| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes materials where electron electron interactions dominate behavior, such as Mott insulators, heavy fermion systems, unconventional superconductors, quantum spin liquids, and charge ordered states. Excludes weakly interacting electron systems that can be described by simple band theory or independent electron models. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates at atomic to nanometer scales where electronic wavefunctions overlap, and at macroscopic scales where emergent phases appear. Time scales span fast electronic motion to slower collective excitations and relaxation dynamics. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Strongly interacting electrons, localized moments, quasiparticles with renormalized mass, collective modes, spin or charge textures, lattice ions, and external fields influencing correlated behavior. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Correlation strength, effective mass, charge order, spin order, energy gap types, coherence scale, susceptibility, and response to temperature or doping. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Phases, excitations, order parameters, lattice electron couplings, collective behaviors, and emergent structures such as magnetic order, charge order, or topological states. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Electron density, spin configuration, interaction parameters, temperature, doping concentration, conductivity, susceptibility, and order parameter magnitudes. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded by correlation parameters, doping level, lattice geometry, electronic occupations, temperature, and external fields controlling phase transitions. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Simplifications include reduced lattice models, nearest neighbor interactions, simplified Hubbard type models, mean field approximations, and symmetry idealizations. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Valid when electronic structure is dominated by local interactions, disorder is moderate, temperature allows stable phases, and simplified interaction terms capture dominant behavior without strong coupling breakdown. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes electron electron interactions drive key phenomena, quantum behavior is essential, emergent phases arise from collective interactions, and lattice structure strongly shapes correlated states. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes quasiparticle concepts remain partially meaningful, simplified lattice models map to real materials, and emergent order reflects underlying interactions even when microscopic details are complex. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires consistency among interaction terms, lattice symmetries, correlation strength, observed phases, and behavior of excitations; no contradictions between model predictions and known phase diagrams. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Entities, variables, and assumptions must produce a unified description linking lattice geometry, interaction strength, emergent order, and transport or magnetic behavior. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Detectable signals include unusual conductivity trends, metal insulator transitions, magnetic order signatures, charge order patterns, heavy effective mass behavior, quantum oscillations, unconventional superconductivity, spin liquid responses, and anomalous heat capacity. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by low temperature requirements, resolution of magnetic or charge probes, precision of transport measurements, noise in quantum oscillation detection, and sensitivity to small energy gaps or weak ordering signals. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses ohms, amperes, volts, meters, seconds, electron volts, kelvins, teslas, and counts or intensity units for scattering, spectroscopy, or magnetic measurements. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments include neutron scattering systems, x-ray scattering, angle resolved photoemission, scanning probe microscopes, transport measurement setups, heat capacity devices, magnetometers, and cryogenic systems. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Quantities such as correlation gap, effective mass, order parameter, susceptibility, and coherence scale are defined through measurement procedures such as spectroscopy, scattering, or transport extraction. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include temperature sweeps, field sweeps, controlled doping, scattering scans, spectroscopy mapping, current voltage measurements, and frequency dependent probes of excitations. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data collected under stable low temperatures, controlled magnetic fields, precise doping levels, fixed scattering geometries, and repeated measurement cycles to ensure reproducibility. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling rules specify multiple doping points, temperature points, field strengths, repeated spectra, and spatial sampling across inhomogeneous materials. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as transport curves, spectral lines, susceptibility plots, scattering patterns, quantum oscillation traces, heat capacity curves, and imaging maps of magnetic or charge order. |
| | Resolution | The granularity or precision with which data is captured. | Determined by detector sensitivity, energy resolution in spectroscopy, momentum resolution in scattering, temperature stability, and precision of magnetic or current measurements. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses reference materials, known scattering standards, magnetic field calibrations, temperature standards, and repeated baseline measurements for transport and spectroscopy tools. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from thermal fluctuations, instrument drift, noise in quantum oscillation detection, sample inhomogeneity, calibration drift, scattering background, and finite resolution in energy or momentum measurements. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include metal insulator transitions, heavy effective mass trends, anomalous temperature dependent resistivity, emergent magnetic or charge order, and unconventional pairing behavior in correlated superconductors. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include lattice symmetry constraints, conserved electron count in certain phases, persistent spin or charge patterns, and stable features of low energy excitations across similar correlated materials. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from strong electron electron repulsion, coupling between local moments and conduction electrons, frustration in lattice geometry, interaction driven localization, and cooperative behavior leading to emergent phases. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include transitions from itinerant to localized behavior, buildup of magnetic or charge order, development of heavy quasiparticles, and sequential changes in coherence with temperature or doping. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include Mott transition, Hubbard interaction, exchange coupling, spin liquid, charge order, heavy fermion, coherence scale, frustration, and emergent quasiparticle. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies systems as Mott insulators, heavy fermion compounds, spin liquids, charge ordered materials, correlated metals, and unconventional superconductors based on interaction strength and emergent order. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Uses equations describing lattice interactions, effective Hamiltonians, transport relationships, susceptibility forms, energy scales, and interaction driven gap formation. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Includes Hubbard type models, Heisenberg models, multi orbital models, heavy fermion models, spin liquid models, dynamical mean field simulations, and lattice based computational models. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Idealizations include reduced dimensionality, nearest neighbor interactions only, single band approximations, symmetric lattices, and simplified coupling terms capturing only dominant correlations. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Models hold when electronic correlations dominate over disorder, when lattice structure is regular, when temperature is low enough for coherent phases, or when long range interactions or strong fluctuations do not overwhelm simplified models. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Includes frameworks linking localization, magnetism, superconductivity, and heavy fermion behavior under strong interaction principles, along with theories connecting spin, charge, and orbital degrees of freedom. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to condensed matter physics, materials science, quantum information, topology, computational physics, and high pressure physics for tuning correlated phases. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments vary temperature, doping, pressure, magnetic field, and lattice strain to test how correlated phases emerge, evolve, or collapse. These manipulations target causal effects on conductivity, magnetic ordering, and coherence. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational approaches measure naturally occurring fluctuations, spontaneous ordering, or slow relaxation processes without imposing external control, especially in systems with fragile or emerging correlated phases. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Tests compare transport curves, scattering spectra, magnetic signatures, and energy gaps against predictions from correlated electron models such as Hubbard or Heisenberg based theories. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Replication is required across different samples, fabrication batches, cryogenic systems, detectors, and laboratories due to material variability and extreme sensitivity to disorder or impurities. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Uses statistical fitting of spectra, extraction of effective mass, evaluation of coherence scales, analysis of noise and fluctuations, and statistical comparison of transport behavior across conditions. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Competing models evaluated on accuracy in predicting phase transitions, spectral features, magnetic or charge ordering, anomalous temperature dependence, and overall consistency with phase diagrams. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors arise from temperature instability, sample inhomogeneity, noise in scattering or photoemission, detector drift, calibration uncertainty, and intrinsic variability across correlated materials. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias minimized using blind temperature sweeps, multiple independent probes, cross checking with scattering and transport, standardized sample preparation, and rigorous control of disorder. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings are reviewed through replication, comparison with alternative theories, detailed evaluation at conferences, and publication in specialized condensed matter venues. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Theories revised when unexpected phases appear, when predicted gaps or ordering patterns are not observed, or when new measurements reveal emergent phenomena not explained by existing models. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires clear reporting of sample purity, preparation, disorder levels, temperature stability, measurement geometry, calibration routines, and assumptions used in modeling. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires accuracy in reporting, avoidance of selective data removal, responsible handling of fragile samples, and adherence to standards for reproducibility and documentation. |