SAT – Domain – Entities

This section fixes what exists for each science at the most basic level. For every field, it lists the kinds of objects that are taken as primitive—particles, fields, bodies, molecules, cells, organisms, agents, institutions, symbols, mathematical structures, and so on. These are not just examples or convenient labels; they are the allowed building blocks of explanation in that domain. If something cannot be expressed in terms of these entities (or compositions of them), it does not properly belong to the field’s internal universe.

Within the Science Analysis Template, 1.2 – Entities sits directly after Boundaries and Scale: after you have said where a science applies and at what scale, this row forces you to say what the world is made of there. Each discipline therefore commits to a specific ontological palette—what counts as a “thing,” what can bear properties, what can enter into relations and processes. This makes the Science Map structurally tight: it prevents vague talk about “systems” and “variables” by requiring every model, law, and method downstream to be grounded in a clearly declared set of underlying entities.

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Science Analysis Template

Below are the results of cycles 1 & 2 of The Science Project

Across the entire Science Map, the Entities section reveals the deepest structural fact about how each discipline understands reality: every field commits to a specific set of “basic things” it treats as real, manipulable, and explanatory.
This section is not descriptive — it is ontological. It shows what must exist for the field’s models and explanations to make sense.

After a full review, here is the complete, clarified synthesis:

1. Each science selects a small set of primitive objects that define its world.

Physics commits to particles, fields, waves, and spacetime.
Chemistry commits to atoms, ions, molecules, bonds, and energy surfaces.
Biology commits to biomolecules, cells, tissues, organisms, and populations.
Social sciences commit to persons, groups, institutions, symbols, and relationships.
Formal sciences commit to abstract structures—sets, formulas, proofs, spaces, functions.

Across all domains, these entity sets function as ontological foundations: the “atoms” of each field’s conceptual universe.

2. These entity-sets are mutually exclusive and mutually supporting.

Physics does not assume cells or institutions exist.
Sociology does not assume electrons or manifolds exist.
Mathematics does not assume matter or energy exist.
Biology does not assume the Standard Model exists as part of its explanatory ontology (though it depends on it).
Economics does not assume chromosomes or quantum fields exist.

Each science is built from a limited ontology tailored to its aims, not from a universal kit.
This prevents fields from collapsing into one another and makes their explanatory power domain-specific.

3. The ontology determines the correct level of explanation.

Because each discipline defines what kinds of things “count,” it implicitly sets:

• what can interact,
• what processes are meaningful,
• what can be measured or modeled,
• what kinds of laws apply,
• what counts as a cause,
• what cannot be reduced further inside the field.

Examples:

• Population genetics cannot talk about “cells deciding” because its entities are alleles, genotypes, and populations.
• Classical mechanics cannot invoke “wavefunctions” because its entities are bodies and forces.
• Syntax cannot use “intentions” because its entities are syntactic categories, features, and structures.
• Cosmology cannot use “species” because its entities are matter fields, radiation fields, and large-scale structure.

The entity list is the filter that decides what explanations are valid.

4. Composite entities build upward, but only through the field’s own rules.

Many sciences accept hierarchical construction:

• Physics → atoms → molecules → materials → planets.
• Biology → molecules → cells → tissues → organs → organisms.
• Sociology → roles → interactions → networks → institutions → systems.

But each field only acknowledges composites built from its own primitives.
The ontology defines which compositions are legitimate and which are foreign or irrelevant.

5. Interdisciplinary fields expose joints between ontologies.

Biophysics, chemical physics, medical physics, geophysics, environmental physics, and other hybrids reveal where entity sets intersect:

• photons + tissues
• molecules + cells
• fields + rocks
• electrons + biological macromolecules
• particles + climate reservoirs
• fluids + planetary interiors

These hybrids work precisely because both sides’ ontologies remain cleanly defined. They operate at the boundary interface where one ontology becomes input to another.

6. Formal sciences provide ontology for reasoning itself.

The formal sciences do not describe the physical or social world; they describe the structure of explanation:

• proof objects
• formulas
• derivations
• functions
• sets
• types
• manifolds
• algebraic elements
• infinite hierarchies
• computable procedures

These entities are scale-free, material-free, and exist only as abstract objects.
They anchor the logical and mathematical backbone supporting all other sciences.

7. The resulting Science Map is ontologically partitioned and non-overlapping.

You now have an atlas where:

• Each science has its own primitive vocabulary.
• No science is defined by its topic alone — only by the entities it accepts as real.
• Boundaries, scales, and methods downstream all depend on these ontological choices.
• You can now distinguish when a field overreaches, when it reduces too far, or when it invokes entities outside its domain.

This is the core achievement:
the Science Project now possesses a full ontological foundation — a clean, non-redundant, interlocking set of entity types spanning every domain of knowledge.

