, selection coefficients (s, h), mutation rate, migration rate, inbreeding coefficient (F), Ne, variance in reproductive success, linkage disequilibrium. |
| Natural Sciences | Biology | Genetics & Evolution | Quantitative Genetics | Trait means, variances, covariances, heritabilities (h², H²), genetic correlations, selection gradients, breeding values, residual variance, additive effect sizes, epistatic interactions, G-matrix structure. |
| Natural Sciences | Biology | Genetics & Evolution | Genomic Evolution & Comparative Genomics | Sequence identity, divergence rates, substitution rates (dN/dS), GC content, genome size, gene-copy number, synteny conservation, mutation spectrum, recombination rate, structural-variation frequency, phylogenetic distances. |
| Natural Sciences | Biology | Genetics & Evolution | Phylogenetics & Systematics | Character states, sequence differences, morphological variation, branch lengths, monophyly, synapomorphies, homoplasy levels, divergence times, taxonomic ranks, tree topology. |
| Natural Sciences | Biology | Genetics & Evolution | Macroevolution & Speciation Theory | Speciation rate, extinction rate, diversification rate, morphological disparity, ecological opportunity, reproductive isolation strength, biogeographic range structure, tempo (gradual vs punctuated), mode (anagenesis vs cladogenesis). |
| Natural Sciences | Biology | Physiology | Cellular & Tissue Physiology | Membrane potential, permeability, stiffness, elasticity, contractility, ion gradients, receptor sensitivity, mechanical tension, transport capacity, and tissue compliance. |
| Natural Sciences | Biology | Physiology | Neurophysiology | Membrane potential, conductance, ion permeability, firing threshold, neurotransmitter concentration, synaptic strength, refractory periods, excitability, and transmission probability. |
| Natural Sciences | Biology | Physiology | Endocrine & Regulatory Physiology | Hormone concentration, receptor affinity, secretion rate, half-life, signal amplification, feedback sensitivity, metabolic effect strength, and rhythmicity (e.g., circadian release patterns). |
| Natural Sciences | Biology | Physiology | Cardiovascular & Respiratory Physiology | Pressure, flow, resistance, compliance, elasticity, oxygen content, CO₂ content, ventilation rate, perfusion rate, cardiac output, stroke volume, airway resistance, and blood-gas partial pressures. |
| Natural Sciences | Biology | Physiology | Metabolic & Energetic Physiology | Metabolic rate, substrate availability, ATP turnover, oxygen consumption, heat production, redox state, fuel preference, pH, and thermodynamic efficiency. |
| Natural Sciences | Biology | Physiology | Renal, Fluid & Homeostatic Physiology | Filtration rate, reabsorption fraction, secretion rate, osmolarity, pH, electrolyte concentration, fluid volume, oncotic pressure, hydrostatic pressure, and permeability. |
| Natural Sciences | Biology | Developmental Biology | Cell Fate & Lineage Specification | Potency levels, gene-expression states, chromatin accessibility, signaling responsiveness, lineage biases, epigenetic marks, regulatory thresholds, positional identity, time-dependent competence windows. |
| Natural Sciences | Biology | Developmental Biology | Pattern Formation & Embryonic Axes | Concentration, diffusion coefficient, degradation rate, signaling-response thresholds, positional identity values, oscillation frequency (segmentation clock), polarity states, symmetry-breaking bias, spatial competence windows. |
| Natural Sciences | Biology | Developmental Biology | Morphogenesis & Tissue-Level Mechanics | Tension, pressure, viscosity, elasticity, contractility, adhesion strength, stiffness, cell polarity, tissue curvature, strain rate, shear stress, mechanical anisotropy. |
| Natural Sciences | Biology | Developmental Biology | Organogenesis & Multi-Tissue Assembly | Tissue identity, inductive potential, mechanical stiffness, adhesion profiles, spatial polarity, lumen pressure, branching frequency, compartment boundaries, pattern anisotropy, cross-tissue signaling responsiveness. |
| Natural Sciences | Biology | Developmental Biology | Growth, Timing, Regeneration & Life-Cycle Transitions | Growth rate, proliferation capacity, regenerative potential, timing thresholds, hormone concentration, metabolic state, circadian phase, differentiation status, senescence markers, life-stage identity. |
