This section identifies what can actually be seen, recorded, or measured in each domain—the concrete signals that tie the theory to evidence. Observables include any phenomenon that produces a detectable output: positions, fields, spectra, currents, reaction rates, images, gene-expression levels, neural spikes, social behaviors, prices, votes, spatial patterns, and so on. In the Science Analysis Template, this row defines the measurement-facing side of a field: which aspects of its systems can leave empirical traces that instruments, experiments, surveys, or simulations can capture and use to test, calibrate, or refine its models.
Science Analysis Template
Below are the results of cycles 1 & 2 of The Science Project
Across all sciences, observables are bounded, repeat-detectable properties or changes—direct or indirect—whose form is scale-dependent, domain-neutral, and precedes interpretation or explanation.
What makes an Observable?
1. Observables Are Properties, Not Explanations
Across every science, an observable is what is directly detected, not why it happens.
- Position, temperature, intensity, concentration, frequency, count, rate
- NOT causes, mechanisms, or interpretations
Universal rule:
Observables describe state, change, or presence — never meaning.
2. Observables Are Always Bounded
No science observes “everything.” Every observable is constrained by:
- Spatial bounds (where)
- Temporal bounds (when)
- Resolution limits (how fine)
- Detection limits (how weak/strong)
Universal pattern:
Every observable exists only within a defined observational window.
3. Observables Are Quantitative or Qualitative — But Trend Toward Quantification
All sciences begin with qualitative observables and, when possible, push toward quantitative ones.
- Qualitative: presence/absence, category, state, type
- Quantitative: magnitude, count, rate, distribution
Universal direction:
Sciences mature by converting qualitative observables into measurable quantities.
4. Observables Are Change-Oriented
Static observables matter less than variation.
Across sciences, what is tracked is:
- Change over time
- Differences across conditions
- Gradients, rates, oscillations, transitions
Universal emphasis:
Observability is strongest where change can be detected.
5. Observables Are Repeat-Detectable, Not One-Off
An observable is only meaningful if it can be:
- Detected again
- Compared across trials, locations, or observers
- Distinguished from noise
Universal constraint:
A one-time, non-repeatable detection is not a stable observable.
6. Observables Are Scale-Dependent
The same phenomenon produces different observables at different scales.
- Microscopic vs macroscopic
- Individual vs population
- Instantaneous vs averaged
Universal reality:
Observables change character when scale changes.
7. Observables Are Indirect More Often Than Direct
Across sciences, many observables are not sensed directly but inferred from indicators.
- Traces, signals, emissions, proxies, readouts
- Still treated as observables if detection is reliable
Universal rule:
Directness is not required; detectability is.
8. Observables Are Domain-Neutral in Form
While content differs, the types of observables recur everywhere:
- Counts
- Rates
- Distributions
- Intensities
- States
- Transitions
Universal pattern:
Sciences differ in what they observe, not how observables are structured.
9. Observables Precede Models and Theories
No science allows theory to define observables retroactively.
- Observables must exist independently of explanation
- Theory organizes observables; it does not create them
Universal ordering:
Observable → Pattern → Model → Theory
10. Observables Are the Lowest Irreducible Evidence Unit
Across all sciences:
- Observables are the atomic units of evidence
- Everything higher-level is built from them
Universal foundation:
If it cannot be observed (directly or indirectly), it cannot ground scientific evidence.
Observations Derive from Properties
and are categorized as such (to see the same groupings below from the perspective of the entity, click the link above):
1. Magnitude
What Magnitude Covers
Magnitude properties answer one question only:
How much?
They assign a quantity to an entity or configuration under a specified measurement frame.
Magnitude concerns amount, not arrangement, change, influence, feasibility, knowledge, or value.
To keep Magnitude pure across all sciences, every magnitude observable must be describable using a fixed, universal set of datapoints. These datapoints do not vary by domain; they vary only by applicability.
Purpose of Magnitude Datapoints
Magnitude datapoints exist to:
- Fully specify a quantity without theory leakage
- Separate world state from knowledge state
- Allow cross-science comparison of observables
- Prevent Structure, Dynamics, Information, or Evaluation from being smuggled into “numbers”
- Make observables stable under reinterpretation and revision
They define the measurement grammar of “how much.”
Magnitude — Universal Datapoints
1. Value Type
Magnitude observables fall into a small set of forms. Treat these as mutually exclusive Value Types.
A. Level (state level at a time)
A quantity at a specific timepoint.
- Examples: population at t, money stock at t, capital stock at t
B. Period-total (integral over a window)
A quantity accumulated over an interval.
- Examples: total output in Q1, total consumption in 2024, total births in a year
C. Rate (per unit time)
A quantity normalized by time.
- Examples: inflation per year, job creation per month, migration per day
D. Density / Intensity (per unit of something else)
A quantity normalized by population, area, capital, etc.
- Examples: GDP per capita, energy per square mile, cases per 100k
E. Index / normalized magnitude (dimensionless)
A scaled magnitude relative to a baseline.
- Examples: CPI index, output index (2015=100)
Rule: every magnitude observable must declare its subtype.
2. Value
The quantity itself
- Numeric or discrete symbolic value
This is the magnitude proper, stripped of interpretation.
3. Unit / Scale
How the value is measured
- Physical units, count units, dimensionless indices
A value without a unit is undefined.
4. Reference Domain
What the magnitude is measured over
- Single entity
- Population
- System
- Region
- Ensemble
- Configuration
Distinguishes “how much of what.”
5. Measurement Context
When, where, or under what conditions the value applies
- Timepoint
- Interval
- Experimental condition
- Observational frame
Anchors the magnitude to a concrete context without invoking dynamics.
6. Bounds / Admissible Range
Logical or physical limits on possible values
- Non-negativity
- Integer constraints
- Upper bounds
- Conservation limits
Encodes feasibility without invoking Constraint laws themselves.
7. Resolution / Precision
Granularity of measurement
- Smallest detectable change
- Rounding rule
- Instrument sensitivity
Separates absence of change from inability to detect change.
8. Normalization / Baseline
Reference used to scale or index the value
- Baseline value
- Reference state
- Normalization constant
Explains comparability without implying evaluation.
9. Aggregation Rule
How multiple measurements were combined
- Sum
- Mean
- Integral
- Count
- Weighted combination
Makes totals and averages explicit rather than assumed.
10. Measurement Method / Instrument
How the value was obtained
- Apparatus
- Protocol
- Algorithm
- Census or counting rule
Preserves reproducibility without introducing Information structure.
11. Uncertainty / Error Characterization
Noise or variability associated with the value
- Error bounds
- Variance
- Confidence interval
- Tolerance
Keeps uncertainty separate from the magnitude itself.
12. Revision / Update Status
Epistemic lifecycle of the recorded value
- Preliminary
- Updated
- Revised
- Final
Distinguishes changes in knowledge from changes in reality.
13. Source Type
Origin of the measurement
- Experimental
- Observational
- Administrative
- Simulated
- Derived
Tracks provenance without affecting the quantity.
If a datapoint answers anything other than “how much,” it does not belong to Magnitude.
- Better/worse → Evaluation
- Change over time → Dynamics
- Influence between entities → Interaction
- Feasibility rules → Constraint
- Knowledge state → Information
- Arrangement or relations → Structure
Magnitude stays clean only if this boundary is enforced.
Magnitude datapoints define the complete and universal grammar for describing quantities across all sciences. They specify amount without interpretation, preserve epistemic clarity, and prevent category leakage at the evidence layer.
2. Structure
What Structure Covers
Structure properties answer one question only:
How are the parts arranged?
They describe configuration, not quantity, not change, not influence, not rules, not knowledge, and not value.
Structure concerns form, relations, and organization that persist when quantities vary and time is frozen.
Purpose of Structure Datapoints
Structure datapoints exist to:
- Specify arrangement without invoking dynamics or causality
- Separate pattern from process
- Make relational descriptions precise and comparable
- Prevent Interaction, Dynamics, or Constraint from being smuggled into “structure”
- Provide a stable descriptive basis for explanation
They define the organizational grammar of systems.
Structure — Universal Datapoints
1. Elements
What components are arranged
- Nodes, parts, units, symbols, agents, components
Structure cannot exist without identifiable elements.
2. Relations
How elements are connected or related
- Adjacency, linkage, ordering, containment, correspondence
Relations define structure; without them there is only a list.
3. Configuration / Pattern Type
Overall form of arrangement
- Chain, lattice, hierarchy, network, tree, grid, manifold, sequence
Distinguishes different kinds of organization with the same elements.
4. Topology
Connectivity independent of metric scale
- Connectedness, adjacency, loops, components, neighborhoods
Captures “who is connected to whom,” not “how strongly.”
5. Dimensionality
Degrees of freedom of the arrangement
- 1D, 2D, 3D, n-dimensional, abstract dimensionality
Prevents confusion between layout and magnitude.
6. Symmetry / Invariants
What remains unchanged under transformation
- Translational symmetry, rotational symmetry, conservation of pattern
Structural identity lives in invariants, not values.