			Element
			Scope Category	1.2 Ontological Commitments
			Sub-Item	Entities
Science Name Link	Branch Name Link	Field Name Link	Definition	The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.).
Natural Sciences	Physics	Classical Physics	Classical Mechanics	The domain assumes the existence of point-particles, rigid bodies, extended bodies, many-body systems, continuous media approximated classically, and celestial bodies treated as classical masses.
Natural Sciences	Physics	Classical Physics	Classical Electromagnetism	Point and distributed charges, current densities, electric fields E, magnetic fields B, electromagnetic waves, scalar and vector potentials (ϕ, A), and macroscopic media such as conductors and dielectrics.
Natural Sciences	Physics	Classical Physics	Classical Thermodynamics	Thermodynamic systems, surroundings, reservoirs, phases of matter, thermodynamic states, and macroscopic properties such as temperature, pressure, and volume.
Natural Sciences	Physics	Classical Physics	Statistical Mechanics (Classical)	Classical point particles with well-defined positions and momenta; ensembles of microstates; phase space; probability distributions; macroscopic observables derived from microscopic variables.
Natural Sciences	Physics	Classical Physics	Optics (Classical Wave Theory)	Electromagnetic waves, wavefronts, rays (as emergent approximations), media (air, glass, water), interfaces, coherence sources, optical fields (E, B), polarization states, and optical systems (lenses, apertures, gratings).
Natural Sciences	Physics	Classical Physics	Acoustics	Pressure fields, particle velocity fields, density fluctuations, sound sources, wavefronts, acoustic media (air, water, solids), boundaries, resonators, and modes of vibration.
Natural Sciences	Physics	Classical Physics	Continuum Mechanics	Continuous media such as fluids, solids, gels, foams, viscoelastic materials, material points, and infinitesimal volume elements used to describe deformation and flow.
Natural Sciences	Physics	Classical Physics	Classical Field Theory	Continuous fields defined over space and time, such as scalar fields, vector fields, tensor fields, potentials, sources like charge or mass distributions, and the spacetime backgrounds through which fields propagate.
Natural Sciences	Physics	Classical Physics	Pre-Relativistic Frameworks	Material particles, rigid bodies, continuous media, classical fields interpreted as disturbances in an assumed background (often the ether), forces acting instantaneously at a distance, and absolute frames of reference.
Natural Sciences	Physics	Modern & Fundamental Physics	Quantum Mechanics	Quantum states, wavefunctions, probability amplitudes, observables, operators, particles modeled as quantum objects, measurement outcomes, and potential energy landscapes.
Natural Sciences	Physics	Modern & Fundamental Physics	Relativistic Quantum Mechanics	Relativistic wavefunctions, spinor states, relativistic particles, antiparticles, conserved currents, and potentials consistent with Lorentz symmetry.
Natural Sciences	Physics	Modern & Fundamental Physics	Special Relativity	Inertial observers, spacetime events, worldlines, reference frames, light signals, particles with relativistic momentum, and spacetime intervals treated as fundamental geometric objects.
Natural Sciences	Physics	Modern & Fundamental Physics	General Relativity	Spacetime as a dynamic geometric structure, mass-energy distributions, worldlines, curvature fields, geodesics, gravitational waves, and stress-energy content of matter and radiation.
Natural Sciences	Physics	Modern & Fundamental Physics	Quantum Field Theory (QFT)	Quantum fields, particles as field excitations, vacuum states, virtual particles, interaction vertices, gauge fields, and conserved quantum numbers associated with symmetries.
Natural Sciences	Physics	Modern & Fundamental Physics	Particle Physics (High-Energy Physics)	Elementary particles, quantum fields, gauge bosons, quarks, leptons, neutrinos, antiparticles, virtual particles, and symmetry generators associated with the Standard Model.
Natural Sciences	Physics	Modern & Fundamental Physics	Nuclear Physics	Protons, neutrons, nuclei, nuclear force carriers, nuclear shells, isotopes, excited nuclear states, decay products, and compound nuclei formed during reactions.
Natural Sciences	Physics	Modern & Fundamental Physics	Quantum Statistical Physics	Indistinguishable particles, quantum states, occupation numbers, quasiparticles, condensates, superfluids, degenerate fermions, collective modes, and interacting many-body wavefunctions.
Natural Sciences	Physics	Modern & Fundamental Physics	Quantum Optics	Photons, quantized electromagnetic fields, atomic and molecular quantum states, cavity modes, nonclassical light states, entangled photon pairs, coherent states, squeezed states, and optical quasiparticles.
Natural Sciences	Physics	Modern & Fundamental Physics	Quantum Information Science	Qubits, quantum gates, entangled systems, quantum channels, error-correcting codes, quantum states, measurement operators, quantum sensors, and quantum communication links.
Natural Sciences	Physics	Theoretical & Mathematical Physics	Symmetry & Group Theory	Groups, algebras, representations, generators, symmetry operations, invariants, transformation rules, group actions on physical or mathematical spaces, and conserved quantities derived from symmetries.
Natural Sciences	Physics	Theoretical & Mathematical Physics	Gauge Theory	Gauge fields, matter fields, gauge bosons (photon, W, Z, gluon), auxiliary fields, ghost fields, spacetime background, and geometric structures used to define symmetry and interactions.
Natural Sciences	Physics	Theoretical & Mathematical Physics	String Theory	Strings, branes, extended objects of various dimensionalities, background spacetime, compact extra dimensions, fields living on branes, and dual descriptions such as gauge or gravity fields depending on the formulation.
Natural Sciences	Physics	Theoretical & Mathematical Physics	Differential Geometry in Physics	Smooth manifolds, points on manifolds, vector fields, differential forms, connections, curvature objects, geodesic paths, and geometric structures assigned to physical fields.
Natural Sciences	Physics	Theoretical & Mathematical Physics	Statistical Field Theory	Fields representing order parameters, fluctuating quantities, correlation functions, probability distributions, noise sources, and coarse-grained degrees of freedom that replace individual particle descriptions.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Mathematical Foundations of Quantum Mechanics	Abstract state vectors, operators, observables, probability measures, transformation rules, density operators, and mathematical structures such as algebras and spaces.
Natural Sciences	Physics	Condensed Matter & Materials Physics	General Mathematical Physics	Mathematical structures such as functions, fields, operators, manifolds, algebraic systems, categories, differential equations, and geometric objects used to represent physical systems.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Solid-State Physics	Lattice sites, atoms in periodic structures, electrons, holes, phonons, quasiparticles, crystal defects, energy bands, and collective modes.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Semiconductor Physics	Electrons, holes, dopant atoms, excitons, charge traps, phonons, electric fields, energy bands, and quasiparticles that represent effective carrier behavior in the solid.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Magnetism & Spin Physics	Spins, magnetic moments, magnetic domains, electrons, lattice ions, exchange interactions, spin waves, magnons, and external magnetic fields.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Superconductivity	Cooper pairs, quasiparticles, superconducting condensate, magnetic vortices, flux lines, lattice vibrations, and external magnetic or electric fields.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Soft Matter Physics	Polymers, micelles, colloidal particles, droplets, surfactants, filaments, networks, liquid crystal molecules, and biological macromolecules.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Nanomaterials & Nanostructures	Nanoparticles, thin films, nanotubes, nanowires, quantum dots, surfaces, interfaces, defects, adsorbed molecules, and fields interacting with nanoscale objects.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Strongly Correlated Electron Systems	Strongly interacting electrons, localized moments, quasiparticles with renormalized mass, collective modes, spin or charge textures, lattice ions, and external fields influencing correlated behavior.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Topological Matter	Bulk bands, edge states, surface states, quasiparticles, topological defects, Berry curvature structures, nodes, domain boundaries, and external fields that probe topological response.