| Natural Sciences | Biology | Developmental Biology | Evolutionary Development (Evo–Devo) | Developmental modularity, pleiotropy, constraint, evolvability, heterochronic timing, spatial deployment of developmental programs, regulatory sensitivity, morphological plasticity, conservation of regulatory motifs. |
| Natural Sciences | Biology | Ecology | Organismal Ecology | Morphology, metabolic rate, thermal tolerance, sensory capability, behavioral patterns, water balance, energetic requirements, stress responses, locomotion ability, and environmental preference ranges. |
| Natural Sciences | Biology | Ecology | Population Ecology | Population size, density, growth rate, carrying capacity, survival rates, fecundity, age distribution, dispersal probability, recruitment, mortality patterns, and demographic elasticity. |
| Natural Sciences | Biology | Ecology | Community Ecology | Species abundance, interaction strength, diversity metrics, trophic position, niche breadth, resource consumption rates, recruitment success, and sensitivity to biotic and abiotic filters. |
| Natural Sciences | Biology | Ecology | Ecosystem Ecology | Productivity, energy flow rates, nutrient concentrations, decomposition rates, assimilation efficiency, turnover time, stoichiometry, storage capacity, and stability/resilience of pools and fluxes. |
| Natural Sciences | Biology | Ecology | Landscape & Spatial Ecology | Patch size, shape, edge density, connectivity, fragmentation level, dispersal distance, spatial autocorrelation, heterogeneity metrics, barrier strength, and landscape permeability. |
| Natural Sciences | Biology | Ecology | Global Ecology & Earth-System Interactions | Productivity at global scales, carbon fluxes, greenhouse-gas concentrations, albedo, aerosol load, evaporation and precipitation patterns, nutrient cycling rates, climate sensitivity, and Earth-system stability metrics. |
| Formal Sciences | Logic | Proof Theory | Proof Calculi | Well-formedness, admissibility, derivability, proof height, proof length, structural position, rule applicability, substitution behavior. |
| Formal Sciences | Logic | Proof Theory | Structural Proof Theory | Structural positions, admissibility, derivability, proof height, proof width, normalization behavior, context sensitivity, permutation behavior of rules. |
| Formal Sciences | Logic | Proof Theory | Proof Theory of Non-Classical Logics | Resource usage, polarity, accessibility, valuation multiplicity (many-valued), relevance constraints, structural-rule admissibility, normalization behavior, cut properties, context sensitivity. |
| Formal Sciences | Logic | Proof Theory | Ordinal & Strength Analysis | Well-foundedness, order type, transfinite rank, reflection height, induction strength, consistency strength, reducibility, ordinal collapsing behavior, recursion-theoretic growth rates. |
| Formal Sciences | Logic | Proof Theory | Proof Complexity | Proof length, proof size, width, space, depth, degree (in algebraic systems), rank, automatizability, p-simulation relationships, lower-bound hardness, derivation structure, branching complexity. |
| Formal Sciences | Logic | Proof Theory | Automated & Interactive Reasoning | Satisfiability, validity, proof completeness, solver soundness, search depth, heuristic strength, tactic correctness, termination, convergence of search, model consistency, constraint propagation behavior. |
| Formal Sciences | Logic | Model Theory | Structures, Languages & Interpretations | Arity, interpretation of symbols, definability, satisfaction, isomorphism type, elementary equivalence, and preservation properties under embeddings. |
| Formal Sciences | Logic | Model Theory | Satisfaction & Definability Theory | Definability status, truth values under assignments, closure under definable operations, arity, quantifier complexity, stability under elementary equivalence. |
| Formal Sciences | Logic | Model Theory | Quantifier Theory & Model Completeness | Quantifier complexity, alternation depth, preservation behavior under embeddings, definability strength, expressiveness, model completeness, quantifier elimination success/failure. |
| Formal Sciences | Logic | Model Theory | Classification Theory | Stability, simplicity, NIP/SOP status, rank values, definability of types, canonicity of independence, saturation degrees, homogeneity patterns. |
| Formal Sciences | Logic | Model Theory | Tame / O-Minimal Model Theory | Tameness, monotonicity, definability, stratification, cell decomposition behavior, continuity of definable functions, dimension invariants. |
| Formal Sciences | Logic | Set Theory | Axiomatic Foundations & Cumulative Hierarchy | Well-foundedness, membership relations, rank, transfinite height, cardinality, definability within stages, closure under ZFC operations, regularity, extensionality. |