7. Hierarchy / Nesting
Levels or containment relationships
- Parent–child, layered, modular, nested structures
Explains scale-independent organization without dynamics.
8. Role Labels
Functional or positional labels within the structure
- Hub, leaf, root, boundary, interior, terminal
Labels describe position, not influence or value.
9. Ordering / Sequence Rule
Whether elements are ordered
- Linear order, partial order, cyclic order, unordered
Ordering is structural, not temporal.
10. Embedding / Representation Space
Space in which the structure is represented
- Physical space, abstract space, symbolic space, coordinate system
Separates structure from its depiction.
11. Structural Constraints
Limits on admissible arrangements
- Fixed degree, allowed connections, forbidden configurations
These are structural admissibility conditions, not behavioral constraints.
12. Granularity Level
Resolution at which structure is described
- Micro, meso, macro
- Fine vs coarse structural description
Prevents accidental mixing of structural scales.
If a datapoint describes change, it is not Structure.
If it describes influence strength or direction, it is not Structure.
If it describes feasibility or rules, it is not Structure.
- Change → Dynamics
- Influence → Interaction
- Rules / limits → Constraint
- Quantities → Magnitude
- Beliefs / signals → Information
- Better / worse → Evaluation
Structure is arrangement only.
Common Failure Cases (to avoid)
- ❌ “Network centrality” → Interaction (influence), not pure structure
- ❌ “Growth of hierarchy” → Dynamics, not structure
- ❌ “Efficient structure” → Evaluation, not structure
- ❌ “Budget hierarchy” → Constraint + Structure (must be split)
Structure datapoints define how system components are arranged, connected, and organized, independently of quantity, time, influence, or value. They provide the invariant organizational backbone on which all other property-categories operate.
3. Dynamics
What Dynamics Covers
Dynamics properties answer one question only:
How does the system change over time?
They describe temporal evolution: motion, growth, decay, adjustment, oscillation, convergence, divergence.
Dynamics is about change itself, not:
- how much exists (Magnitude),
- how parts are arranged (Structure),
- who influences whom (Interaction),
- what is allowed (Constraint),
- what is known (Information),
- or what is better (Evaluation).
Purpose of Dynamics Datapoints
Dynamics datapoints exist to:
- Encode time-dependent behavior explicitly
- Separate change from cause, quantity, and structure
- Make predictions and trajectories comparable across sciences
- Prevent Interaction or Evaluation from being smuggled in as “rates”
- Define what counts as a causal variable in a domain
They define the temporal grammar of systems.
Dynamics — Universal Datapoints
1. State Variable
What quantity or configuration is changing
- Position, population, concentration, belief, parameter value
Dynamics requires a state that can differ across time.
2. Time Parameter
What time reference governs the change
- Continuous time
- Discrete time steps
- Event-indexed time
Without a time parameter, change is undefined.
3. Rate / Rule of Change
How the state variable changes
- Derivative
- Difference
- Transition rule
- Update function
This is the minimal mathematical content of dynamics.
4. Direction of Change
Whether change increases, decreases, oscillates, or reverses
- Positive / negative
- Cyclic
- Bidirectional
Prevents collapsing dynamics into unsigned magnitudes.
5. Trajectory / Path
Sequence of states over time
- Time series
- Phase path
- State sequence
Distinguishes instantaneous rates from realized evolution.
6. Timescale
Characteristic speed of evolution
- Fast / slow
- Relaxation time
- Half-life
- Characteristic period
Keeps rate and temporal relevance aligned.
7. Regime / Stability Class
Qualitative behavior of the dynamics
- Stable
- Unstable
- Metastable
- Oscillatory
- Chaotic
Dynamics is not only about speed, but about behavior type.
8. Initial Condition
Starting state from which evolution proceeds
Required to make trajectories determinate.
9. Terminal / Attractor State
State toward which the system evolves (if any)
- Fixed point
- Limit cycle
- Absorbing state
Describes long-run behavior without invoking Evaluation.
10. Lag / Inertia
Delay between cause and response
- Time lag
- Adjustment delay
- Memory length
Captures temporal persistence without implying structure or interaction.
11. Perturbation Sensitivity
Response to small disturbances
- Linear response
- Sensitivity
- Local instability
Still about change, not about who caused it.
12. Reversibility
Whether the dynamics can be undone
- Reversible
- Irreversible
- Path-dependent
A fundamental temporal property across sciences.
If a datapoint explains why change occurs, it is not Dynamics.
If it identifies who affects whom, it is not Dynamics.
- Cause → Interaction
- Limits on motion → Constraint
- Quantity level → Magnitude
- Pattern of connections → Structure
- Uncertainty about evolution → Information
- Desired outcome → Evaluation
Dynamics describes how change unfolds, not why it exists or whether it is good.
Common Failure Cases (to avoid)
- ❌ “Fiscal multiplier dynamics” → Interaction + Dynamics (must be split)
- ❌ “Efficient convergence” → Evaluation leakage
- ❌ “Network diffusion” → Structure + Interaction + Dynamics (must be decomposed)
- ❌ “Potential growth path” → Evaluation unless purely descriptive
Dynamics datapoints define how system states evolve over time, capturing rates, trajectories, and stability properties without importing causality, structure, feasibility, uncertainty, or value.
4. Interaction
What Interaction Covers
Interaction properties answer one question only:
What influences what, and how?
They describe inter-entity influence: forces, couplings, incentives, signaling, feedback, correlations that transmit effects between distinct components.
Interaction is relational and directional.
It is not:
- quantity (Magnitude),
- arrangement (Structure),
- temporal evolution itself (Dynamics),
- feasibility limits (Constraint),
- uncertainty or beliefs (Information),
- or value judgment (Evaluation).
Purpose of Interaction Datapoints
Interaction datapoints exist to:
- Make causal and influence relationships explicit
- Separate who affects whom from how things change
- Prevent Structure (networks) or Dynamics (rates) from silently doing causal work
- Enable clean causal, strategic, and propagative reasoning
- Define what counts as interdependence in a domain
They define the influence grammar of systems.
Interaction — Universal Datapoints
1. Source Entity
The entity exerting influence
Interaction cannot exist without a source.
2. Target Entity
The entity receiving influence
Distinguishes interaction from internal dynamics.
3. Directionality
Whether influence is one-way or mutual
- Unidirectional
- Bidirectional
- Asymmetric
Prevents collapsing interaction into undirected correlation.
4. Interaction Type
The mode of influence
- Force
- Coupling
- Incentive
- Signal
- Constraint-mediated influence
- Correlation channel
Names how influence is transmitted, not how strong it is.
5. Coupling Strength
Magnitude of influence
- Weak / strong
- Sensitivity
- Elasticity
- Coefficient
Still interaction, not magnitude, because it refers to effect between entities.
6. Sign / Polarity
Whether influence amplifies or dampens
- Positive
- Negative
- Mixed
Prevents conflating “exists” with “helps” or “hurts” (Evaluation).
7. Interaction Scope
Where the interaction applies
- Local vs global
- Pairwise vs group
- Conditional vs unconditional
Defines domain of influence without invoking structure.
8. Mediation Channel
What carries the influence
- Field
- Medium
- Institution
- Protocol
- Signaling pathway
Separates interaction from structure or information.
9. Latency / Delay
Time between action and effect
Temporal aspect of influence, not evolution of state itself.
10. Feedback Presence
Whether influence loops back
- None
- Positive feedback
- Negative feedback
Structural + dynamic consequences are downstream; this just marks the loop.
11. Context Dependence
Conditions under which interaction applies
- State-dependent
- Threshold-dependent
- Regime-dependent
Prevents assuming interactions are unconditional.
12. Stability of Interaction
Whether the interaction itself persists or changes
- Fixed
- Adaptive
- Transient
About persistence of influence relation, not system evolution.
If a datapoint describes change in a state variable, it is not Interaction.
If it describes arrangement of entities, it is not Interaction.
- Change rate → Dynamics
- Network layout → Structure
- Limits on behavior → Constraint
- Quantity levels → Magnitude
- Beliefs / uncertainty → Information
- Desirability → Evaluation
Interaction only specifies influence relations, nothing else.
Common Failure Cases (and how SAT fixes them)
- ❌ “Network centrality” → Structure + Interaction (split: topology vs influence)
- ❌ “Multiplier” → Interaction (strength) not Dynamics
- ❌ “Learning from others” → Interaction (signal) + Information (belief update)
- ❌ “Efficient incentives” → Evaluation leakage
Interaction datapoints define how entities influence one another, specifying direction, mode, strength, and scope of influence without importing quantities, arrangements, temporal evolution, feasibility limits, uncertainty, or value judgments.
5. Constraint
What Constraint Covers
Constraint properties answer one question only:
What is not allowed?
They describe limits on the space of possible states or behaviors—boundaries, capacities, conservation rules, admissibility conditions, feasibility regions.
Constraint is about exclusion, not:
- quantity (Magnitude),
- arrangement (Structure),
- change (Dynamics),
- influence (Interaction),
- uncertainty or beliefs (Information),
- or desirability (Evaluation).