Natural Sciences	Physics	Condensed Matter & Materials Physics	Materials Science (Physical Perspective)	Atoms, ions, electrons, defects, grains, phases, microstructures, interfaces, dislocations, vacancies, clusters, and external fields that influence material behavior.
Natural Sciences	Physics	Astrophysics & Cosmology	Stellar Astrophysics	Stars, stellar cores, envelopes, magnetic fields, plasma, photons, neutrinos, nuclear species, convection zones, radiative zones, shock fronts, and compact remnants such as white dwarfs, neutron stars, and stellar mass black holes.
Natural Sciences	Physics	Astrophysics & Cosmology	Galactic Astrophysics	Stars, gas clouds, dust, magnetic fields, cosmic rays, molecular clouds, spiral arms, dark matter halos, star clusters, black holes, and interstellar medium components.
Natural Sciences	Physics	Astrophysics & Cosmology	Extragalactic Astrophysics	External galaxies, galaxy clusters, dark matter halos, intergalactic gas, active galactic nuclei, jets, starburst galaxies, merging galaxies, cosmic filaments, and large scale gravitational structures.
Natural Sciences	Physics	Astrophysics & Cosmology	Cosmology	Space, time, matter, radiation, dark matter, dark energy, cosmic background radiation, baryons, neutrinos, primordial fluctuations, cosmic structures, and cosmological fields.
Natural Sciences	Physics	Astrophysics & Cosmology	High-Energy Astrophysics	Compact objects, accretion disks, relativistic particles, magnetic fields, shock fronts, jets, high energy photons, cosmic rays, pair plasmas, and extreme states of matter such as degenerate matter or quark matter.
Natural Sciences	Physics	Astrophysics & Cosmology	Gravitational Astrophysics	Planets, moons, atmospheres, surfaces, interiors, mantles, cores, magnetic fields, rings, minor bodies, exoplanets, debris disks, and external influences such as host stars or stellar radiation.
Natural Sciences	Physics	Astrophysics & Cosmology	Planetary Science & Exoplanets	Planets, moons, atmospheres, surfaces, cores, mantles, magnetic fields, ring systems, minor bodies, exoplanets, debris disks, and external influences such as host stars and stellar radiation.
Natural Sciences	Physics	Astrophysics & Cosmology	Astrochemistry & Interstellar Medium Physics	Atoms, ions, molecules, radicals, dust grains, polycyclic aromatic hydrocarbons, interstellar radiation fields, cosmic rays, magnetic fields, gas clouds, shock fronts, and diffuse, dense, or ionized ISM phases.
Natural Sciences	Physics	Astrophysics & Cosmology	Astrobiology	Molecules, prebiotic precursors, microbial life, potential extraterrestrial life forms, biosignature gases, organic compounds, planetary environments, energy sources, water or solvent systems, and geochemical substrates.
Natural Sciences	Physics	Plasma & Fluid Physics	Fluid Dynamics	Fluids (liquids and gases), flow fields, velocity fields, pressure fields, vorticity structures, shock fronts, boundaries, and external forces such as gravity or rotation.
Natural Sciences	Physics	Plasma & Fluid Physics	Hydrodynamics (Ideal Fluids)	Conducting fluids, plasma, ions, electrons, magnetic fields, electric fields, current densities, pressure fields, vorticity fields, shock fronts, and wave modes such as Alfvén or magnetosonic waves.
Natural Sciences	Physics	Plasma & Fluid Physics	Magnetohydrodynamics (MHD)	Conducting fluids, ions, electrons, plasma, magnetic fields, electric fields, currents, vorticity structures, shocks, wave modes, flux tubes, and current sheets.
Natural Sciences	Physics	Plasma & Fluid Physics	Plasma Physics (General)	Ions, electrons, neutral particles, electromagnetic fields, currents, waves, collective modes, charge separation regions, shocks, double layers, and plasma boundaries.
Natural Sciences	Physics	Plasma & Fluid Physics	Space & Astrophysical Plasmas	Ions, electrons, neutral particles, current sheets, shocks, magnetic fields, electric fields, plasma waves, turbulence structures, reconnection regions, filaments, and astrophysical boundaries such as magnetopauses or termination shocks.
Natural Sciences	Physics	Plasma & Fluid Physics	Fusion Plasma Physics	Ions, electrons, neutral particles, fusion fuel species, electromagnetic fields, current channels, turbulence structures, edge and core plasma regions, divertors, and plasma boundary layers.
Natural Sciences	Physics	Plasma & Fluid Physics	Computational Fluid & Plasma Physics	Numerical grid cells, particles (in particle methods), field variables, boundary conditions, turbulence structures, waves, shocks, reconnection sites, and discretized representations of fluids or plasmas.
Natural Sciences	Physics	Plasma & Fluid Physics	Non-Newtonian & Complex Fluids	Macromolecules, polymer chains, suspended particles, micelles, droplets, colloids, gels, granular elements, networks, solvent molecules, and internal structural degrees of freedom such as orientation or stretch.
Natural Sciences	Physics	Plasma & Fluid Physics	High-Energy-Density Physics (HEDP)	Electrons, ions, radiation fields, shock fronts, ablation fronts, compressed materials, highly ionized atoms, dense plasmas, radiation-driven waves, instabilities such as Rayleigh-Taylor or Richtmyer-Meshkov, and mixed-phase states of matter.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Biophysics	Biomolecules, proteins, DNA, RNA, lipids, cells, membranes, cytoskeletal elements, ion channels, molecular motors, mechanical forces, energy fields, neural signals, and biological macroscopic structures.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Medical Physics	Photons, electrons, protons, neutrons, radionuclides, electromagnetic fields, radiation beams, detectors, tissue-equivalent materials, imaging contrast agents, dose distributions, and therapeutic devices.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Geophysics	Rocks, minerals, melts, fluids, seismic waves, faults, plates, mantle convection cells, magnetic fields, gravity fields, heat fluxes, volcanic systems, ice sheets, groundwater, sediment layers, and crust–mantle–core structural layers.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Optics & Photonics	Photons, electromagnetic fields, optical modes, wavefronts, beams, pulses, mirrors, lenses, gratings, nonlinear media, optical fibers, detectors, emitters, and quantum states of light.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Computational Physics	Particles, fields, grid cells, lattice sites, wavefunctions, probability densities, solver variables, boundary conditions, numerical fluxes, discrete operators, and physical constants encoded in algorithms.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Engineering Physics	Materials, structures, devices, sensors, actuators, particles, fields, forces, circuits, control elements, energy carriers, fluids, thermal pathways, wave modes, engineered components, and system-level assemblies governed by physical laws.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Chemical Physics	Electrons, nuclei, atoms, molecules, radicals, ions, phonons, photons, intermolecular potentials, reaction coordinates, transition states, energy surfaces, and condensed-phase environments.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Environmental & Climate Physics	Atmospheric gases, aerosols, water vapor, clouds, ocean water masses, sea ice, land surfaces, radiation fields, greenhouse gases, heat fluxes, circulation cells, pressure systems, and energy reservoirs.
Natural Sciences	Physics	Interdisciplinary & Applied Physics	Applied Materials Physics	Atoms, ions, electrons, lattice structures, defects, dislocations, grains, phases, phonons, magnons, excitons, quasiparticles, interfaces, surfaces, microstructural features, and functional material domains.
Natural Sciences	Chemistry	Physical Chemistry	Quantum Chemistry	Wavefunctions, electrons, nuclei, atomic/molecular orbitals, basis sets, potential energy surfaces, quantized states.
Natural Sciences	Chemistry	Physical Chemistry	Statistical Mechanics	Microstates, particles, ensembles, phase-space points, energy levels, probability distributions, constraints.
Natural Sciences	Chemistry	Physical Chemistry	Thermodynamics	Thermodynamic systems, surroundings, reservoirs, phases, interfaces, macrostates.