| Formal Sciences | Logic | Set Theory | Constructibility & Inner Models | Definability, minimality, absoluteness, coherence across levels, fine-structure ranks, canonical well-orderings, condensation, elementary substructure properties. |
| Formal Sciences | Logic | Set Theory | Large Cardinal Theory | Strength, reflection, indescribability, closure under definability, embedding critical point, height, consistency strength, combinatorial consequences (tree properties, partition relations). |
| Formal Sciences | Logic | Set Theory | Forcing & Independence Theory | Genericity, preservation, absoluteness, chain conditions (ccc, properness), closure properties, cardinal preservation, definability, forcing equivalence, independence strength. |
| Formal Sciences | Logic | Set Theory | Descriptive Set Theory | Definability level, measurability, Baire property, perfect set property, complexity (Borel rank, projective level), reducibility degrees, regularity properties under determinacy. |
| Formal Sciences | Logic | Computability Theory | Models of Computation & Recursive Function Theory | Computability, partiality, halting, divergence, function totality, reduction behavior, recursion depth, normalization, determinism or nondeterminism, effective enumerability. |
| Formal Sciences | Logic | Computability Theory | Recursively Enumerable (r.e.) Sets & Degrees | Enumerability, partiality, reducibility strength, completeness, degree equivalence, jump operator behavior, monotonicity under reductions, injury levels, limit approximations, density or sparsity of enumerations. |
| Formal Sciences | Logic | Computability Theory | Reducibility & Degrees of Unsolvability | Relative computability, completeness, reducibility strength, degree equivalence, closure under reductions, monotonicity of jumps, existence of incomparable degrees, structural density or gaps. |
| Formal Sciences | Logic | Computability Theory | Arithmetical & Analytical Hierarchies | Quantifier complexity, definability rank, reducibility hardness, completeness, closure properties, monotonicity under jump operators, stability under relativization, inclusion relationships (Σₙ ⊆ Σₙ₊₁). |
| Formal Sciences | Mathematics | Algebra | Group Theory | Associativity, identity, invertibility, closure, order of element, group order, normality, commutativity (in Abelian groups), conjugation properties, homomorphic images/kernels, orbit and stabilizer properties. |
| Formal Sciences | Mathematics | Algebra | Ring Theory | Additive commutativity, associativity, distributivity, presence/absence of multiplicative identity, commutativity of multiplication (in commutative rings), presence of units, factorization properties (UFD, PID), characteristic, nilpotence, integrality. |
| Formal Sciences | Mathematics | Algebra | Field Theory | Commutativity of addition and multiplication, distributivity, existence of inverses, characteristic, extension degree, algebraicity/transcendence, normality, separability, completeness (for valued fields), residue fields. |
| Formal Sciences | Mathematics | Algebra | Module Theory | Bilinearity, distributivity, associativity of scalar action, existence of kernels and cokernels, torsion, rank, projectivity, injectivity, flatness, exactness, annihilation behavior, decomposition properties. |
| Formal Sciences | Mathematics | Algebra | Linear Algebra | Linearity (additivity + scalar multiplication), dimension, independence, spanning, invertibility, orthogonality, norms, rank, determinant, spectral properties, singularity, stability under linear combinations. |
| Formal Sciences | Mathematics | Algebra | Representation Theory | Linearity of action; invariance of subspaces; reducibility/irreducibility; complete reducibility (in semisimple settings); character orthogonality relations; weight-space decomposition; Schur’s Lemma properties; highest/lowest weights; multiplicities. |
| Formal Sciences | Mathematics | Algebra | Universal Algebra | Closure under operations; satisfaction of identities; homomorphic images; subalgebra closure; congruence permutability/modularity; existence of free objects; equational definability; algebraic invariants dependent solely on operations and identities. |
| Formal Sciences | Mathematics | Algebra | Algebraic Combinatorics | Ordering relations; symmetry; multiplicities; enumeration parameters; dimension counts; eigenvalues of combinatorial matrices; weight and root structures; combinatorial statistics (inversions, descents, major index); algebraic invariants (Schur positivity, unimodality). |