Purpose of Constraint Datapoints
Constraint datapoints exist to:
- Define the shape of the possibility space
- Make forbidden states explicit
- Separate limits from causes
- Prevent Evaluation (“should”) from masquerading as necessity (“must”)
- Anchor prediction by ruling out impossible trajectories
They define the feasibility grammar of systems.
Constraint — Universal Datapoints
1. Constrained Entity / Variable
What the constraint applies to
- State variable
- Configuration
- Action
- System component
A constraint must constrain something.
2. Constraint Type
Kind of limitation imposed
- Boundary
- Capacity
- Conservation
- Admissibility
- Exclusivity
Prevents mixing physical, logical, and institutional limits.
3. Forbidden States
States or configurations that cannot occur
- Explicitly excluded values or regions
This is the ontological core of constraint.
4. Permitted Region
States that remain feasible
- Complement of forbidden states
- Feasible set / domain
Defines possibility by exclusion, not preference.
5. Boundary Definition
Where the limit lies
- Threshold
- Inequality
- Domain edge
- Conservation surface
Separates “has a limit” from “where the limit is.”
6. Binding Status
Whether the constraint is active
- Binding
- Non-binding
- Conditional
Constraints can exist without currently restricting behavior.
7. Universality / Scope
Where and when the constraint applies
- Universal
- Context-specific
- Local
- Regime-dependent
Prevents accidental overgeneralization.
8. Constraint Origin
Source of the constraint
- Physical
- Biological
- Logical
- Institutional
- Mathematical
Identifies provenance without invoking causality.
9. Hardness
Whether violation is possible
- Hard (cannot be violated)
- Soft (can be violated at cost)
- Approximate
Keeps penalties separate from Evaluation.
10. Tolerance / Slack
Degree of allowable deviation
- Margin
- Buffer
- Elasticity range
Allows realism without abandoning constraint purity.
11. Interaction with Other Constraints
How multiple constraints combine
- Independent
- Nested
- Redundant
- Conflicting
Necessary once systems exceed one constraint.
12. Enforcement Condition
What triggers recognition of violation
- Logical inconsistency
- Physical impossibility
- Rule breach detection
Describes recognition, not punishment or response.
If it explains why something happens, it is not Constraint.
If it ranks outcomes, it is not Constraint.
- Cause → Interaction
- Change path → Dynamics
- Quantity → Magnitude
- Arrangement → Structure
- Beliefs / uncertainty → Information
- Better / worse → Evaluation
Constraint only answers “allowed vs forbidden.”
Common Failure Cases (and SAT corrections)
- ❌ “Budget pressure” → Interaction (incentive), not Constraint
- ❌ “Optimal feasible set” → Evaluation leakage
- ❌ “Law causes behavior” → Interaction + Constraint (must split)
- ❌ “Stability constraint” → Structure + Dynamics (needs decomposition)
Constraint datapoints define the boundaries of feasibility by explicitly specifying forbidden and permitted states, shaping the possibility space without invoking causality, quantity, uncertainty, or value.
6. Information
What Information Covers
Information properties answer one question only:
What can be known, encoded, distinguished, or predicted—and with what limits?
They describe epistemic state, not physical state: uncertainty, signal content, complexity, resolution, definability, noise, and learnability.
Information is about knowledge and representation, not:
- how much exists (Magnitude),
- how things are arranged (Structure),
- how they change (Dynamics),
- who influences whom (Interaction),
- what is allowed (Constraint),
- or what is better (Evaluation).
Purpose of Information Datapoints
Information datapoints exist to:
- Separate world state from knowledge state
- Make uncertainty and limits of description explicit
- Ground inference, prediction, learning, and communication
- Prevent beliefs or expectations from masquerading as quantities or causes
- Define what is in principle observable or knowable in a domain
They define the epistemic grammar of systems.
Information — Universal Datapoints
1. Information Content
What is encoded or distinguished
- Symbolic content
- Signal states
- Descriptive distinctions
Information must have content; otherwise there is nothing to know.
2. Carrier / Medium
Where the information resides
- Physical medium
- Biological substrate
- Symbol system
- Memory structure
Separates information from the thing it describes.
3. Uncertainty
Degree of indeterminacy
- Noise
- Entropy
- Variance
- Ambiguity
Information is defined relative to uncertainty.
4. Resolution / Granularity
Fineness of distinguishable states
- Bit depth
- Spatial resolution
- Conceptual granularity
Prevents collapsing coarse and fine descriptions.
5. Signal vs Noise Distinction
What counts as informative
- Signal definition
- Noise characterization
- Filtering criteria
Without this distinction, information content is undefined.
6. Observability / Accessibility
Whether information can be accessed
- Observable
- Partially observable
- Hidden
- Latent
Separates existence of information from availability of information.
7. Encoding Scheme
How information is represented
- Code
- Language
- Mapping
- Symbol system
Encoding shapes what distinctions are possible.
8. Update / Learning Rule
How information changes when new evidence arrives
- Bayesian update
- Algorithmic learning
- Adaptive revision
About knowledge change, not system dynamics.
9. Predictive Power
How well information supports prediction
- Forecast accuracy
- Compression efficiency
- Generalization capacity
Epistemic effectiveness, not desirability.
10. Complexity Measure
Descriptive cost of information
- Kolmogorov complexity
- Description length
- Model class size
Separates “more detailed” from “more complex.”
11. Redundancy / Correlation
Overlap or dependence among information pieces
- Mutual information
- Correlated signals
- Redundant encoding
About informational structure, not causal interaction.
12. Definability / Expressibility
What can be stated or specified within the representational system
- Definable vs undefinable
- Expressive limits
- Language constraints
Captures formal limits on description.
If it describes the physical state itself, it is not Information.
If it explains why something happens, it is not Information.
- Quantity → Magnitude
- Arrangement → Structure
- Change over time → Dynamics
- Influence → Interaction
- Feasibility → Constraint
- Better / worse → Evaluation
Information describes knowledge about systems, not the systems themselves.
Common Failure Cases (and SAT corrections)
- ❌ “Beliefs cause actions” → Information + Interaction (must split)
- ❌ “Expected utility” → Information + Evaluation (must split)
- ❌ “Entropy production” → Dynamics + Information (must decompose)
- ❌ “Data quality” → Information (epistemic), not Evaluation
Information datapoints define what can be known, distinguished, encoded, and predicted about a system, explicitly separating epistemic limits from physical structure, dynamics, influence, feasibility, and value.
7. Evaluation
What Evaluation Covers
Evaluation properties answer one question only:
Better or worse according to what criterion?
They assign comparative value to states, outcomes, configurations, or trajectories. Evaluation introduces ordering, preference, optimality, or fitness—explicitly and nowhere else.
Evaluation is about ranking and judgment, not:
- quantity (Magnitude),
- arrangement (Structure),
- change (Dynamics),
- influence (Interaction),
- feasibility (Constraint),
- or knowledge (Information).
Purpose of Evaluation Datapoints
Evaluation datapoints exist to:
- Make normative criteria explicit
- Separate description from judgment
- Prevent “better/worse” from being smuggled into other categories
- Anchor optimization, selection, and decision-making cleanly
- Expose a science’s implicit worldview instead of hiding it
They define the normative grammar of systems.
Evaluation — Universal Datapoints
1. Evaluated Entity / State
What is being judged
- State
- Outcome
- Configuration
- Trajectory
Evaluation must apply to something.
2. Evaluation Criterion
The standard used to judge
- Fitness
- Efficiency
- Stability
- Accuracy
- Optimality
- Cost
Without a criterion, “better” is meaningless.
3. Comparator / Reference
What the entity is compared against
- Another state
- Baseline
- Ideal
- Threshold
- Counterfactual
Evaluation is inherently comparative.
4. Ordering Type
How comparisons are structured
- Total order
- Partial order
- Ranking
- Binary acceptable / unacceptable
Prevents forcing false precision.
5. Direction of Preference
What counts as improvement
- Higher is better
- Lower is better
- Target is better
- Distance-minimizing
Makes the value direction explicit.
6. Aggregation Rule
How multiple criteria or components are combined
- Weighted sum
- Lexicographic
- Max–min
- Threshold-based
Separates value structure from quantity aggregation.
7. Context / Domain of Validity
Where the evaluation applies
- Environmental context
- Institutional setting
- Regime
- Population
Prevents universalizing local values.
8. Optimality Concept
What “best” means
- Global optimum
- Local optimum
- Satisficing
- Evolutionary stable
Clarifies aspiration without implying feasibility.
9. Tradeoff Structure
What must be sacrificed to improve
- Pareto tradeoffs
- Opportunity cost
- Frontier shape
Keeps conflict explicit instead of hidden.
10. Tolerance / Acceptability Margin
How much deviation is acceptable
- Threshold
- Indifference band
- Robustness zone
Prevents binary thinking where it doesn’t belong.
11. Stability of Evaluation
Whether criteria are fixed or changing
- Fixed
- Adaptive
- Context-shifting
Describes values themselves, not system dynamics.