Natural Sciences	Chemistry	Physical Chemistry	Kinetics & Reaction Dynamics	Reactants, products, intermediates, transition states, activated complexes, energy surfaces, colliding particles.
Natural Sciences	Chemistry	Physical Chemistry	Spectroscopy	Photons, electronic states, vibrational/rotational modes, excited states, transition dipoles, scattering centers, chromophores.
Natural Sciences	Chemistry	Physical Chemistry	Electrochemistry	Electrons, ions, redox couples, electrodes, electrolytes, electric double layers, charge carriers, solvated species, reaction intermediates.
Natural Sciences	Chemistry	Physical Chemistry	Surface & Interface Science	Surface atoms, adsorbates, defects, steps, terraces, interfaces, electric double layers, surface charges, thin films, molecular overlayers.
Natural Sciences	Chemistry	Physical Chemistry	Colloid & Solution Chemistry	Solvents, solutes, colloidal particles, micelles, surfactants, ions, polymers, droplets, aggregates, interfacial layers, hydration shells.
Natural Sciences	Chemistry	Physical Chemistry	Chemical Physics	Atoms, molecules, electronic states, vibrational/rotational modes, potential energy surfaces, photons, phonons, reactive intermediates, collisional partners.
Natural Sciences	Chemistry	Organic Chemistry	Structural & Mechanistic Organic Chemistry	Atoms, functional groups, bonds, electrons, orbitals, intermediates (carbocations, carbanions, radicals), transition states, conformers, reactive sites.
Natural Sciences	Chemistry	Organic Chemistry	Stereochemistry & Conformational Analysis	Atoms, stereocenters, conformers, rotamers, diastereomers, enantiomers, meso forms, conformational transition states, torsional angles, symmetry elements.
Natural Sciences	Chemistry	Organic Chemistry	Synthetic Organic Chemistry	Reactants, reagents, catalysts, intermediates, transition states, protecting groups, functional groups, stereocenters, scaffolds, synthetic building blocks, reaction manifolds.
Natural Sciences	Chemistry	Organic Chemistry	Physical Organic Chemistry	Atoms, bonds, functional groups, reactive intermediates, transition states, molecular orbitals, substituent fields, charge distributions, solvent environments.
Natural Sciences	Chemistry	Organic Chemistry	Organometallic Organic Chemistry	Metal centers, ligands, organometallic complexes, oxidation states, coordination geometries, catalytic intermediates, metal-alkyls, metal-hydrides, metallacycles, reactive organometallic species.
Natural Sciences	Chemistry	Organic Chemistry	Polymer Chemistry (Carbon-based)	Monomers, repeating units, polymers, oligomers, radicals, chain ends, catalysts/initiators, propagating species, tacticity elements, crosslinks, copolymer segments.
Natural Sciences	Chemistry	Organic Chemistry	Bioorganic Chemistry	Biomolecules (amino acids, peptides, nucleotides, sugars, lipids), cofactors, enzymes, substrates, intermediates, transition states, catalytic residues, reactive oxygen species, synthetic analogs.
Natural Sciences	Chemistry	Organic Chemistry	Natural Products Chemistry	Primary/secondary metabolites, polyketides, terpenes, alkaloids, peptides, glycosides, cofactors, biosynthetic enzymes, intermediates, precursors, chiral pool building blocks.
Natural Sciences	Chemistry	Organic Chemistry	Medicinal Chemistry	Small molecules, drug candidates, lead compounds, metabolites, receptors, enzymes, transporters, cofactors, prodrugs, pharmacophores, bioisosteres, ADMET species.
Natural Sciences	Chemistry	Inorganic Chemistry	Main-Group Chemistry	Elements of the s- and p-block, ions, covalent molecules, hypervalent species, clusters, main-group radicals, anions/cations, Lewis acids/bases, polyatomic frameworks.
Natural Sciences	Chemistry	Inorganic Chemistry	Transition-Metal Chemistry	Metal centers, ligands, coordination complexes, oxidation states, spin states, d-orbitals, coordination geometries, electron configurations, catalytic intermediates, metal clusters.
Natural Sciences	Chemistry	Inorganic Chemistry	f-Block Chemistry	Lanthanide ions, actinide ions, coordination complexes, f-orbitals, 4f/5f electrons, oxidation states, ligand fields, f-element clusters, organolanthanides/actinides, mixed-valent systems.
Natural Sciences	Chemistry	Inorganic Chemistry	Coordination Chemistry	Metal ions, ligands, complexes, coordination spheres, counterions, oxidation states, spin states, coordination geometries, chelates, macrocycles, supramolecular hosts.
Natural Sciences	Chemistry	Inorganic Chemistry	Solid-State Chemistry	Atoms/ions in lattices, unit cells, crystal structures, defects (vacancies, interstitials), electrons/holes, phonons, surfaces, grain boundaries, solid solutions, extended frameworks.
Natural Sciences	Chemistry	Analytical Chemistry	Qualitative Analysis	Analytes, functional groups, ions, molecules, atoms, fragments, precipitates, colorimetric species, spectral signatures, matrix components, contaminants, interfering species.
Natural Sciences	Chemistry	Analytical Chemistry	Quantitative Analysis	Analytes, standards, calibration curves, internal standards, blanks, matrix components, reagents, instrument responses, noise sources, statistical distributions, uncertainty terms.
Natural Sciences	Chemistry	Analytical Chemistry	Separation Science	Analytes, mobile phases, stationary phases, ions, molecules, solvent systems, membranes, sorbents, charged species, micelles, droplets, gels, interfaces, matrix components.
Natural Sciences	Chemistry	Analytical Chemistry	Instrumental Analysis	Analytes, photons, ions, electrons, detectors, transducers, instrumental components, noise sources, calibration standards, signals, baselines, matrix components.
Natural Sciences	Chemistry	Biochemistry	Structural Biochemistry	Amino acids, nucleotides, proteins, nucleic acids, motifs, domains, secondary/tertiary/quaternary structures, macromolecular complexes, water networks, ions, chaperones, folding intermediates.
Natural Sciences	Chemistry	Biochemistry	Enzymology	Enzymes, substrates, products, cofactors (NAD⁺, FAD, metal ions), transition states, intermediates, catalytic residues, regulatory molecules, allosteric sites, isoenzymes, enzyme–inhibitor complexes.
Natural Sciences	Chemistry	Biochemistry	Metabolism & Bioenergetics	Metabolites, intermediates, cofactors (ATP, NAD⁺/NADH, FAD/FADH₂, CoA), enzymes, pathways, complexes (ETC), proton gradients, transporters, carriers, redox couples, thermodynamic states.
Natural Sciences	Chemistry	Biochemistry	Molecular Biology & Gene Expression	DNA, RNA, nucleotides, genes, promoters, enhancers, transcription factors, RNA polymerases, ribosomes, nucleosomes, epigenetic marks, regulatory RNAs, spliceosomes, chaperones, replication complexes.
Natural Sciences	Chemistry	Biochemistry	Cellular Biochemistry	Organelles, metabolites, enzymes, structural proteins, membranes, lipids, transporters, chaperones, cytoskeletal components, signaling molecules, vesicles, proton gradients, reactive oxygen species, quality-control machinery.
Natural Sciences	Chemistry	Biochemistry	Membrane Biochemistry	Lipids (phospholipids, sphingolipids, sterols), membrane proteins (channels, pumps, receptors), lipid rafts, vesicles, transporters, anchors, glycoconjugates, curvature-inducing proteins, ion gradients.
Natural Sciences	Chemistry	Biochemistry	Protein Chemistry	Amino acids, peptides, proteins, domains, motifs, disulfide bonds, side chains, post-translational modifications (PTMs), cofactors, folding intermediates, aggregates, protein complexes, chaperones.
Natural Sciences	Chemistry	Biochemistry	Biochemical Genetics	Genes, alleles, mutations, enzymes, metabolites, RNA transcripts, regulatory elements, protein complexes, biochemical pathways, inheritance units, molecular defects, compensatory pathways, modifier genes.
Natural Sciences	Earth & Space Sciences	Geology	Mineralogy & Crystallography	Atoms, ions, crystal lattices, unit cells, defects, mineral species, solid solutions, polymorphs, crystal faces, bonds, symmetry elements, phonons, inclusion phases, microstructures.
Natural Sciences	Earth & Space Sciences	Geology	Petrology	Minerals, melts, fluids, rock bodies, mineral assemblages, textures, xenoliths, inclusions, reaction rims, metamorphic zones, sedimentary components, metamorphic facies, grain boundaries, porosity, fractures.
Natural Sciences	Earth & Space Sciences	Geology	Structural Geology & Tectonics	Faults, folds, shear zones, joints, fractures, plates, blocks, lithosphere, asthenosphere, stress fields, strain markers, lineations, foliations, fabrics, ductile shear bands, rigid bodies, microstructures.