| Formal Sciences | Mathematics | Mathematical Analysis | Real Analysis | Continuity, uniform continuity, differentiability, integrability, convergence (pointwise, uniform, almost everywhere), measurability, boundedness, completeness, compactness, total variation, Lipschitz behavior, monotonicity. |
| Formal Sciences | Mathematics | Mathematical Analysis | Complex Analysis | Holomorphy, Cauchy–Riemann equations, complex differentiability, analyticity, conformality, harmonicity, residue values, meromorphy, isolated singularities, growth rates, boundedness, normal families, compactness in domain geometry. |
| Formal Sciences | Mathematics | Mathematical Analysis | Functional Analysis | Normability, completeness, orthogonality, boundedness, continuity, compactness, spectrum type (point, continuous, residual), convergence modes (strong, weak, weak-*), reflexivity, uniform boundedness, linearity, self-adjointness, positivity, unitarity. |
| Formal Sciences | Mathematics | Mathematical Analysis | Harmonic Analysis | Linearity, convolution structure, orthogonality, decay of coefficients, boundedness of operators, regularity/smoothness, oscillation, frequency localization, integrability, spectral support, invariance under translation/rotation/group action. |
| Formal Sciences | Mathematics | Mathematical Analysis | Differential Equations (ODE/PDE) | Linearity vs nonlinearity; order of equation; ellipticity, parabolicity, hyperbolicity; regularity/smoothness; stability; uniqueness; existence; blow-up behavior; conservation laws; dissipation; invariants; symmetry properties; well-posedness. |
| Formal Sciences | Mathematics | Geometry & Topology | Differential Geometry | Smoothness, differentiability class, curvature, torsion, metric structure, parallel transport behavior, orientation, volume forms, geodesic completeness. |
| Formal Sciences | Mathematics | Geometry & Topology | Algebraic Geometry | Dimension, smoothness/singularity, irreducibility, integrality, degree, cohomological invariants, birational type, local ring structure, positivity properties (ampleness, nefness). |
| Formal Sciences | Mathematics | Geometry & Topology | Metric Geometry | Distances, lengths, geodesicity, curvature bounds (via triangle comparison), diameters, Lipschitz constants, injectivity radius, doubling properties, bounded turning, completeness. |
| Formal Sciences | Mathematics | Geometry & Topology | Point-Set Topology | Openness, closedness, compactness, connectedness, Hausdorff property, regularity, normality, completeness (in metric contexts), convergence behavior of nets/filters. |
| Formal Sciences | Mathematics | Geometry & Topology | Homotopy Theory | Homotopy invariance, contractibility, connectivity, fundamental group behavior, higher homotopy groups, long exact sequences, lifting properties, stability phenomena. |
| Formal Sciences | Mathematics | Geometry & Topology | Knot Theory | Crossing number, linking number, knot invariants, chirality, fiberedness, genus, Alexander polynomial, Jones polynomial, signature, hyperbolic volume, complement topology. |
| Formal Sciences | Mathematics | Number Theory | Elementary Number Theory | Divisibility, primality, gcd/lcm structure, modular equivalence, multiplicative structure, order mod n, residue behavior, parity, factorization uniqueness. |
| Formal Sciences | Mathematics | Number Theory | Algebraic Number Theory | Degree of extensions, discriminant, ramification behavior, splitting of primes, ideal class numbers, unit rank, norm/trace values, residue field characteristics, integrality, local/global solvability. |
| Formal Sciences | Mathematics | Number Theory | Analytic Number Theory | Analytic continuation, functional equations, zero distributions, asymptotic behavior, mean values, error terms, orthogonality relations, Euler-product factorization, growth rates. |
| Formal Sciences | Mathematics | Number Theory | Arithmetic Geometry | Rational solvability, integrality, reduction types, good/bad reduction, height growth, local–global compatibility, behavior under specialization, Galois action on cohomology, Diophantine obstructions (e.g., Brauer–Manin). |
| Formal Sciences | Mathematics | Number Theory | Modular and Automorphic Forms | Automorphy, holomorphy, weight, level, character, growth conditions, eigenvalue structure, Hecke multiplicativity, L-function analytic continuation, functional equations, representation-theoretic decompositions. |