12. Justification Type
Why this criterion is used
- Evolutionary
- Functional
- Ethical
- Institutional
- Axiomatic
Makes worldview commitments visible without defending them.
If it describes what is, it is not Evaluation.
If it describes what causes, it is not Evaluation.
- Quantity → Magnitude
- Arrangement → Structure
- Change → Dynamics
- Influence → Interaction
- Feasibility → Constraint
- Knowledge / belief → Information
Evaluation describes preference and ranking only.
Common Failure Cases (and SAT corrections)
- ❌ “Efficient growth rate” → Dynamics + Evaluation (must split)
- ❌ “Rational choice” → Evaluation + Information (must split)
- ❌ “Stable equilibrium is good” → Structure/Dynamics + Evaluation (must split)
- ❌ “Optimal policy causes outcome” → Evaluation + Interaction (must split)
Evaluation datapoints define how systems distinguish better from worse outcomes by making criteria, comparisons, and value structures explicit, without contaminating descriptive, causal, feasibility, or epistemic analysis.
| Element | 2. Evidence Layer | |||
|---|---|---|---|---|
| Scope Category | 2.1 Observable Phenomena | |||
| Sub-Item | Observables | |||
| Science Name Link | Branch Name Link | Field Name Link | Definition | The aspects of the domain that can produce detectable signals accessible to measurement. |
| Natural Sciences | Physics | Classical Physics | Classical Mechanics | Measurable manifestations of motion such as position, displacement, velocity, acceleration, forces, periods of oscillation, energies, momenta, and trajectories of bodies. |
| Natural Sciences | Physics | Classical Physics | Classical Electromagnetism | Measurable electromagnetic quantities such as electric fields, magnetic fields, voltage, current, charge accumulation, wave amplitude/intensity, frequency, polarization, and induced EM effects (e.g., induction, radiation). |
| Natural Sciences | Physics | Classical Physics | Classical Thermodynamics | Measurable thermodynamic quantities such as temperature, pressure, volume, heat flow, work, entropy changes, phase transitions, and equilibrium properties. |
| Natural Sciences | Physics | Classical Physics | Statistical Mechanics (Classical) | Macroscopic quantities derived from underlying microscopic ensembles: temperature, pressure, volume, energy, heat capacity, entropy, compressibility, fluctuations, correlation functions, and phase-transition behavior. |
| Natural Sciences | Physics | Classical Physics | Optics (Classical Wave Theory) | Measurable optical quantities such as intensity, irradiance, wavelength, frequency, phase, polarization, interference fringes, diffraction patterns, refraction angles, and spectral distributions. |
| Natural Sciences | Physics | Classical Physics | Acoustics | Measurable acoustic quantities such as sound pressure level, particle velocity, frequency, wavelength, phase, amplitude, intensity, spectra, reverberation time, and impulse responses. |
| Natural Sciences | Physics | Classical Physics | Continuum Mechanics | Detectable mechanical signals such as displacement, deformation, velocity fields, flow patterns, strain, stress, pressure, shear rate, wave propagation, and structural response under applied loads. |
| Natural Sciences | Physics | Classical Physics | Classical Field Theory | Detectable field quantities such as field strength, field direction, potential values, energy density, flux, wave propagation, force effects on test particles, and spatial variations of field intensity. |
| Natural Sciences | Physics | Classical Physics | Pre-Relativistic Frameworks | Classical motion of bodies, forces, accelerations, waves in media, heat transfer, fluid flow, and pre-Maxwell electromagnetic effects interpreted through instantaneous or medium-based models. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Mechanics | Measurable quantum behaviors such as discrete spectral lines, tunneling rates, interference fringes, spin orientations, transition probabilities, energy level shifts, coherence times, and quantized conductance. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Relativistic Quantum Mechanics | Measurable relativistic-quantum effects such as relativistic energy shifts, spin polarization, particle–antiparticle signatures, high-velocity scattering data, anomalous magnetic moments, and relativistic corrections to atomic spectra. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Special Relativity | Relativistic effects measurable in experiments: time dilation, length contraction, Doppler shift, aberration of light, relativistic momentum, and energy changes in high-velocity particles. |
| Natural Sciences | Physics | Modern & Fundamental Physics | General Relativity | Detectable gravitational effects such as gravitational redshift, time dilation in gravitational fields, light bending, perihelion precession, gravitational waves, black hole shadows, orbital decay of binary systems, and geodesic motion of matter and light. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Field Theory (QFT) | Detectable QFT phenomena include particle scattering events, decay rates, cross-sections, annihilation signatures, pair production, vacuum polarization effects, interference of quantum fields, and energy-level shifts such as the Lamb shift. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Particle Physics (High-Energy Physics) | Measurable particle-physics quantities such as scattering events, energy deposition in detectors, particle tracks, decay products, missing energy signatures, resonance peaks, cross-sections, and branching ratios. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Nuclear Physics | Detectable nuclear phenomena such as alpha, beta, and gamma decay; neutron capture; fission and fusion events; reaction cross-sections; nuclear energy levels; decay chains; neutron emission; and gamma-ray spectra. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Statistical Physics | Observable quantum-statistical effects include Bose-Einstein condensation, fermionic degeneracy, superfluidity, quantum phase transitions, collective excitations, quasiparticle behavior, heat-capacity anomalies, and coherence phenomena in many-body systems. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Optics | Observable quantities include photon counts, interference fringes, squeezing levels, coherence times, Rabi oscillations, cavity emission spectra, atomic excitation probabilities, and signatures of entanglement such as correlated photon detection. |
| Natural Sciences | Physics | Modern & Fundamental Physics | Quantum Information Science | Observable quantum-information quantities include qubit measurement outcomes, gate-fidelity signals, coherence decay, entanglement correlations, error-syndrome patterns, interference fringes, teleportation success rates, and quantum key distribution statistics. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Symmetry & Group Theory | Observable consequences of symmetry include conserved quantities, degenerate energy levels, selection rules, transformation behavior of fields, invariant interaction patterns, and symmetry-breaking signatures such as mass splittings or phase transitions. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Gauge Theory | 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. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | String Theory | 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. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Differential Geometry in Physics | Observable effects shaped by geometric structure include curvature-dependent gravitational behavior, particle motion along geodesic paths, interference patterns influenced by geometric phases, and field behavior connected to geometric constraints. |
| Natural Sciences | Physics | Theoretical & Mathematical Physics | Statistical Field Theory | Observable quantities include correlation functions, fluctuation magnitudes, order parameter values, susceptibility peaks, critical exponents, temporal relaxation patterns, and stochastic response signals. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Mathematical Foundations of Quantum Mechanics | Observable phenomena include measurement outcomes such as energy levels, position readings, spin results, interference patterns, and probability distributions reconstructed from repeated trials. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | General Mathematical Physics | Observables depend on the physical domain being modeled. Typical observables include field values, waveforms, trajectories, energy distributions, spatial patterns, and any measurable quantity reconstructed using mathematical models. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Solid-State Physics | Detectable signals include electrical conductivity, resistivity, optical absorption, band gaps, phonon spectra, magnetization, electronic transport behavior, crystal symmetry signatures, and scattering patterns. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Semiconductor Physics | Detectable signals include current flow, voltage response, photoluminescence, absorption spectra, carrier lifetime signatures, mobility measurements, junction characteristics, and temperature-dependent transport behavior. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Magnetism & Spin Physics | Detectable signals include magnetization curves, hysteresis loops, spin polarization, magnetic resonance signals, spin wave spectra, domain structures, magnetic noise spectra, and temperature-dependent magnetic responses. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Superconductivity | Detectable signals include zero resistance, sudden drops in resistivity at the critical temperature, Meissner effect expulsion of magnetic fields, flux quantization, magnetic vortices, critical field behavior, and persistent currents. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Soft Matter Physics | Detectable signals include viscosity changes, elastic responses, flow curves, relaxation times, microstructural rearrangements, scattering patterns, phase separation, droplet motion, and texture formation in liquid crystals. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Nanomaterials & Nanostructures | Detectable signals include size-dependent optical spectra, quantum emission lines, surface charge shifts, mechanical stiffness changes, structural images of nanoscale features, electron transport behavior, and adsorption signatures. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Strongly Correlated Electron Systems | 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. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Topological Matter | Detectable signals include quantized conductance, robust edge or surface state transport, anomalous Hall responses, suppressed backscattering, band inversion signatures, nodal point features, and characteristic surface spectroscopy results. |