Natural Sciences	Earth & Space Sciences	Geology	Sedimentology & Stratigraphy	Sediment grains, particles, clasts, matrix, cement, fossils, sedimentary structures, beds, facies, stratigraphic units, sequences, unconformities, accommodation space, fluid flows, depositional systems.
Natural Sciences	Earth & Space Sciences	Geology	Geomorphology	Landforms, channels, hillslopes, dunes, beaches, deltas, glaciers, soils, sediments, regolith, rivers, ice masses, vegetation, weathering profiles, drainage networks, tectonic blocks, climate forcing systems.
Natural Sciences	Earth & Space Sciences	Geology	Geophysics	Seismic waves, stress/strain fields, gravity fields, magnetic fields, electrical conductivity, heat flow, lithosphere/asthenosphere, mantle plumes, faults, discontinuities, density anomalies, geophysical sensors, subsurface layers.
Natural Sciences	Earth & Space Sciences	Geology	Geochemistry	Elements, isotopes, ions, minerals, fluids, melts, gases, complexes, colloids, organic molecules, geochemical reservoirs, phases, interfaces, chemical species, defects, dissolution/precipitation sites.
Natural Sciences	Earth & Space Sciences	Geology	Paleontology	Organisms, fossils, skeletal elements, trace fossils, microfossils, ichnotaxa, communities, ecosystems, extinction events, stratigraphic ranges, taphonomic agents, evolutionary lineages.
Natural Sciences	Earth & Space Sciences	Geology	Hydrogeology	Groundwater, aquifers, aquitards, pores, fractures, faults, recharge zones, springs, wells, contaminants, dissolved ions, flow paths, hydraulic barriers, storage zones, capillary fringes, vadose zone.
Natural Sciences	Earth & Space Sciences	Geology	Economic & Applied Geology	Orebodies, mineral grains, hydrothermal fluids, magmatic systems, sedimentary basins, traps/seals, reservoirs, source rocks, structural traps, alteration halos, faults, fractures, aquifers, geothermal reservoirs, drilling infrastructure.
Natural Sciences	Earth & Space Sciences	Meteorology	Dynamic Meteorology	Assumes the existence of air parcels, pressure fields, temperature fields, moisture fields, planetary rotation, gravitational forcing, and continuous fluid masses treated as a deformable medium.
Natural Sciences	Earth & Space Sciences	Meteorology	Thermodynamic Meteorology	Air parcels, water vapor, cloud droplets, ice crystals, heat reservoirs, radiative fluxes, thermodynamic surfaces (isentropes), and vertical layers of the atmosphere.
Natural Sciences	Earth & Space Sciences	Meteorology	Cloud Physics & Microphysics	Cloud droplets, ice crystals, supercooled water, graupel, hail, aerosols acting as CCN/IN, water vapor, hydrometeors, rimed particles, and phase-transition interfaces.
Natural Sciences	Earth & Space Sciences	Meteorology	Synoptic & Mesoscale Meteorology	Air masses, fronts, cyclones, anticyclones, mesoscale convective systems, jet streaks, squall lines, boundary-layer structures, baroclinic zones, vorticity centers, convergence zones, and terrain-forced circulations.
Natural Sciences	Earth & Space Sciences	Meteorology	Atmospheric Physics & Chemistry	Photons, gas molecules, radicals, ions, aerosols, clouds, reactive intermediates (e.g., OH, NOx, HOx), trace gases, radiation fields, optical paths, and chemical reservoirs.
Natural Sciences	Earth & Space Sciences	Meteorology	Climatology & Climate Dynamics	Atmosphere, oceans, sea ice, land surface, biosphere, radiation fields, greenhouse gases, aerosols, climate modes, feedback loops, and slow components such as deep-ocean circulations and cryospheric reservoirs.
Natural Sciences	Earth & Space Sciences	Oceanography	Physical Oceanography	Water masses, currents, waves, eddies, gyres, air–sea interface, density layers, stratification boundaries, turbulence fields, boundary layers, sea ice, heat/salt anomalies, pressure fields, Coriolis field.
Natural Sciences	Earth & Space Sciences	Oceanography	Chemical Oceanography	Dissolved ions, trace metals, nutrients, gases, organic compounds, particles, colloids, ligands, complexes, aerosols, hydrothermal fluids, riverine inputs, sediments, redox species.
Natural Sciences	Earth & Space Sciences	Oceanography	Biological Oceanography	Phytoplankton, zooplankton, bacterioplankton, viruses, nekton, benthos, larvae, marine snow, microbial consortia, food webs, trophic levels, functional groups, ecosystems, carbon pools, nutrients, dissolved organic matter.
Natural Sciences	Earth & Space Sciences	Oceanography	Geological Oceanography	Sediment particles, minerals, microfossils, sedimentary layers, lithified deposits, submarine volcanoes, mid-ocean ridges, hydrothermal vents, seamounts, trenches, abyssal plains, methane hydrates, turbidity currents, sediment plumes.
Natural Sciences	Biology	Molecular Biology	Nucleic Acid Biology	DNA, RNA, nucleotides, nitrogenous bases, phosphates, chromatin structures, replication forks, polymerases, helicases, ligases, RNA-processing complexes, ribonucleoproteins, and repair intermediates.
Natural Sciences	Biology	Molecular Biology	Gene Regulation & Epigenetics	Regulatory DNA sequences (promoters, enhancers, silencers, insulators), transcription factors, chromatin remodelers, nucleosomes, histones, histone modifiers, noncoding RNAs, DNA methylation machinery, and 3D chromatin structures.
Natural Sciences	Biology	Molecular Biology	Protein Biology	Amino acids, polypeptide chains, protein domains, folded structures, protein complexes, enzymes, molecular motors, chaperones, post-translational modifications, cofactors, ligands, substrates, and interaction networks.
Natural Sciences	Biology	Molecular Biology	Molecular Complexes & Information Flow	Protein complexes, ribosomes, replisomes, spliceosomes, chromatin remodelers, transcriptional hubs, signaling complexes, scaffold proteins, membrane microdomains, regulatory RNPs, and dynamic phase-separated condensates.
Natural Sciences	Biology	Molecular Biology	Molecular Methods & Technologies	Instruments, reagents, sequencing platforms, imaging systems, molecular tags, probes, enzymes, synthetic constructs, engineered nucleic acids/proteins, reporter systems, calibration standards, and computational analysis tools.
Natural Sciences	Biology	Cell Biology	Cell Structure & Organelles	Organelles (nucleus, mitochondria, ER, Golgi, lysosome, peroxisome), cytoskeletal systems, membranes, vesicles, protein complexes, scaffolding assemblies.
Natural Sciences	Biology	Cell Biology	Cellular Dynamics & Trafficking	Vesicles, motor proteins (kinesin, dynein, myosin), cytoskeletal filaments, cargo molecules, membrane domains, Rab GTPases, SNAREs, tethering complexes, endosomes, lysosomes, transport intermediates.
Natural Sciences	Biology	Cell Biology	Cell Signaling & Communication	Receptors (GPCRs, RTKs), ligands, intracellular messengers (Ca²⁺, cAMP, IP₃), GTPases, kinases, phosphatases, scaffolding proteins, transcription factors, junctional complexes, electrical synapse components.
Natural Sciences	Biology	Cell Biology	Cell Cycle, Fate & Death	Cyclins, CDKs, checkpoints, DNA replication complexes, spindle machinery, apoptotic proteins (caspases, BCL-2 family), necroptotic machinery (RIPK1/3, MLKL), autophagy regulators, transcription factors controlling lineage fate, chromatin states, cell-identity markers.
Natural Sciences	Biology	Cell Biology	Cell Interactions & Microenvironment	ECM components (collagen, laminin, fibronectin), integrins, cadherins, cell–cell junction proteins, secreted factors, gradients, fibroblasts, immune cells, niche cells, mechanical forces, stiffness landscapes, matrix-degrading enzymes (MMPs), structural scaffolds.
Natural Sciences	Biology	Cell Biology	Cell Morphology & Motility	Actin filaments, microtubules, intermediate filaments, motor proteins (myosin, kinesin, dynein), focal adhesions, integrins, Rho-family GTPases, membrane protrusions (lamellipodia, filopodia, blebs), contractile networks, polarity complexes.
Natural Sciences	Biology	Genetics & Evolution	Classical & Transmission Genetics	Genes, alleles, chromosomes, loci, gametes, zygotes, linkage groups, recombination events.
Natural Sciences	Biology	Genetics & Evolution	Population Genetics	Alleles, genotypes, gene pools, populations, demes, migrants, mutations, selection coefficients, fitness values, effective population size (Ne), drift events.
Natural Sciences	Biology	Genetics & Evolution	Quantitative Genetics	Quantitative traits, genetic values, breeding values, environmental effects, additive/dominance/epistatic components, variance components (VA, VD, VI), heritability measures, selection differentials, phenotypic distributions.
