| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes theoretical frameworks where the fundamental entities are one-dimensional strings or higher-dimensional extended objects. Includes superstrings, branes, dualities, and higher-dimensional compact spaces. Excludes point-particle-only models, classical field theories without extended objects, and low-energy physics when string effects decouple. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates at extremely small length scales far below current experimental reach, near the Planck scale. Also operates at high-energy theoretical regimes, extra spatial dimensions, and regimes involving strong quantum gravity effects. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | 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. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Tension of strings, allowed vibration modes, dimensionality of objects, coupling strengths, geometric properties of compact dimensions, conserved charges, and supersymmetry-related attributes in some versions. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Extended objects, processes involving splitting and joining of strings, relations defined by dualities, and geometric structures such as compact spaces and higher-dimensional manifolds. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | String vibration states, brane positions, background geometric parameters, coupling constants, and values specifying the shape and size of extra dimensions. |
| | Parameterization | How variables encode and represent the system’s state. | System states encoded by string modes, brane configurations, background geometry, and parameters defining compactification, symmetry, and coupling. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Treating strings as perfectly smooth, approximating extra dimensions with simple geometric shapes, assuming supersymmetry, working in weak-coupling or strong-coupling limits, and using simplified backgrounds such as flat space or specific curved spaces. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Approximations valid only in regimes where coupling is weak, background curvature is small relative to string scale, or specific duality limits apply. Classical string descriptions fail when full quantum effects dominate. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes extended objects as fundamental, spacetime with more than four dimensions, continuity of geometry, presence of quantum gravity, and the possibility of dual descriptions connecting different physical pictures. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes mathematical structures used are physically meaningful, extra dimensions exist though hidden, supersymmetry may be present even if not observable, and dualities provide equivalent descriptions of the same physics. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Demands anomaly cancellation, consistent string interactions, coherent compactification choices, and no contradictions between different dual pictures. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Requires that extended objects, background geometry, coupling rules, and dualities form a unified and mutually compatible structure, producing a consistent theory of quantum gravity and particle interactions. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | No direct observable signals from strings or branes exist at accessible energies. Indirect observables include patterns in particle spectra, symmetry structures, coupling relationships, cosmological signatures, and possible deviations from standard physics at high energies or small scales. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Current instruments cannot probe the extremely small length scales or high energies required to directly detect strings. Existing detectors are limited to low-energy effective consequences rather than fundamental string behavior. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses standard physics units such as meters, seconds, electron volts, and cosmological units when comparing predictions to observational data. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Relies on indirect observational tools such as particle colliders, astrophysical observatories, gravitational wave detectors, and cosmological measurements rather than instruments specifically designed for strings. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Terms like compactification, spectrum prediction, or brane configuration are defined by how theoretical models map onto measurable quantities such as particle masses, coupling constants, or cosmological parameters. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures involve translating string models into low-energy predictions through compactification choices, parameter scans, effective field theory matching, and comparison with observational constraints. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Protocols follow standard physics data collection practices in cosmology, particle physics, and astrophysics, since string theory has no direct detection channel; data comes from existing experiments interpreted through model frameworks. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling is determined by available experimental data such as collider events, cosmic microwave background measurements, gravitational wave signals, and astrophysical observations. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Includes particle event records, cosmological temperature maps, gravitational wave time series, astrophysical spectra, and numerical outputs from theoretical simulations. |
| | Resolution | The granularity or precision with which data is captured. | Resolution depends on the underlying experimental device, such as collider detector granularity, telescope sensitivity, or gravitational wave timing precision. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses known particle processes, astrophysical standards, instrument benchmarks, and consistency checks across different observational platforms. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from detector limitations, cosmological model uncertainties, statistical noise, background contamination, and theoretical uncertainties in mapping string models to observable quantities. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Includes regularities such as quantized vibration modes of strings, relationships between geometry and particle properties, duality relations connecting different theories, and stable patterns linking extended objects to force behavior and particle spectra. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include conserved quantities from symmetry structures, quantities preserved under dualities, topological charges, and geometric invariants of compact dimensions that remain unchanged across different descriptions. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from the behavior of strings and branes, including splitting and joining processes, vibrational patterns generating particle states, and duality-driven links between different physical pictures such as gauge and gravity descriptions. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include sequences of interactions where strings interact, join, or separate; networks where branes collide or intersect; and multi-step duality chains connecting different theoretical regimes. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include string, brane, compactification, duality, worldsheet, extra dimension, background geometry, spectrum, and moduli. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies structures by type of string theory, type of brane, dimensionality, choice of compactification, presence or absence of supersymmetry, and type of duality relating theories. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Uses formal constructs describing string motion, worldsheet dynamics, interactions between extended objects, and consistency conditions needed for well-defined models; often reliant on advanced geometry and algebra. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Includes compactification models, brane-world models, duality-based models, effective field theories derived from higher-dimensional setups, and simplified representations of string interactions. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Simplified models include flat-background strings, supersymmetric idealizations, reduced-dimensionality setups, and truncated models where only a subset of modes or interactions is kept. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Approximations hold in specific limits such as weak coupling, large volume of compact dimensions, high symmetry backgrounds, or special duality-related regimes. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | String theory itself serves as a unifying framework connecting gauge interactions, gravity, and extended-object dynamics under a single structure; M-theory acts as a broader organizing framework tying together multiple versions. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to cosmology, quantum gravity, particle physics, condensed matter through emergent string-like behavior, mathematics through geometry and topology, and information theory through duality relations. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | String theory has no direct experimental design pathway because its fundamental scales cannot be manipulated. Instead, designs focus on adjusting assumptions within the theory, modifying compactification choices, or exploring parameter spaces to test internal causal claims and consistency conditions. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Relies entirely on systematic use of existing observational data from particle physics, astrophysics, gravitational waves, and cosmology. There is no direct manipulation; observations are used to test whether low-energy consequences of string models are compatible with measured phenomena. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Hypotheses are tested by comparing predicted particle spectra, coupling relations, symmetry patterns, or cosmological features to available data. Consistency checks replace direct experimental validation. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Validation occurs when independent theoretical groups reproduce the same internal consistency results, duality predictions, or low-energy implications using different methods or compactification assumptions. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Uses statistical evaluations of how well derived low-energy models match real data such as particle masses, coupling values, or cosmological parameters, even though the connection remains indirect. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Compares models based on mathematical consistency, simplicity of compactification, stability of solutions, ability to reproduce standard physics, and robustness of predictions across parameter changes. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors arise from theoretical approximations, incomplete knowledge of compactification spaces, truncations of mode expansions, and uncertainties when mapping high-energy theory to low-energy observations. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias is controlled by using multiple independent derivations, publishing detailed assumptions, cross-checking with dual descriptions, and applying identical evaluation criteria across different model families. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Theoretical results undergo review through seminars, publications, conferences, and cross-group replication. Ideas are debated and evaluated for consistency, coherence, and compatibility with known physics. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Revision occurs when inconsistencies are found, when compactification choices fail to produce realistic physics, or when dualities require reformulating the underlying picture. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires explicit disclosure of assumptions, compactification choices, parameter ranges, computational shortcuts, and any approximations used in deriving predictions. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires honesty in presenting limitations, avoiding overstating experimental relevance, accurately reporting assumptions, and maintaining openness in collaboration and publication. |