| Natural Sciences | Physics | Condensed Matter & Materials Physics | Materials Science (Physical Perspective) | Detectable signals include mechanical stress strain behavior, phase transition signatures, microstructure evolution, thermal expansion, electrical conductivity changes, optical absorption, magnetic response, and defect related signals. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Stellar Astrophysics | Detectable signals include stellar luminosity, spectrum, color, surface temperature, variability, pulsations, radial velocity, magnetic activity, stellar winds, neutrino flux, and signatures of nuclear burning stages. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Galactic Astrophysics | Detectable signals include stellar light curves, spectra, gas emission lines, dust absorption features, radio signals from gas clouds, star formation tracers, supernova remnants, rotation curves, metallicity gradients, and large scale galactic morphology. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Extragalactic Astrophysics | Detectable signals include galaxy spectra, redshifts, multi band luminosities, star formation indicators, cluster X ray emission, radio jets, gravitational lensing patterns, large scale clustering, and intergalactic absorption features. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Cosmology | Detectable signals include cosmic microwave background temperature and polarization, galaxy redshift distributions, supernova brightness curves, baryon acoustic oscillation features, gravitational lensing patterns, large scale structure clustering, and primordial abundance ratios. |
| Natural Sciences | Physics | Astrophysics & Cosmology | High-Energy Astrophysics | Detectable signals include X ray and gamma ray emission, hard spectra, fast variability, pulsations, bursts, relativistic jets, nonthermal radiation, shock signatures, neutrinos, and cosmic ray flux. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Gravitational Astrophysics | Detectable signals include planetary transits, radial velocity shifts, direct imaging brightness, thermal emission, reflected light curves, atmospheric spectra, surface composition signatures, orbital motion, magnetic field indicators, and gravitational interactions. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Planetary Science & Exoplanets | Detectable signals include planetary transits, radial velocity shifts, direct imaging brightness, thermal emission, reflected light curves, planetary spectra, orbital motion, surface composition signatures, atmospheric absorption features, phase curves, and timing variations. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrochemistry & Interstellar Medium Physics | Detectable signals include molecular emission lines, atomic absorption lines, dust extinction curves, infrared vibrational features, radio line intensities, chemical abundance ratios, ionization signatures, shock tracers, and continuum emission from dust or gas. |
| Natural Sciences | Physics | Astrophysics & Cosmology | Astrobiology | Detectable signals include atmospheric gas ratios, spectral absorption features, surface reflectance patterns, organic molecule signatures, temporal variability linked to biological cycles, isotopic fractionation, mineralogical indicators, and chemical disequilibria in planetary environments. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fluid Dynamics | Detectable signals include velocity fields, pressure variations, vorticity structures, turbulence intensity, shock waves, flow separation, boundary layer thickness, temperature fields, and particle trajectories in tracer studies. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Hydrodynamics (Ideal Fluids) | Detectable signals include magnetic field fluctuations, plasma flow velocities, current sheets, shocks, Alfvén waves, magnetosonic waves, reconnection signatures, turbulence spectra, plasma density variations, and thermal or nonthermal emissions linked to magnetic processes. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Magnetohydrodynamics (MHD) | Observable signals include magnetic field fluctuations, plasma flow velocities, current sheet formation, shock fronts, Alfvén waves, magnetosonic waves, plasma density variations, reconnection outflows, turbulence spectra, and thermal or nonthermal emissions tied to magnetic processes. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Plasma Physics (General) | Observable signals include plasma density fluctuations, temperature variations, electric and magnetic field changes, wave modes, turbulence spectra, particle energy distributions, shock fronts, sheaths, instabilities, and emission lines from ionized species. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Space & Astrophysical Plasmas | Observable signals include magnetic field fluctuations, plasma density variations, flow velocities, shock fronts, current sheets, Alfvén waves, magnetosonic waves, auroral emissions, thermal and nonthermal radiation, particle distribution functions, and turbulence spectra. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Fusion Plasma Physics | Observable signals include plasma temperature profiles, density profiles, magnetic field fluctuations, radiation spectra, neutron production rates, fusion reaction products, edge localized modes, turbulence levels, current profiles, and signals from instabilities or disruptions. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Computational Fluid & Plasma Physics | Observable outputs include velocity fields, pressure fields, density fields, temperature distributions, magnetic field evolution, electric field evolution, vorticity structures, shocks, waves, turbulence spectra, transport fluxes, and particle distribution functions in kinetic simulations. |
| Natural Sciences | Physics | Plasma & Fluid Physics | Non-Newtonian & Complex Fluids | Observable signals include nonlinear stress–strain behavior, shear-thinning or thickening trends, normal stress differences, yield-stress onset, viscoelastic relaxation, thixotropic decay, particle migration, microstructural orientation, flow-induced alignment, and time-dependent viscosity changes. |
| Natural Sciences | Physics | Plasma & Fluid Physics | High-Energy-Density Physics (HEDP) | Observable signals include shock breakout signatures, compression profiles, x ray emission spectra, neutron yields, ionization levels, absorption features, plasma opacity changes, ablation front motion, instability growth rates, warm dense matter reflectivity, and time resolved temperature or density evolution. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Biophysics | Observable signals include ion channel currents, membrane potentials, molecular binding rates, fluorescence intensities, protein folding transitions, cellular forces, diffusion trajectories, structural conformations, biomechanical deformations, neural firing patterns, and optical or mechanical responses of biological tissues. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Medical Physics | Observable signals include X ray attenuation, gamma ray counts, CT voxel intensities, MRI relaxation signals, ultrasound echoes, charged particle depth dose profiles, positron emission distributions, radiation scatter patterns, detector current, portal imaging signals, and ionization chamber readings. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Geophysics | Observable signals include seismic waveforms, ground motion, gravity anomalies, magnetic field variations, electrical resistivity, heat flow measurements, GPS displacement, strain accumulation, volcanic gas emissions, groundwater level changes, and remote sensing of surface deformation. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Optics & Photonics | Observable signals include intensity patterns, interference fringes, diffraction patterns, phase shifts, spectral lines, beam profiles, pulse shapes, polarization states, fluorescence emission, scattering signatures, transmission and reflection coefficients, and photon count statistics. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Computational Physics | Observable signals include simulation output fields such as density, velocity, temperature, pressure, field strength, particle trajectories, correlation functions, energy spectra, solver residuals, convergence curves, and numerical stability patterns. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Engineering Physics | Observable signals include displacement, vibration spectra, stresses and strains, temperature fields, heat flux, voltage, current, electromagnetic field strength, optical intensity, acoustic pressure, fluid velocity, structural deformation, and device response curves. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Chemical Physics | Observable signals include absorption spectra, emission spectra, reaction rate curves, scattering intensities, vibrational peaks, rotational transitions, mass spectra, diffusion tracks, ionization yields, fluorescence lifetimes, correlation functions, and thermochemical measurements such as enthalpy or heat capacity. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Environmental & Climate Physics | Observable signals include surface temperature, atmospheric pressure, humidity, wind speed, ocean temperature profiles, salinity, sea level, greenhouse gas concentration, radiation fluxes, cloud cover, precipitation, ice extent, albedo, and atmospheric composition spectra. |
| Natural Sciences | Physics | Interdisciplinary & Applied Physics | Applied Materials Physics | Observable signals include diffraction patterns, optical spectra, electrical resistance, thermal conductivity, stress–strain curves, magnetization hysteresis loops, photoluminescence, carrier mobility, defect signatures, microstructural images, phase-transition signatures, and compositional maps. |