Natural Sciences	Biology	Genetics & Evolution	Genomic Evolution & Comparative Genomics	Genomes, genes, gene families, orthologs, paralogs, mutations, substitutions, transposable elements, syntenic blocks, structural variants, conserved elements, ancestral genome reconstructions, phylogenetic trees.
Natural Sciences	Biology	Genetics & Evolution	Phylogenetics & Systematics	Taxa (species, genera, families), characters (morphological, molecular), phylogenetic trees, clades, lineages, ancestral nodes, evolutionary models, diagnostic traits, barcode sequences.
Natural Sciences	Biology	Genetics & Evolution	Macroevolution & Speciation Theory	Species, lineages, clades, reproductive barriers, geographic ranges, ecological niches, diversification events, extinction events, macroevolutionary trends, speciation modes, phylogenies.
Natural Sciences	Biology	Physiology	Cellular & Tissue Physiology	Cells, tissues, extracellular matrix, cell junctions, membranes, ion channels, receptors, cytoskeleton, interstitial fluid, signaling molecules, contractile proteins, and mechanical load-bearing structures.
Natural Sciences	Biology	Physiology	Neurophysiology	Neurons, glial cells, ion channels, receptors, synapses, neurotransmitters, action potentials, dendrites, axons, myelin, interneuronal networks, neuromodulators, and extracellular ionic environments.
Natural Sciences	Biology	Physiology	Endocrine & Regulatory Physiology	Hormones, receptors, endocrine glands, target tissues, signaling pathways, second messengers, feedback circuits, regulatory axes (HPA, HPG, HPT), carrier proteins, and metabolic effectors.
Natural Sciences	Biology	Physiology	Cardiovascular & Respiratory Physiology	Heart chambers, vessels, capillaries, alveoli, blood cells, hemoglobin, ventilation structures, respiratory muscles, receptors (baroreceptors, chemoreceptors), autonomic centers, and regulatory hormones.
Natural Sciences	Biology	Physiology	Metabolic & Energetic Physiology	Metabolites, enzymes, mitochondria, substrates (glucose, lipids, amino acids), ATP/ADP pools, redox carriers (NAD⁺/NADH, FAD/FADH₂), metabolic pathways, hormonal regulators, and thermogenic tissues.
Natural Sciences	Biology	Physiology	Renal, Fluid & Homeostatic Physiology	Nephrons, glomeruli, tubules, transporters, channels, pumps, filtrate, interstitial fluid, blood plasma, electrolytes (Na⁺, K⁺, Cl⁻, HCO₃⁻), hormones (RAAS, ADH, ANP), and acid–base buffers.
Natural Sciences	Biology	Developmental Biology	Cell Fate & Lineage Specification	Stem cells, progenitors, differentiated lineages, transcription factors, signaling gradients, fate determinants, lineage trees, regulatory networks, chromatin states, asymmetric cell-division machinery.
Natural Sciences	Biology	Developmental Biology	Pattern Formation & Embryonic Axes	Morphogens, receptors, signaling pathways (Hedgehog, Wnt, BMP, Nodal), gradients, positional-value fields, patterning modules, segmentation clocks, organizer regions, symmetry-breaking cues, boundary-forming factors, Hox clusters.
Natural Sciences	Biology	Developmental Biology	Morphogenesis & Tissue-Level Mechanics	Cells, tissues, epithelial sheets, cytoskeletal networks, adhesion complexes, extracellular matrix (ECM), force-generating modules (actomyosin), mechanical stresses, curvature fields, tissue boundaries, junctional networks.
Natural Sciences	Biology	Developmental Biology	Organogenesis & Multi-Tissue Assembly	Tissue primordia, organ buds, epithelial tubes, mesenchymal condensations, vascular networks, neural inputs, signaling centers, morphogen gradients, ECM compartments, lumenal cavities, branching modules.
Natural Sciences	Biology	Developmental Biology	Growth, Timing, Regeneration & Life-Cycle Transitions	Growth factors, hormones, stem cells, progenitors, differentiated cells, regeneration niches, morphogenetic signals, timing regulators (circadian clocks, developmental timers), checkpoints, blastema structures, life-stage modules (larval, juvenile, adult).
Natural Sciences	Biology	Developmental Biology	Evolutionary Development (Evo–Devo)	Gene regulatory networks (GRNs), developmental modules, enhancers and cis-regulatory elements, transcription factors, signaling pathways (Wnt, Hedgehog, BMP), conserved patterning genes (Hox, Pax, Sox), morphological traits, embryonic domains, ancestral developmental programs.
Natural Sciences	Biology	Ecology	Organismal Ecology	Individual organisms, microhabitats, environmental resources, predators, competitors, physiological systems, morphological structures, behavioral units (actions), sensory cues, and environmental constraints.
Natural Sciences	Biology	Ecology	Population Ecology	Individuals aggregated into populations, demographic classes (age, size, sex), resources influencing population growth, density-regulating factors, dispersal agents, and environmental drivers affecting population-level change.
Natural Sciences	Biology	Ecology	Community Ecology	Species, guilds, functional groups, trophic levels, interaction networks, resources, habitat patches, niches, environmental filters, and interaction-modifying environmental factors.
Natural Sciences	Biology	Ecology	Ecosystem Ecology	Energy pools, nutrient pools, primary producers, consumers, decomposers, detritus, soil organic matter, abiotic reservoirs, flux pathways, water and carbon flows, and ecosystem compartments.
Natural Sciences	Biology	Ecology	Landscape & Spatial Ecology	Habitat patches, matrices, corridors, barriers, landscape elements, spatial networks, dispersal pathways, species distributions, movement routes, land-use types, and environmental gradients.
Natural Sciences	Biology	Ecology	Global Ecology & Earth-System Interactions	Global biomes, planetary biogeochemical reservoirs, atmospheric gases, ocean circulation cells, terrestrial carbon sinks, large-scale disturbance regimes, climate-forcing agents, global flux networks, and Earth-system components.
Formal Sciences	Logic	Proof Theory	Proof Calculi	Formulas, sequents, contexts, inference rules, proof trees, derivations, metavariables, structural rules.
Formal Sciences	Logic	Proof Theory	Structural Proof Theory	Sequents, contexts, structural rules (exchange, weakening, contraction), proof trees, derivations, cut steps, substitutions, structural transformations, inference schemas.
Formal Sciences	Logic	Proof Theory	Proof Theory of Non-Classical Logics	Non-classical sequents, labeled sequents, worlds/accessible indices (in modal systems), resources (linear/affine), relevance constraints, polarity annotations, structural-rule variants, logic-specific inference rules.
Formal Sciences	Logic	Proof Theory	Ordinal & Strength Analysis	Ordinals (up to and beyond ε₀, Γ₀, Bachmann–Howard, and larger systems), well-orderings, proof-theoretic hierarchies, reflection schemas, induction rules, recursive function hierarchies, combinatorial principles (e.g., WOP(α)).
Formal Sciences	Logic	Proof Theory	Proof Complexity	Propositional formulas, CNF/DNF representations, circuits, derivation DAGs, refutation proofs, inference rules, proof systems (Resolution, Frege, Extended Frege, Cutting Planes, Polynomial Calculus, Nullstellensatz), complexity classes.
Formal Sciences	Logic	Proof Theory	Automated & Interactive Reasoning	Logical formulas, terms, proof objects, solver states, heuristics, decision procedures, search trees, tactic scripts, interactive proof states, constraint sets, models and countermodels, rewrite rules, unification artifacts.
Formal Sciences	Logic	Model Theory	Structures, Languages & Interpretations	Structures (𝔐), domains (
Formal Sciences	Logic	Model Theory	Satisfaction & Definability Theory	Structures (𝔐), domains (
Formal Sciences	Logic	Model Theory	Quantifier Theory & Model Completeness	Formulas in prenex form, quantifiers (∃, ∀), quantifier blocks, quantifier rank, Skolem functions, structures, embeddings, elementary substructures, diagrams.
Formal Sciences	Logic	Model Theory	Classification Theory	Theories, models, types, formulas, definable sets, ranks (Morley rank, U-rank), forking/dividing relations, independence relations, saturated models.
Formal Sciences	Logic	Model Theory	Tame / O-Minimal Model Theory	O-minimal structures, definable sets, definable functions, cells, dimensions, projections, fibers, definable groups, types over parameters, Skolem functions in tame settings.
Formal Sciences	Logic	Set Theory	Axiomatic Foundations & Cumulative Hierarchy	Sets, ordinals, cardinals, cumulative hierarchy levels (V_\alpha), functions, relations, combinatorial structures, transfinite sequences, foundational axioms (ZFC).
