| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes field-based descriptions of systems with many degrees of freedom, including critical phenomena, phase transitions, stochastic dynamics, and continuous limits of lattice models. Excludes systems with few degrees of freedom where field descriptions are unnecessary and purely microscopic models without coarse-grained interpretation. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates across microscopic, mesoscopic, and macroscopic scales, especially near critical points where long-range correlations dominate. Applies to condensed matter systems, statistical ensembles, and large-scale stochastic processes. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Fields representing order parameters, fluctuating quantities, correlation functions, probability distributions, noise sources, and coarse-grained degrees of freedom that replace individual particle descriptions. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Correlation lengths, susceptibilities, fluctuation sizes, coupling strengths, noise amplitudes, and coarse-grained field values characterizing system behavior. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Continuous fields, stochastic processes, interaction terms, symmetry classes, renormalization structures, and universality classes describing behavior independent of microscopic detail. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Field values over space and time, probability distributions, temperature, interaction strengths, correlation lengths, and noise parameters. |
| | Parameterization | How variables encode and represent the system’s state. | System states encoded through field configurations, statistical weights, effective couplings, and coarse-grained descriptors determined by renormalization flow or stochastic rules. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Mean-field approximations, Gaussian approximations, neglect of microscopic detail, use of simplified noise models, reduction to symmetric interactions, and coarse-graining that removes small-scale structure. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Idealizations hold when fluctuations are small, when symmetry assumptions apply, when coarse-graining is appropriate, or when the system is far from strong-coupling or strongly nonlinear regimes. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes randomness in fluctuations, continuity of fields, existence of statistical ensembles, applicability of coarse-graining, and deterministic evolution of averaged quantities alongside stochastic contributions. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes universality across different microscopic systems, validity of renormalization methods, and that field-based descriptions capture essential large-scale behavior despite ignoring individual particle motion. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Field equations, stochastic rules, and renormalization flows must not conflict; probability distributions must remain well-defined; approximations must maintain internal statistical consistency. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Fields, interaction rules, noise models, and ensemble definitions must form a coherent whole that links microscopic randomness with macroscopic behavior and allows consistent predictive modeling. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Observable quantities include correlation functions, fluctuation magnitudes, order parameter values, susceptibility peaks, critical exponents, temporal relaxation patterns, and stochastic response signals. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by detector resolution, noise floors, sampling rate, and the ability to resolve small-scale fluctuations or long-range correlations near critical points. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses standard physical units such as meters, seconds, temperature units, energy units, and dimensionless quantities used to express critical exponents and scaling relations. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments include microscopes, imaging devices, magnetometers, calorimeters, sensors for stochastic processes, high-speed cameras, and systems for tracking fluctuations in time or space. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Quantities such as correlation length, order parameter amplitude, relaxation time, and fluctuation strength are defined through specific measurement or reconstruction procedures. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include repeated sampling of fluctuating systems, image processing of spatial patterns, time-series measurement, averaging over ensembles, and computing correlation functions from raw data. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data collected under fixed temperature, controlled environmental conditions, steady driving forces, or specified statistical ensembles; uses standardized runs and repeatable sampling intervals. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling rules determine how many configurations are measured, how often measurements occur, and how representative the sampled region is of the overall stochastic system. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as time series, spatial maps, stochastic trajectories, images of fluctuating fields, histograms of values, and ensemble-averaged quantities. |
| | Resolution | The granularity or precision with which data is captured. | Precision determined by detector granularity, sampling frequency, noise level, and spatial resolution of imaging or sensor arrays. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses known reference behaviors, stable background signals, controlled noise sources, and repeated measurements of standard systems to ensure accurate fluctuation and correlation measurements. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from thermal noise, sensor limitations, finite sample size, environmental disturbances, averaging over limited ensembles, and approximations used to compute correlation or response quantities. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include scaling laws near critical points, universal behavior independent of microscopic detail, field correlations that follow power laws, and relations between fluctuations and responses. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include critical exponents, universality classes, symmetry properties, conservation rules in stochastic dynamics, and structural invariants preserved under coarse-graining or renormalization. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from collective behavior of many interacting degrees of freedom, coarse-grained field evolution, noise-driven dynamics, feedback loops among correlations, and renormalization flows that shape large-scale behavior. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include sequences of fluctuation growth, correlation spreading, relaxation toward equilibrium, noise-driven transitions, and renormalization steps connecting microscopic and macroscopic descriptions. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core concepts include field, fluctuation, order parameter, correlation length, scaling law, universality class, noise term, renormalization, and coarse-graining. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies systems by symmetry type, dimensionality, interaction structure, noise characteristics, equilibrium vs non-equilibrium behavior, and membership in universality classes. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Formal structures include field evolution equations, stochastic differential equations, scaling relations, flow equations for parameters, and expressions relating correlations to responses. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Includes Ising-like field models, Landau-type models, coarse-grained effective field models, stochastic field models, and renormalization-based models capturing long-range behavior. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Idealizations include mean-field models, Gaussian approximations, linearized stochastic equations, symmetry-reduced models, and simplified interaction terms used to capture key dynamics. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Approximations hold in high dimensions, weak-coupling regimes, large system sizes, near-symmetry limits, or when fluctuations are small; they break down near strong-coupling or strongly nonlinear behavior. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Renormalization group theory acts as a unifying framework connecting different systems through scaling and universality; ties statistical mechanics to quantum field theory. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Connects to condensed matter physics, quantum field theory, probability theory, chaos theory, fluid dynamics, and biological or economic systems showing collective stochastic behavior. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments are designed to vary temperature, external fields, noise levels, or interaction strengths to observe how fluctuations, correlations, and phase transitions respond. Controlled manipulation allows testing of causal relationships predicted by field models. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational approaches measure naturally occurring fluctuations, spatial patterns, relaxation dynamics, or noise-driven behavior without direct intervention; used in systems where manipulation is impractical or impossible. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Hypotheses are tested by comparing predicted correlation functions, critical exponents, relaxation times, or fluctuation magnitudes to measured data using statistical thresholds. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Results must be reproduced using different samples, detectors, numerical simulations, experimental setups, or statistical ensembles to confirm robustness. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Uses statistical tools to interpret noisy or incomplete data; includes averaging over ensembles, computing uncertainties, filtering time series, and estimating correlation functions. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Compares models using fit quality, predictive stability, scaling accuracy, ability to reproduce universal behavior, and robustness to noise or parameter variation. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors come from sensor noise, finite sampling, environmental variability, numerical approximation limits, and uncertainties in estimating correlations or response functions. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias is reduced through standardized sampling, multiple ensemble measurements, blind data processing, independent replication, and consistent calibration procedures. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings undergo review through publication, replication by other groups, cross-comparison with numerical simulations, and critique in conferences or seminars. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Models are revised when predictions differ from data, when scaling laws fail, when renormalization paths need adjustment, or when new measurements reveal previously unmodeled interactions. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires clear disclosure of data collection methods, noise treatment, assumptions in coarse-graining, statistical tools used, and limitations of the model. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires honest reporting of uncertainties, avoidance of selective data use, transparency about model assumptions, and adherence to scientific integrity standards in data handling and publication. |