| Natural Sciences | Chemistry | Physical Chemistry | Quantum Chemistry | Absorption/emission spectra, photoelectron signals, scattering patterns, electron density distributions, reaction energetics, vibrational/rotational transitions. |
| Natural Sciences | Chemistry | Physical Chemistry | Statistical Mechanics | Fluctuations, probability distributions, heat flow, pressure, volume changes, correlations, phase transitions, relaxation behaviors. |
| Natural Sciences | Chemistry | Physical Chemistry | Thermodynamics | Heat flow, temperature changes, pressure variations, phase transitions, work exchange, volume changes, calorimetric responses. |
| Natural Sciences | Chemistry | Physical Chemistry | Kinetics & Reaction Dynamics | Time-dependent concentration changes, reaction rates, product distributions, intermediate lifetimes, molecular scattering signals, energy transfer signatures. |
| Natural Sciences | Chemistry | Physical Chemistry | Spectroscopy | Absorption peaks, emission lines, scattering intensities, fluorescence lifetimes, Raman shifts, NMR chemical shifts, time-resolved transients. |
| Natural Sciences | Chemistry | Physical Chemistry | Electrochemistry | Cell voltage, current, concentration changes, electrode potential shifts, impedance spectra, charge–discharge curves, diffusion-limited currents, gas evolution signals. |
| Natural Sciences | Chemistry | Physical Chemistry | Surface & Interface Science | Adsorption isotherms, contact angles, surface tension changes, work-function shifts, spectroscopic signatures at interfaces, STM/AFM topography, catalytic turnover signals. |
| Natural Sciences | Chemistry | Physical Chemistry | Colloid & Solution Chemistry | Turbidity changes, scattering intensity, sedimentation behavior, viscosity shifts, conductivity, zeta potential, particle-size distributions, solubility changes, phase separation. |
| Natural Sciences | Chemistry | Physical Chemistry | Chemical Physics | Spectral lines, scattering intensities, energy-transfer signatures, reaction cross-sections, molecular-beam distributions, relaxation curves, coherent oscillations. |
| Natural Sciences | Chemistry | Organic Chemistry | Structural & Mechanistic Organic Chemistry | Reaction rates, product distributions, stereochemical outcomes, color changes, pH changes, heat release, spectroscopic shifts indicating intermediates or transition-state proximity. |
| Natural Sciences | Chemistry | Organic Chemistry | Stereochemistry & Conformational Analysis | Optical rotation, NMR coupling patterns, chemical-shift differences, NOE enhancements, conformer populations, IR band shifts, diastereomeric ratios, temperature-dependent conformer interconversion. |
| Natural Sciences | Chemistry | Organic Chemistry | Synthetic Organic Chemistry | Reaction progress (color change, gas evolution, precipitation), product formation, yield, stereochemical outcomes, TLC migration, chromatographic retention, NMR/IR changes. |
| Natural Sciences | Chemistry | Organic Chemistry | Physical Organic Chemistry | Reaction rates, equilibrium shifts, isotope effects, substituent-dependent changes in rate or selectivity, activation parameters, spectral signatures of intermediates, solvent-dependent reactivity. |
| Natural Sciences | Chemistry | Organic Chemistry | Organometallic Organic Chemistry | Color changes, redox shifts, ligand-exchange signals, catalytic turnover rates, formation of metallacycles, oxidative-addition signatures, migratory insertion behavior, gas uptake/release. |
| Natural Sciences | Chemistry | Organic Chemistry | Polymer Chemistry (Carbon-based) | Viscosity changes, molecular-weight growth, polymer precipitation, phase separation, turbidity, gel formation, thermal transitions (Tg, Tm), Raman/IR shifts, NMR signatures of tacticity. |
| Natural Sciences | Chemistry | Organic Chemistry | Bioorganic Chemistry | Reaction rates in enzyme or biomimetic systems, binding events, pH-dependent reactivity, conformational changes, fluorescence signals, UV–Vis shifts, redox transitions, product profiles. |
| Natural Sciences | Chemistry | Organic Chemistry | Natural Products Chemistry | UV–Vis absorption, NMR signatures, MS fragmentation patterns, optical rotation, chromatographic behavior, bioactivity profiles, color changes, precipitation, enzyme-mediated transformation. |
| Natural Sciences | Chemistry | Organic Chemistry | Medicinal Chemistry | Binding signals, enzyme inhibition, receptor activation/inactivation, cell viability changes, pharmacokinetic curves, metabolic transformations, toxicity markers, fluorescence/absorbance shifts. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Main-Group Chemistry | Color changes, precipitation, gas evolution, conductivity shifts, redox potentials, IR/Raman vibrational signatures, UV–Vis absorption, NMR shifts, thermal decomposition patterns. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Transition-Metal Chemistry | Color changes (d–d transitions), magnetic responses, redox potential shifts, ligand substitution signals, spin crossover, catalytic turnover, gas uptake/release, coordination changes. |
| Natural Sciences | Chemistry | Inorganic Chemistry | f-Block Chemistry | Characteristic f–f transitions (Laporte-forbidden), sharp emission lines (Ln³⁺), broad charge-transfer bands (An), magnetic responses, redox-state changes, coordination shifts, radioluminescence, solvatochromism. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Coordination Chemistry | Color changes from d–d/LMCT/MLCT transitions, changes in UV–Vis spectra, magnetic behavior (spin states), ligand substitution signatures, redox shifts, coordination-number changes, precipitation/dissolution. |
| Natural Sciences | Chemistry | Inorganic Chemistry | Solid-State Chemistry | Diffraction patterns, conductivity changes, magnetic responses, phase transitions, color changes, phonon/vibrational modes, heat capacity anomalies, thermal expansion, defect-related signals. |
| Natural Sciences | Chemistry | Analytical Chemistry | Qualitative Analysis | Color changes, precipitate formation, gas evolution, pH shifts, spectral peaks (IR/NMR/UV–Vis), flame tests, odor signatures, fragmentation patterns (MS), chromatographic retention patterns. |
| Natural Sciences | Chemistry | Analytical Chemistry | Quantitative Analysis | Signal intensity, absorbance/fluorescence, peak area, mass-to-charge counts, conductivity, charge transfer, titration endpoints, weight/volume changes, instrument drift, blank noise levels. |
| Natural Sciences | Chemistry | Analytical Chemistry | Separation Science | Retention times, migration times, peak shapes, peak widths, peak asymmetry, solvent front movement, band broadening, color zones, conductance changes, pH shifts, membrane permeation rates, extraction layer formation. |
| Natural Sciences | Chemistry | Analytical Chemistry | Instrumental Analysis | Absorbance/emission peaks, m/z ion signals, chromatographic peaks, voltammograms, current/potential curves, thermal transitions, resonance frequencies, scattering signals, detector counts, baseline drift. |
| Natural Sciences | Chemistry | Biochemistry | Structural Biochemistry | X-ray diffraction patterns, NMR chemical shifts/NOEs/RDCs, cryo-EM density maps, circular dichroism spectra, fluorescence quenching, FRET signals, hydrogen-exchange rates, SAXS profiles, unfolding/refolding curves. |
| Natural Sciences | Chemistry | Biochemistry | Enzymology | Reaction-rate changes, substrate depletion, product formation, absorbance/fluorescence shifts, heat release (calorimetry), pH changes, binding curves, stopped-flow transients, isotope effects, allosteric switching behaviors. |
| Natural Sciences | Chemistry | Biochemistry | Metabolism & Bioenergetics | ATP/ADP/AMP ratios, oxygen consumption, CO₂ production, NADH/NAD⁺ redox signals, fluorescence from metabolic cofactors, calorimetric heat flow, pH changes, membrane potential shifts, metabolite level changes, isotopic enrichment in flux studies. |
| Natural Sciences | Chemistry | Biochemistry | Molecular Biology & Gene Expression | Transcript abundance changes, promoter activation, protein-expression levels, fluorescent reporter output, chromatin accessibility, DNA–protein binding events, ribosome occupancy, RNA splicing patterns, RNA degradation curves, epigenetic modifications. |
| Natural Sciences | Chemistry | Biochemistry | Cellular Biochemistry | Fluorescence signals, organelle morphology changes, calcium spikes, membrane potential fluctuations, metabolite-level shifts, protein localization changes, vesicle trafficking, cytoskeletal dynamics, redox shifts, pH changes. |
| Natural Sciences | Chemistry | Biochemistry | Membrane Biochemistry | Fluorescence intensity changes in membranes, lipid-phase transitions, FRAP recovery curves, membrane-potential shifts, Ca²⁺/ion flux signals, curvature changes, vesicle budding/fusion, protein relocalization, lipid-domain formation, permeability changes. |
| Natural Sciences | Chemistry | Biochemistry | Protein Chemistry | Absorbance/fluorescence changes, circular dichroism signals, unfolding transitions, UV/visible spectra, NMR chemical shifts, MS peptide masses/fragments, SDS-PAGE band patterns, aggregation/turbidity, enzymatic activity shifts, PTM signatures. |
| Natural Sciences | Chemistry | Biochemistry | Biochemical Genetics | Altered metabolite levels, abnormal enzyme activity, shifted kinetic curves, accumulation of toxic intermediates, misfolded proteins, altered PTM patterns, aberrant RNA expression, variant-specific protein stability, organelle dysfunction, phenotypic traits arising from biochemical defects. |
| Natural Sciences | Earth & Space Sciences | Geology | Mineralogy & Crystallography | X-ray diffraction peaks, crystal habit, cleavage/fracture patterns, optical interference colors, refractive indices, birefringence, Raman/IR vibrational modes, luminescence, density changes, magnetic/electrical responses, phase transitions. |
| Natural Sciences | Earth & Space Sciences | Geology | Petrology | Mineral assemblages, grain size, foliation/lineation, porphyroblasts, zoning, reaction rims, melt inclusions, vesicles, phenocryst textures, mineral chemistry variations, color index, modal proportions, xenoliths, exsolution textures. |