Formal Sciences	Logic	Set Theory	Constructibility & Inner Models	Constructible sets, levels (L_\alpha), ordinals, parameters for definability, fine-structure sequences, sharps (e.g., (0^\sharp)), core models (K), directed systems of inner models.
Formal Sciences	Logic	Set Theory	Large Cardinal Theory	Large cardinals, elementary embeddings (j: V \to M), critical points, ultrafilters, extenders, ultrapower models, canonical inner models approximating large cardinals.
Formal Sciences	Logic	Set Theory	Forcing & Independence Theory	Forcing posets ((\mathbb{P}, \leq)), conditions, dense sets, filters, generics, names, valuations, Boolean-valued models, complete Boolean algebras, ground models, forcing extensions.
Formal Sciences	Logic	Set Theory	Descriptive Set Theory	Reals, Borel sets, analytic sets, projective sets, Polish spaces, continuous maps, trees, pointclasses, equivalence relations, scales, norms, determinacy games.
Formal Sciences	Logic	Computability Theory	Models of Computation & Recursive Function Theory	Turing machines, tapes, states, transition functions, λ-terms, combinators, μ-recursive function clauses, register contents, partial computable functions, oracles, encodings of data, Gödel numbers.
Formal Sciences	Logic	Computability Theory	Recursively Enumerable (r.e.) Sets & Degrees	r.e. sets, partial computable functions, enumeration operators, Turing functionals, degree elements, reducibility relations, complete r.e. sets (e.g., K), priority requirements, finite/infinite injury modules, approximation stages.
Formal Sciences	Logic	Computability Theory	Reducibility & Degrees of Unsolvability	Sets of naturals, decision problems, reducibility maps, oracle machines, degree elements, jump operators (A′, A″, …), equivalence classes under reducibility, minimal-pair constructions.
Formal Sciences	Logic	Computability Theory	Arithmetical & Analytical Hierarchies	Sets of naturals, sets of reals, arithmetical formulas, analytical formulas, quantifiers (∃, ∀; ∃f, ∀f), Turing jumps, reducibility operators, indices for definable sets, lightface/boldface classes, oracle structures.
Formal Sciences	Mathematics	Algebra	Group Theory	Group elements, identity element, inverses, group operations, subgroups, cosets, quotient groups, homomorphisms, automorphisms, group actions, generators, relations, conjugacy classes.
Formal Sciences	Mathematics	Algebra	Ring Theory	Ring elements, additive identity (0), multiplicative identity (1) when present, ideals, prime ideals, maximal ideals, homomorphisms, quotient rings, polynomial elements, matrices, units, zero divisors.
Formal Sciences	Mathematics	Algebra	Field Theory	Field elements, additive and multiplicative identities, inverses, field extensions, bases, algebraic elements, transcendental elements, embeddings, automorphisms, valuations, minimal polynomials, splitting fields.
Formal Sciences	Mathematics	Algebra	Module Theory	Module elements, ring scalars, submodules, quotient modules, homomorphisms, exact sequences, bases (when they exist), generators, relations, tensor products, annihilators, direct sums/products, projective/injective modules.
Formal Sciences	Mathematics	Algebra	Linear Algebra	Vectors, scalars, matrices, linear maps, bases, subspaces, eigenvalues, eigenvectors, linear systems, inner products, orthonormal sets, projections, canonical forms.
Formal Sciences	Mathematics	Algebra	Representation Theory	Vectors, linear maps, representation homomorphisms, group/algebra elements, invariant subspaces, irreducible components, characters, weights, roots, modules, basis elements, intertwiners, tensor factors.
Formal Sciences	Mathematics	Algebra	Universal Algebra	Carrier sets, operations, term functions, identities (equations), homomorphisms, subalgebras, quotient algebras, congruence relations, free algebras, varieties, clones of operations.
Formal Sciences	Mathematics	Algebra	Algebraic Combinatorics	Partitions; Young diagrams; tableaux; permutations; posets; graphs; monomials; symmetric functions; polynomials; representations; characters; weight vectors; Coxeter generators; adjacency matrices; incidence matrices.
Formal Sciences	Mathematics	Mathematical Analysis	Real Analysis	Real numbers, sequences, functions, sets, open/closed sets, measurable sets, metrics, intervals, neighborhoods, derivatives, integrals, measures, σ-algebras, function spaces (e.g., Lᵖ), compact/connected sets.
Formal Sciences	Mathematics	Mathematical Analysis	Complex Analysis	Complex numbers, complex functions, analytic functions, contours/paths, open sets in ℂ or ℂⁿ, power series, residues, singularities, branch points, harmonic functions, complex differentials, conformal maps, analytic continuation structures, Riemann surfaces (when needed).
Formal Sciences	Mathematics	Mathematical Analysis	Functional Analysis	Vectors (often functions), norms, inner products, linear operators, bounded/unbounded operators, dual elements, Banach/Hilbert spaces, distributions, functionals, kernels, spectra, eigenvalues, compact operators, projections, orthonormal bases, weak limits.
Formal Sciences	Mathematics	Mathematical Analysis	Harmonic Analysis	Functions, distributions, Fourier transforms, convolution kernels, eigenfunctions, spectral measures, characters on groups, representations, maximal operators, wavelets, atoms (Hardy space), singular kernels, frequency bands, multipliers.
Formal Sciences	Mathematics	Mathematical Analysis	Differential Equations (ODE/PDE)	Unknown functions; derivatives (first, higher-order, partial); vector fields; flows; operators (Laplace, divergence, gradient, Hessian, etc.); boundary and initial data; Green’s functions; fundamental solutions; weak/distributional solutions; nonlinear operators; semigroups of operators.
Formal Sciences	Mathematics	Geometry & Topology	Differential Geometry	Smooth manifolds, charts, atlases, tangent/cotangent spaces, differential forms, metrics, connections, curvature tensors, geodesics, flows, tensor fields.
Formal Sciences	Mathematics	Geometry & Topology	Algebraic Geometry	Varieties, schemes, spectra of rings, morphisms, ideals, coordinate rings, divisors, line bundles, sheaves, cohomology classes, moduli points, function fields.
Formal Sciences	Mathematics	Geometry & Topology	Metric Geometry	Metric spaces, length spaces, geodesics, distance functions, balls, curves, comparison triangles, isometries, Lipschitz maps, tangent cones (in nonsmooth contexts), Gromov–Hausdorff limits.
Formal Sciences	Mathematics	Geometry & Topology	Point-Set Topology	Sets, topologies, open/closed sets, bases, subbases, continuous maps, nets, filters, closures, interiors, products, quotient spaces.
Formal Sciences	Mathematics	Geometry & Topology	Homotopy Theory	Spaces, paths, homotopies, loops, spheres (S^n), homotopy classes ([X,Y]), fibrations, cofibrations, homotopy fibers, CW-complexes, spectra, stable homotopy types.
Formal Sciences	Mathematics	Geometry & Topology	Knot Theory	Knots, links, embeddings of (S^1), link components, knot diagrams, Reidemeister moves, Seifert surfaces, fundamental group of the knot complement, polynomial invariants, crossing data.
Formal Sciences	Mathematics	Number Theory	Elementary Number Theory	Integers, primes, composite numbers, divisors, residues, congruence classes, arithmetic functions (φ, μ, τ, σ), integer sequences, Diophantine solutions.
Formal Sciences	Mathematics	Number Theory	Algebraic Number Theory	Number fields, rings of integers, prime ideals, fractional ideals, units, class groups, Galois groups, valuations, completions, local fields, ramification data, norm/trace maps.
Formal Sciences	Mathematics	Number Theory	Analytic Number Theory	Zeta functions, L-functions, Dirichlet characters, primes, arithmetic functions (Λ, μ, τ, σ, φ), exponential sums, Dirichlet series, Euler products, zeros and poles of analytic functions.
Formal Sciences	Mathematics	Number Theory	Arithmetic Geometry	Varieties over number fields, arithmetic schemes, rational points, integral points, primes and places of number fields, reduction maps, heights, Galois representations, ℓ-adic cohomology classes, Néron models.
Formal Sciences	Mathematics	Number Theory	Modular and Automorphic Forms	Modular forms, cusp forms, Eisenstein series, Hecke operators, q-expansions, Dirichlet characters, automorphic representations, adele groups, local components, L-functions, Fourier coefficients, weight/level structures.
Formal Sciences	Mathematics	Number Theory	Transcendental Number Theory	Transcendental numbers, algebraic numbers, heights of algebraic numbers, auxiliary polynomials, linear forms in logarithms, Baker-type quantities, exponential values, special constants (e, π), Diophantine-approximation functions.