| Formal Sciences | Mathematics | Number Theory | Transcendental Number Theory | Transcendence, algebraic independence, approximation strength, irrationality measure, lower bounds for linear forms, nonvanishing constraints, complexity of algebraic relations. |
| Social Sciences | Anthropology | Human Evolutionary Anthropology | Morphology; genetic variation; fitness; life-history traits; locomotion; diet; tool use; ecological adaptation; cranial capacity; behavioral repertoires; phenotypic plasticity; population structure; reproductive success metrics. | |
| Social Sciences | Anthropology | Kinship, Descent & Domestic Organization | Relatedness, authority, inheritance rights, marital ties, caregiving obligations, residence patterns (patrilocal, matrilocal, neolocal), descent rules (patrilineal, matrilineal, bilateral), generational depth, kinship terminology, gendered divisions of labor, household stability. | |
| Social Sciences | Anthropology | Ritual, Cultural Practice & Symbolic Systems | Symbolic meaning; performativity; sacredness/profanity; emotional intensity; social cohesion; structural patterning; encoded values; repetition; transformation; embodiment; communicative force; mnemonic durability; interpretive flexibility. | |
| Social Sciences | Anthropology | Subsistence Systems, Environment & Human Adaptation | Productivity, seasonality, risk, resilience, efficiency, sustainability, mobility, labor demands, caloric return, storage capacity, ecological variability, patchiness, biodiversity, demographic pressure, technological intensity. | |
| Social Sciences | Anthropology | Material Culture, Technology & Archaeological Interpretation | Material composition, durability, wear patterns, technological complexity, production cost, functional attributes, stylistic traits, depositional context, spatial association, taphonomic alteration, transformation sequences, cultural transmission pathways. | |
| Social Sciences | Anthropology | Ethnographic Method & Comparative Analysis | Lived experience, perspective, meaning, normativity, variability, social structure, context dependence, communicative practice, behavioral regularity, cultural patterning, interpretive coherence, symbolic expression. | |
| Social Sciences | Economics | Choice (Microeconomic Foundations) | Completeness, transitivity, continuity, convexity (preferences); risk aversion, prudence, impatience; diminishing marginal utility; technological productivity; costs; beliefs; information quality; optimization behavior (first-order conditions, KKT conditions). | |
| Social Sciences | Economics | Interaction (Markets, Strategy & Mechanisms) | Strategic rationality; incentive compatibility; dominance; best-response structure; equilibrium existence; stability; efficiency; information conditions; externalities; complementarities or substitutability; market thickness; coordination properties; monotonicity in mechanism outcomes. | |
| Social Sciences | Economics | Aggregation & Dynamics (Macroeconomic Systems) | Aggregability; stability/instability; dynamic adjustment; persistence; cyclicality; growth rate; inflation inertia; propagation mechanisms; rigidities (price, wage, financial); expectations formation (rational, adaptive). | |
| Social Sciences | Geography (Human) | Spatial Patterns & Spatial Analysis | Distance, density, clustering, dispersion, connectivity, accessibility, centrality, spatial autocorrelation, spatial anisotropy, heterogeneity, scale dependence, spatial gradients, directionality, contiguity, adjacency. | |
| Social Sciences | Geography (Human) | Mobility, Flows & Connectivity | Speed, cost, frequency, directionality, volume, latency, congestion, capacity, connectivity, accessibility, resilience, centrality, reach, flow intensity, path dependence, friction of distance, time–space compression. | |
| Social Sciences | Geography (Human) | Human–Environment Interaction & Landscape Modification | Productivity, resilience, vulnerability, carrying capacity, ecological diversity, soil fertility, hydrological stability, energy flows, pollution loads, erosion intensity, landscape connectivity, disturbance magnitude, anthropogenic pressure, sustainability, environmental inertia, resource scarcity. | |
| Social Sciences | Geography (Human) | Place, Territory & Spatial Experience | Attachment, meaning, identity, belonging, exclusion, power, control, affordance, visibility, symbolic value, territoriality, memory, affect, spatial perception, orientation, enclosure, openness, accessibility, legibility. | |
