| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes theories where interactions come from local gauge symmetry, such as Yang-Mills, QED, QCD, electroweak theory, and the Standard Model. Excludes global-symmetry-only systems, non-gauge classical theories, and non-field models. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates at quantum and subatomic spatial scales, relativistic time scales, and high-energy particle-interaction regimes; appears in some condensed-matter systems as an effective gauge structure. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | 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. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Gauge charges, coupling strengths, representation labels, particle masses, field strength values, and gauge redundancy. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Fields, interaction processes, relations including symmetry transformations and covariant derivatives, and structures such as groups and bundles. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Gauge potentials, matter field values, field strength values, coupling strengths, gauge-fixing parameters, and symmetry-breaking values such as the Higgs field value. |
| | Parameterization | How variables encode and represent the system’s state. | States represented by full field configurations across spacetime together with couplings, symmetry-breaking values, and gauge choices; physical data expressed through gauge-invariant combinations. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Treating fields as smooth; using perturbation expansions; applying linear gauge fixing; neglecting nonperturbative topology; describing bound states via effective models. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Perturbation theory works only at weak coupling; continuum approximations fail at very small scales; flat-spacetime assumptions break down with strong gravity; effective descriptions are valid only within their scale range. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Fields assumed to exist on smooth spacetime; interactions are local; Lorentz symmetry holds; classical equations are deterministic while quantum evolution is probabilistic; group structures determine possible interactions. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Gauge symmetry is a redundancy, so only gauge-invariant quantities are observable; mathematical structures like groups and bundles are assumed adequate; spacetime dimension and signature are fixed; standard quantization methods apply. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | The theory must avoid anomalies and non-unitary behavior; constraints and quantization rules must align; renormalization must preserve gauge symmetry. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Fields, variables, symmetry groups, and structural assumptions must form a unified gauge system where interactions come from covariant derivatives and only gauge-invariant quantities represent observables. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Scattering cross sections, particle collision outcomes, decay rates, energy and momentum distributions, charge interactions, radiation patterns, jet formation, hadron production, and gauge-invariant quantities derived from field behavior. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by collider energy, detector granularity, signal-to-noise ratios, background events, timing precision, and material constraints of particle detectors; some predicted particles or modes remain beyond reach due to insufficient energy. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Standard units include electron volts for energy, meters for position, seconds for time, inverse femtobarns for luminosity, and counts or rates for detection events. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Particle detectors, calorimeters, tracking chambers, time-of-flight systems, magnetic spectrometers, beam monitors, photomultiplier arrays, silicon sensors, and high-energy colliders such as the LHC. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Quantities such as cross section, decay rate, event momentum, and particle identity are defined by specific reconstruction rules, detector responses, and statistical thresholds used in analysis. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Steps include event triggering, data filtering, track reconstruction, energy deposition measurement, timing analysis, and applying particle identification rules; all performed using standardized, reproducible protocols. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Formal processes include controlled accelerator operation, synchronized detector readout, fixed trigger conditions, consistent run configurations, and documented operating parameters. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Data samples determined by run periods, beam conditions, trigger selections, detector acceptance windows, and statistical requirements for event significance. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Raw evidence appears as time series signals, detector hits, energy deposit maps, event records, particle tracks, and aggregated collision data sets. |
| | Resolution | The granularity or precision with which data is captured. | Defined by detector granularity, timing precision, magnetic field strength for momentum resolution, energy calibration quality, and digital recording precision. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Requires adjusting detector gains, aligning tracking components, calibrating energy scales, checking magnetic fields, and validating timing systems through known reference events and test signals. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Characterized by statistical noise, systematic detector bias, background contamination, misidentification rates, uncertainty in reconstruction algorithms, and environmental fluctuations affecting data quality. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Regularities include how charges interact through gauge fields, the rule that interactions arise from local symmetry, the dependence of forces on coupling strengths, and stable patterns such as asymptotic freedom and confinement in non-abelian theories. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Conserved quantities linked to symmetry, including charge conservation, energy and momentum conservation, and invariants associated with gauge symmetry such as gauge-invariant combinations of fields and observables. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Interactions are generated by how fields respond to local symmetry operations; forces arise from exchange of gauge bosons; field self-interaction in non-abelian cases produces behavior such as confinement and running coupling. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Causal pathways include sequences of particle interactions through gauge boson exchange, reaction chains in scattering events, and multi-step interaction networks in composite particle formation. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include gauge symmetry, gauge field, matter field, coupling constant, gauge boson, covariant derivative, running coupling, symmetry breaking, and vacuum expectation value. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Systems classified by gauge group type, representation category, interaction strength, symmetry structure, and whether the theory is abelian or non-abelian. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Uses differential field equations, covariant derivative structures, conservation relations, and renormalization formulas; expresses interactions through symmetry-driven terms and derivative operators. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Includes high-energy scattering models, effective field theories, symmetry-breaking models, running-coupling models, and simplified gauge-field models used for predictions and analysis. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Examples include linearized field models, weak-coupling approximations, classical gauge-field treatments, abelianized versions of complex systems, and effective models for bound states. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Valid in regimes such as weak coupling, high energy, or large distance where approximations hold; transitions to different behaviors in strong coupling, low energy, or symmetry-broken conditions. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Includes frameworks like the Standard Model connecting multiple gauge symmetries into one system; grand unified models linking groups together at higher energy. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Connects to quantum field theory, particle physics, condensed-matter physics through emergent gauge fields, cosmology through early-universe symmetry roles, and mathematics through group theory and geometry. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Uses controlled high-energy collisions to test causal predictions of gauge interactions by adjusting beam energy, detector configuration, trigger settings, or interaction environment. Allows targeted tests of coupling behavior, particle production, and predicted signatures of gauge symmetry. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Relies on systematic collection of naturally occurring particle events without direct manipulation of variables, such as cosmic rays, astrophysical signals, indirect decay signatures, or environmental particle fluxes captured by detectors. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Evaluates whether predicted event distributions, decay rates, or interaction patterns match observed data using statistical thresholds, confidence intervals, and goodness-of-fit tests. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Requires independent confirmation of results by different detectors, experiments, or collaborations, often across separate accelerators or observation environments. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Uses statistical rules to draw conclusions from collision data, including background subtraction, likelihood fitting, confidence level estimation, and signal extraction from noise. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Compares models using prediction accuracy, simplicity, robustness across parameter ranges, and goodness-of-fit to measured event distributions. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Identifies random noise, systematic bias, detector inefficiency, modeling assumptions, and environmental fluctuations; quantifies uncertainty through error bars and systematic error budgets. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Minimizes subjectivity or instrument-related bias by using blinded analyses, control samples, standardized calibration, and predefined selection rules. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings undergo internal collaboration review and external peer review, including replication by other groups and open critique during conferences, workshops, and publication processes. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Models are updated or replaced when new data contradict predictions, such as adjusting coupling values, adding effective terms, modifying symmetry assumptions, or refining approximations. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires clear disclosure of analysis methods, detector conditions, data cuts, assumptions, uncertainties, statistical procedures, and limitations of the study. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Ensures responsible treatment of data, avoidance of fabrication or selective reporting, honest representation of uncertainty, and adherence to collaboration-wide ethical guidelines for analysis and publication. |