Social Sciences	Anthropology		Human Evolutionary Anthropology	Hominins, primates, populations, fossils, bones, genomes, phenotypes, ecological niches, selection pressures, migration pathways, cultural traits affecting fitness, paleoenvironments.
Social Sciences	Anthropology		Kinship, Descent & Domestic Organization	Persons, kin categories, lineages, clans, households, affines (in-laws), consanguines (blood relatives), descent groups, marriage partners, caregivers, inheritance objects (land, property), domestic groups, genealogical relations.
Social Sciences	Anthropology		Ritual, Cultural Practice & Symbolic Systems	Ritual actors; roles (priest, initiate, officiant, witness); symbols; gestures; objects; spaces; narratives; cosmologies; cultural meanings; ritual scripts; sensory cues; material artifacts; emotional states; normative expectations; cultural codes.
Social Sciences	Anthropology		Subsistence Systems, Environment & Human Adaptation	Human groups, resources, landscapes, ecosystems, species targeted for subsistence, technologies, tools, shelters, mobility routes, climate systems, soils, water sources, domesticated plants/animals, knowledge systems, energy flows, carrying capacity.
Social Sciences	Anthropology		Material Culture, Technology & Archaeological Interpretation	Artifacts, ecofacts, features, sites, tools, materials (stone, clay, metal, bone), manufacturing traces, waste products (debitage), spatial distributions, residues, structures, technologies, production sequences, cultural styles, taphonomic agents, stratigraphic layers.
Social Sciences	Anthropology		Ethnographic Method & Comparative Analysis	Persons, households, social groups, cultural practices, narratives, performances, institutions, knowledge systems, categories of meaning, embodied experience, field sites, cultural patterns, cross-cultural variables.
Social Sciences	Economics		Choice (Microeconomic Foundations)	Individuals, firms, preferences, utility functions, production technologies, budgets, prices, constraints, beliefs, probabilities, time horizons, risk profiles, information signals.
Social Sciences	Economics		Interaction (Markets, Strategy & Mechanisms)	Agents, firms, goods, prices, quantities, payoff functions, beliefs, strategies, market institutions, contracts, signals, types (in asymmetric information models), mechanisms, allocation rules, matching objects (students–schools, workers–firms), equilibria.
Social Sciences	Economics		Aggregation & Dynamics (Macroeconomic Systems)	Representative or heterogeneous agents; households; firms; government; central bank; aggregate capital; labor; productivity (TFP); shocks (technology, policy, preference, financial); expectations; markets (goods, labor, capital, money).
Social Sciences	Geography (Human)		Spatial Patterns & Spatial Analysis	Locations, places, regions, spatial units, human populations, built structures, networks, flows, boundaries, spatial fields, distance-decay surfaces, geographic features, spatial clusters, nodes, edges, polygons, administrative units.
Social Sciences	Geography (Human)		Mobility, Flows & Connectivity	People, vehicles, goods, messages, data packets, infrastructure nodes (stations, ports, hubs), pathways (roads, rails, air corridors), links in transportation/digital networks, origin–destination pairs, flows, bottlenecks, barriers, friction surfaces, time–space prisms, mobility regimes.
Social Sciences	Geography (Human)		Human–Environment Interaction & Landscape Modification	Humans, communities, technologies, tools, infrastructure, ecosystems, soils, water systems, vegetation, animals, climate regimes, geomorphological features, land covers, resources, feedback loops, hazards, settlement systems, engineered landscapes.
Social Sciences	Geography (Human)		Place, Territory & Spatial Experience	Places, territories, boundaries, landscapes, dwellings, routes, symbolic sites, sacred/ritual spaces, identity groups, spatial narratives, cognitive maps, spatial practices, affective responses, territorial markers, border regimes, spatial claims, cultural landscapes.
Social Sciences	Linguistics		Phonetics & Phonology	Speech sounds (segments), articulatory gestures, acoustic features (formants, pitch, duration), phonemes, allophones, features (+voice, +nasal, etc.), syllables, prosodic units, stress domains, tone units, phonological rules/constraints.
Social Sciences	Linguistics		Morphology	Morphemes, stems, roots, affixes, templates, morphological features (tense, number, case, aspect, gender), agreement markers, morphological paradigms, allomorphs, morphophonemic rules.
Social Sciences	Linguistics		Syntax	Syntactic categories (N, V, A, P), constituents (NP, VP, TP, CP), features (φ-features, case, tense, aspect), heads, specifiers, complements, traces/copies, movement chains, dependency relations.
Social Sciences	Linguistics		Semantics	Meanings, semantic features, predicates, arguments, referents, events, propositions, truth values, possible worlds, thematic roles, semantic types (e.g., e, t), quantifiers, variables, domains of discourse.
Social Sciences	Linguistics		Pragmatics	Speakers, hearers, intentions, beliefs, common ground, discourse contexts, referential domains, presupposition sets, implicatures, pragmatic constraints, discourse moves, speech acts.
Social Sciences	Political Science		Political Institutions & Formal Political Order	Political institutions; constitutions; legislatures; executives; courts; bureaucratic agencies; electoral laws; party systems; veto players; policy agendas; jurisdictions; formal rules; procedures; political authority structures; federal units; international institutions (when binding).
Social Sciences	Political Science		Political Behavior, Mobilization & Collective Action	Individuals; voters; activists; groups; organizations; identities; preferences; beliefs; attitudes; networks; communication channels; leaders/entrepreneurs; political messages; mobilization resources; grievances; collective goals.
Social Sciences	Political Science		Governance, Policy Formation & State Capacity	Governments; ministries; bureaucratic agencies; public officials; regulatory bodies; policy instruments; administrative procedures; budgets; state infrastructure; oversight institutions; enforcement agencies; policy networks; public-services delivery systems.
Social Sciences	Political Science		International Relations & Global Order	States; governments; militaries; international organizations (UN, WTO, IMF); alliances; non-state actors (NGOs, MNCs, insurgents); norms; treaties; capabilities; interests; international regimes; global markets; territory; borders; security commitments.
Social Sciences	Psychology		Cognitive Processes & Mental Architecture	Cognitive representations, mental schemas, working-memory buffers, attention systems, perceptual modules, long-term memory stores, decision rules, processing pathways, cognitive architectures (symbolic, connectionist, hybrid).
Social Sciences	Psychology		Learning, Conditioning & Behavioral Mechanisms	Stimuli, responses, reinforcers, punishers, cues, contingencies, conditioned/unconditioned stimuli, learned associations, habit loops, discriminative stimuli, reinforcement schedules, behavioral chains.
Social Sciences	Psychology		Emotion, Motivation & Affect Regulation	Emotional states, affective valence and arousal, motivational drives, reward signals, physiological responses, appraisal processes, affect-regulation strategies, stress hormones, autonomic responses.
Social Sciences	Psychology		Development, Individual Differences & Psychometrics	Individuals, developmental stages, traits, abilities, latent variables, item responses, factor structures, measurement scales, growth trajectories, normative developmental benchmarks, variance components.
Social Sciences	Sociology		Social Interaction Mechanisms	Individuals, roles, identities, norms, expectations, gestures, symbols, emotions, interaction cues, social scripts, definitions of situations, shared meanings.
Social Sciences	Sociology		Social Structure Mechanisms	Social positions, roles, stratification systems, institutions, organizations, status groups, class categories, mobility pathways, structural boundaries, legal/organizational rules, cultural schema, structural resources.
Social Sciences	Sociology		Social Network & Relational Dynamics	Actors (individuals, groups, organizations), ties (strong/weak), structural positions, relational roles, network edges, multiplex ties, flows of information, influence, support, and resources.