| Social Sciences | Linguistics | Phonetics & Phonology | Voicing, nasality, place/manner of articulation, duration, pitch (F0), intensity, phonotactic legality, feature composition, syllable weight, stress prominence, tone category, prosodic boundary strength. | |
| Social Sciences | Linguistics | Morphology | Productivity, transparency, morphological complexity, compositionality, feature specification, paradigm completeness, regularity/irregularity, allomorphic alternation conditions, morphotactic constraints. | |
| Social Sciences | Linguistics | Syntax | Hierarchical structure, constituency, c-command, agreement relations, case assignment, word-order patterns, selectional properties, locality constraints, phase structure, derivational history. | |
| Social Sciences | Linguistics | Semantics | Truth conditions, entailment relations, semantic compatibility, selectional restrictions, argument structure, scope relations, monotonicity, reference stability, type requirements, aspectual class. | |
| Social Sciences | Linguistics | Pragmatics | Informativeness, relevance, politeness level, indirectness, felicity conditions, presuppositional strength, contextual fit, discourse coherence, speaker commitment, conversational implicature strength. | |
| Social Sciences | Political Science | Political Institutions & Formal Political Order | Authority allocation; rule enforcement; separation of powers; centralization vs decentralization; procedural transparency; accountability; stability vs volatility; institutional capacity; veto strength; agenda-setting power; legal legitimacy; institutional rigidity or adaptability. | |
| Social Sciences | Political Science | Political Behavior, Mobilization & Collective Action | Preferences; attitudes; partisanship; ideology; identity salience; social embeddedness; group norms; trust and cooperation; coordination capacity; grievance intensity; perceived efficacy; network connectivity; emotional activation; susceptibility to persuasion. | |
| Social Sciences | Political Science | Governance, Policy Formation & State Capacity | Administrative capacity; enforcement strength; corruption levels; bureaucratic professionalism; policy coherence; regulatory effectiveness; fiscal extraction ability; implementation fidelity; institutional resilience; coordination efficiency; organizational fragmentation or cohesion. | |
| Social Sciences | Political Science | International Relations & Global Order | Sovereignty; power (material, soft, institutional); credibility; commitment; interdependence; polarity; regime strength; compliance; deterrence capability; vulnerability; legitimacy; risk tolerance; strategic uncertainty; economic openness. | |
| Social Sciences | Psychology | Cognitive Processes & Mental Architecture | Capacity limits, processing speed, representational fidelity, attentional focus, memory strength, activation levels, cognitive load, decision thresholds, error rates, pattern-recognition accuracy. | |
| Social Sciences | Psychology | Learning, Conditioning & Behavioral Mechanisms | Response strength, reinforcement value, contingency strength, learning rate, generalization gradients, extinction resistance, habit strength, discriminability, latency, frequency, reward prediction error. | |
| Social Sciences | Psychology | Emotion, Motivation & Affect Regulation | Intensity, valence, arousal, motivational strength, persistence, regulation success, physiological activation, thresholds of emotional triggering, resilience, mood stability, hedonic value. | |
| Social Sciences | Psychology | Development, Individual Differences & Psychometrics | Stability, change, reliability, validity, trait levels, ability strengths, developmental rate, measurement error, factor loadings, item difficulty, discrimination, response thresholds, inter-individual variance. | |
| Social Sciences | Sociology | Social Interaction Mechanisms | Emotional states, role commitments, expectations, perceived legitimacy, social cues, interpretive frames, symbolic meanings, interactional power, situational clarity/ambiguity. | |
| Social Sciences | Sociology | Social Structure Mechanisms | Power differentials, resource distribution, role obligations, institutional authority, inequality levels, mobility rates, group boundaries, rule enforcement strength, structural opportunities/constraints. | |
| Social Sciences | Sociology | Social Network & Relational Dynamics | Tie strength, reciprocity, centrality, brokerage, cohesion, structural equivalence, multiplexity, clustering, transitivity, homophily, diffusion thresholds, relational stability/volatility. |