| Natural Sciences | Earth & Space Sciences | Geology | Structural Geology & Tectonics | Fault scarps, fold geometries, joint sets, shear zones, foliations, lineations, boudinage, microstructures, displacement offsets, slickensides, earthquake locations, GPS motions, crustal thickness changes, seismic anisotropy. |
| Natural Sciences | Earth & Space Sciences | Geology | Sedimentology & Stratigraphy | Grain size/sorting, sedimentary structures (ripples, dunes, cross-bedding, mudcracks), bedding thickness, facies transitions, bioturbation textures, color changes, fossil assemblages, unconformities, stratigraphic stacking patterns, chemical laminations, graded beds. |
| Natural Sciences | Earth & Space Sciences | Geology | Geomorphology | Slope angles, channel geometry, sediment transport rates, bedform migration, shoreline change, dune movement, glacier motion, landslides, river avulsion, erosion/deposition patterns, drainage-network evolution, terrace formation, rockfall/failure events. |
| Natural Sciences | Earth & Space Sciences | Geology | Geophysics | Seismic wave travel times, waveforms, amplitudes, ground motion; gravity anomalies; magnetic anomalies; electrical resistivity/EM responses; heat-flow values; GNSS displacement; InSAR deformation fields; seismicity patterns; geoid variations; microseismic noise; planetary magnetic-field variations. |
| Natural Sciences | Earth & Space Sciences | Geology | Geochemistry | Elemental concentrations, isotope ratios, mineral compositions, fluid chemistry (pH, Eh, ions), precipitation/dissolution textures, alteration halos, weathering profiles, gas fluxes, adsorption signals, redox gradients, speciation patterns. |
| Natural Sciences | Earth & Space Sciences | Geology | Paleontology | Fossil bones, shells, teeth, impressions, trace fossils (tracks, burrows, coprolites), microfossils, mineralized tissues, carbon films, articulated vs disarticulated remains, bedding-plane assemblages, diversity patterns, extinction horizons, biogeographic ranges. |
| Natural Sciences | Earth & Space Sciences | Geology | Hydrogeology | Water levels in wells, hydraulic head changes, spring discharge, stream–aquifer interactions, tracer breakthroughs, contaminant plumes, groundwater flow directions, saturation changes, seepage faces, salinity gradients, pumping-drawdown responses. |
| Natural Sciences | Earth & Space Sciences | Geology | Economic & Applied Geology | Ore-grade distributions, alteration halos, mineral assemblages, geochemical anomalies, geophysical anomalies (gravity, magnetic, EM, seismic), reservoir pressure/temperature, porosity/permeability logs, fluid compositions, drill core lithology, shows of hydrocarbons or mineralization, fracture networks. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Dynamic Meteorology | Wind speed and direction, pressure fields, temperature fields, humidity, vorticity, vertical motion, cloud-motion vectors, atmospheric waves, jet streams, fronts, and circulation patterns measurable by remote sensing or in-situ instruments. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Thermodynamic Meteorology | Temperature profiles, humidity profiles, dewpoint, lapse rates, cloud-base height, cloud-top temperature, radiative fluxes, stability indices (CAPE, CIN), phase changes, and vertical heat/moisture transport. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Cloud Physics & Microphysics | Cloud droplet spectra, ice crystal habits, liquid and ice water content, reflectivity, depolarization signals, radiances, particle fall speeds, cloud boundaries, precipitation onset, and aerosol concentrations. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Synoptic & Mesoscale Meteorology | Pressure patterns, fronts, wind fields, temperature gradients, humidity distributions, vorticity centers, radar reflectivity, Doppler velocity signatures, cloud-top temperatures, storm structures, boundary-layer features, and mesoscale convergence zones. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Atmospheric Physics & Chemistry | Gas concentrations, aerosol size distributions, radiative fluxes, spectral absorption/emission signatures, ozone columns, particulate optical properties, trace-gas plumes, NOx/VOC levels, photolysis rates, and scattering signals. |
| Natural Sciences | Earth & Space Sciences | Meteorology | Climatology & Climate Dynamics | Long-term temperature trends, precipitation patterns, sea-level rise, ocean heat content, radiative fluxes, greenhouse-gas concentrations, sea-ice extent, circulation indices (ENSO, NAO), paleoclimate proxies, and large-scale variability modes. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Physical Oceanography | Sea-surface height, currents, temperature, salinity, density structure, waves, tides, ocean color, mixed-layer depth, internal waves, turbulence, eddies, sea ice extent, heat/salt fluxes, stratification, upwelling/downwelling. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Chemical Oceanography | Nutrient concentrations, dissolved oxygen, pH, alkalinity, DIC/TOC/DOC, trace metals, major ions, redox gradients, particulate loads, gas exchange rates, hydrothermal plumes, riverine chemical signatures, sediment–water fluxes. |
| Natural Sciences | Earth & Space Sciences | Oceanography | Biological Oceanography | Chlorophyll-a, phytoplankton/zooplankton abundance, microbial counts, primary productivity, optical properties, particulate organic carbon (POC), dissolved organic matter (DOM), fluorescence, oxygen utilization, blooms, diel vertical migration, biogenic particle flux (marine snow). |
| Natural Sciences | Earth & Space Sciences | Oceanography | Geological Oceanography | Sediment thickness, grain-size distributions, mineralogy, sediment accumulation rates, microfossil assemblages, seafloor morphology, magnetic lineations, seismic reflections, heat flow, hydrothermal plumes, turbidity currents, methane seeps, bioturbation structures. |
| Natural Sciences | Biology | Molecular Biology | Nucleic Acid Biology | Detectable features such as nucleotide sequences, base-pairing patterns, methylation status, chromatin accessibility, replication fork movement, transcriptional activity, RNA structures, and nucleic acid damage signatures. |
| Natural Sciences | Biology | Molecular Biology | Gene Regulation & Epigenetics | Detectable features include chromatin accessibility, histone marks, DNA methylation levels, transcription-factor binding, regulatory RNA abundance, enhancer–promoter interactions, transcriptional output, and chromatin compaction states. |
| Natural Sciences | Biology | Molecular Biology | Protein Biology | Detectable protein properties such as folding state, secondary/tertiary structure, enzymatic activity, ligand binding, PTM status, oligomerization, interaction networks, and conformational changes. |
| Natural Sciences | Biology | Molecular Biology | Molecular Complexes & Information Flow | Detectable features include complex assembly/disassembly, interaction frequencies, conformational shifts, signal-transduction events, spatial localization patterns, phase-separation behavior, and throughput of biochemical information. |
| Natural Sciences | Biology | Molecular Biology | Molecular Methods & Technologies | Detectable signals include fluorescence emission, absorbance spectra, sequencing reads, electrophoretic band patterns, mass-spec peaks, imaging contrast, probe binding intensity, molecular mobility, and reaction kinetics. |
| Natural Sciences | Biology | Cell Biology | Cell Structure & Organelles | Organelle morphology, membrane topology, vesicle trafficking, cytoskeletal dynamics, protein localization patterns, organelle fusion/fission events, pH-dependent fluorescence, ion fluxes, and structural rearrangements. |
| Natural Sciences | Biology | Cell Biology | Cellular Dynamics & Trafficking | Vesicle movement trajectories, motor-protein stepping behavior, fusion/fission events, cargo loading/unloading, membrane budding, endocytosis kinetics, organelle repositioning, diffusion patterns, Rab switching, and cytoskeletal track usage. |
| Natural Sciences | Biology | Cell Biology | Cell Signaling & Communication | Ligand–receptor binding events, receptor clustering, phosphorylation changes, second-messenger pulses (Ca²⁺ spikes, cAMP waves), activation of kinases or transcription factors, membrane potential changes, synaptic release, cell–cell junction signaling, reporter-gene activation. |
| Natural Sciences | Biology | Cell Biology | Cell Cycle, Fate & Death | Cyclin oscillations, checkpoint activation, DNA replication progression, chromosome condensation, spindle assembly, caspase activation, mitochondrial outer-membrane permeabilization, chromatin-state transitions, lineage-marker expression, senescence-associated phenotypes. |
| Natural Sciences | Biology | Cell Biology | Cell Interactions & Microenvironment | Cell–cell adhesion formation, junction assembly/disassembly, traction forces, cell spreading, ECM remodeling, stiffness sensing, gradient formation, chemotaxis, durotaxis, paracrine factor diffusion, immune cell infiltration, niche-factor secretion, migration trajectories. |
| Natural Sciences | Biology | Cell Biology | Cell Morphology & Motility | Protrusion dynamics (lamellipodia, filopodia, blebs), actin polymerization waves, focal-adhesion formation and turnover, cytoskeletal reorganization, migration trajectories, cell-shape transitions, traction-force patterns, polarity establishment and switching, microtubule dynamics. |
| Natural Sciences | Biology | Genetics & Evolution | Classical & Transmission Genetics | Segregation ratios in offspring, phenotypic ratios, linkage deviations from independent assortment, recombination frequencies, pedigree inheritance patterns, gamete-genotype distributions. |
| Natural Sciences | Biology | Genetics & Evolution | Population Genetics | Allele-frequency changes across generations, deviations from Hardy–Weinberg expectations, genotype-count distributions, recombination-derived LD patterns, signatures of drift in small populations, migration-driven allele introgression, and selection-driven changes in fitness-associated alleles. |
| Natural Sciences | Biology | Genetics & Evolution | Quantitative Genetics | Continuous phenotypic variation, parent–offspring resemblance, sibling resemblance, trait heritability patterns, response to selection, variance shifts across generations, genetic correlations among traits, distributional changes after selection. |
| Natural Sciences | Biology | Genetics & Evolution | Genomic Evolution & Comparative Genomics | Sequence divergence patterns, conserved motifs, ortholog/paralog relationships, gene-family expansions/contractions, genome rearrangements (inversions, fusions, fissions), synteny conservation, substitution-rate variation, TE insertions, phylogenetic branching patterns. |
| Natural Sciences | Biology | Genetics & Evolution | Phylogenetics & Systematics | Character-state variation, sequence divergence, morphological differences, shared derived traits (synapomorphies), branching patterns in phylogenetic trees, bootstrap or posterior support values, biogeographic patterns, species-boundary signals. |
| Natural Sciences | Biology | Genetics & Evolution | Macroevolution & Speciation Theory | Fossil lineage splitting and extinction patterns, morphological transitions, biogeographic range shifts, diversification bursts or slowdowns, reproductive isolation markers, hybrid zones, sister-clade asymmetry, lineage-through-time curves, and trait divergence across species. |
| Natural Sciences | Biology | Physiology | Cellular & Tissue Physiology | Membrane potentials, ion fluxes, intracellular Ca²⁺ signals, mechanical deformation, contraction events, epithelial transport rates, tissue stiffness, and changes in cell morphology. |
| Natural Sciences | Biology | Physiology | Neurophysiology | Action potentials, synaptic potentials, ionic currents, neurotransmitter release, intracellular Ca²⁺ transients, oscillatory rhythms, firing-rate changes, sensory receptor potentials, and network synchronization. |
| Natural Sciences | Biology | Physiology | Endocrine & Regulatory Physiology | Plasma hormone levels, secretion pulses, metabolic readouts (glucose, lipids), receptor activation, downstream signaling activity, glandular output rhythms, stress-response markers, and electrolyte balance shifts. |
| Natural Sciences | Biology | Physiology | Cardiovascular & Respiratory Physiology | Blood pressure waves, ECG traces, heart sounds, airflow patterns, lung volumes, oxygen/CO₂ levels, ventilation rate, perfusion distribution, pulse oximetry signals, and gas-exchange curves. |
| Natural Sciences | Biology | Physiology | Metabolic & Energetic Physiology | Oxygen consumption (VO₂), carbon dioxide production (VCO₂), respiratory quotient (RQ/RER), blood glucose, lactate levels, ATP turnover indicators, metabolic heat output, substrate-oxidation signals, and exercise-induced metabolic shifts. |
| Natural Sciences | Biology | Physiology | Renal, Fluid & Homeostatic Physiology | Filtration markers, urine flow, urine osmolarity, electrolyte concentrations, blood pH, bicarbonate levels, plasma osmolarity, blood volume indicators, RAAS/ADH activity markers, and acid–base compensation responses. |
| Natural Sciences | Biology | Developmental Biology | Cell Fate & Lineage Specification | Changes in transcription-factor expression, shifts in chromatin accessibility, asymmetric segregation of determinants, lineage branching events, potency-state transitions, signaling-gradient responsiveness, and differentiation markers across developmental time. |
| Natural Sciences | Biology | Developmental Biology | Pattern Formation & Embryonic Axes | Morphogen gradients, spatial expression domains, boundary-sharpening events, organizer activity, symmetry-breaking cues, segmentation-oscillation waves, axis-polarity markers, positional-response thresholds, embryonic pattern defects under perturbation. |
| Natural Sciences | Biology | Developmental Biology | Morphogenesis & Tissue-Level Mechanics | Tissue deformation, epithelial folding, convergent extension, cell intercalation, contractile pulses, junctional tension changes, cell-shape transitions, tissue-flow fields, curvature formation, ECM remodeling, and mechanical-stress patterns. |
| Natural Sciences | Biology | Developmental Biology | Organogenesis & Multi-Tissue Assembly | Tissue primordia positioning, epithelial–mesenchymal interactions, budding and branching events, lumen formation and expansion, compartment-boundary emergence, coordinated tissue flows, ECM deposition patterns, cross-tissue signaling responses, vascular ingression, and organ-shape acquisition over time. |
| Natural Sciences | Biology | Developmental Biology | Growth, Timing, Regeneration & Life-Cycle Transitions | Growth curves, size changes, proliferation rates, timing of developmental events, regeneration onset and progression, circadian or developmental oscillations, hormone-level changes, life-stage transitions (molting, metamorphosis), blastema formation, wound closure dynamics. |
| Natural Sciences | Biology | Developmental Biology | Evolutionary Development (Evo–Devo) | Changes in gene-expression patterns across species; shifts in enhancer activity; alterations in developmental timing (heterochrony); spatial redeployment of regulatory programs (heterotopy); morphological variants in embryos and adults; conserved and divergent GRN modules; embryonic-pattern differences aligned to phylogeny. |
| Natural Sciences | Biology | Ecology | Organismal Ecology | Observable signals include movement patterns, habitat selection, body temperature, behavioral actions, foraging rates, physiological metrics, stress responses, territorial displays, migration timing, and microhabitat use. |
| Natural Sciences | Biology | Ecology | Population Ecology | Population counts, birth and death events, age/size distribution, immigration/emigration events, density patterns, recruitment levels, survival of cohorts, and fluctuations in population abundance over time. |
| Natural Sciences | Biology | Ecology | Community Ecology | Species presence/absence, abundance patterns, species richness, diversity indices, trophic interactions, behavioral interactions, resource use patterns, species turnover, and spatial aggregation or dispersion. |
| Natural Sciences | Biology | Ecology | Ecosystem Ecology | Detectable signals include biomass levels, primary productivity, respiration rates, nutrient concentrations, decomposition activity, carbon/water fluxes, trophic-flow metrics, and changes in pool sizes across time. |
| Natural Sciences | Biology | Ecology | Landscape & Spatial Ecology | Detectable signals include species spatial distributions, patch occupancy patterns, dispersal routes, landscape fragmentation, connectivity gradients, habitat-use mosaics, edge effects, and spatial autocorrelation. |
| Natural Sciences | Biology | Ecology | Global Ecology & Earth-System Interactions | Detectable global signals: atmospheric CO₂, methane, aerosol optical depth, global NPP, surface temperature patterns, ocean heat content, vegetation cover, ice-sheet extent, precipitation trends, and large-scale nutrient fluxes. |
| Formal Sciences | Logic | Proof Theory | Proof Calculi | Derivation steps, rule applications, sequent transformations, proof-tree expansions, closure of tableaux branches, admissibility of rules, derivability judgments (⊢). |
| Formal Sciences | Logic | Proof Theory | Structural Proof Theory | Sequent transformations, rule applications, context rearrangements, structural rule effects (exchange, weakening, contraction), cut steps and their eliminations, derivation shapes, normalization sequences. |
| Formal Sciences | Logic | Proof Theory | Proof Theory of Non-Classical Logics | Labeled-sequent transformations, modal rule applications, resource-sensitive rule usage, relevance-preserving steps, multi-valued rule firings, accessibility propagation, cut behavior in non-classical systems, normalization traces. |
| Formal Sciences | Logic | Proof Theory | Ordinal & Strength Analysis | Ordinal assignments to theories, proof-theoretic reductions, termination of transfinite induction, collapsing-function behavior, derivation length bounds, reflection principle activation, growth-rate comparisons in recursive hierarchies. |
| Formal Sciences | Logic | Proof Theory | Proof Complexity | Proof lengths, proof sizes, widths of clauses, space usage, degree of algebraic derivations, depth of proof trees, performance of proof search, lower-bound hardness instances, simulation relations between proof systems. |
| Formal Sciences | Logic | Proof Theory | Automated & Interactive Reasoning | Solver decisions, branching behavior, search-tree growth, tactic execution traces, proof-state transitions, model generation, constraint propagation steps, unification attempts, backtracking behavior, time-to-solve, failure modes. |
| Formal Sciences | Logic | Model Theory | Structures, Languages & Interpretations | Truth values of formulas in structures, definable sets/functions, satisfaction patterns, homomorphism behavior, embedding properties, isomorphism invariants. |
| Formal Sciences | Logic | Model Theory | Satisfaction & Definability Theory | Truth values of formulas under assignments, definable sets/functions, failure or success of definability, quantifier-elimination behavior, type realizations, preservation under embeddings. |
| Formal Sciences | Logic | Model Theory | Quantifier Theory & Model Completeness | Truth conditions of quantified formulas, quantifier-elimination success/failure, preservation under embeddings, alternation depth effects, definability changes after Skolemization, model-completeness behavior. |
| Formal Sciences | Logic | Model Theory | Classification Theory | Stability behavior, forking/dividing patterns, type multiplicities, rank values (Morley rank, U-rank), independence configurations, saturation behavior, classification dividing lines. |
| Formal Sciences | Logic | Model Theory | Tame / O-Minimal Model Theory | Definable sets in one variable (finite unions of points and intervals), monotonicity of definable functions, cell decomposition, definable continuity, dimension behavior. |
| Formal Sciences | Logic | Set Theory | Axiomatic Foundations & Cumulative Hierarchy | Rank of sets, ordinal progression, transfinite recursion behavior, membership patterns, well-founded chains, combinatorial principles derived from ZFC, consequences of axioms. |
| Formal Sciences | Logic | Set Theory | Constructibility & Inner Models | Definability patterns in (L), level-by-level construction (L_\alpha), condensation behavior, fine-structure signatures, presence/absence of sharps, elementary substructure patterns, canonical well-orderings. |
| Formal Sciences | Logic | Set Theory | Large Cardinal Theory | Embeddings (j : V \to M), critical points, measurable ultrafilters, extender sequences, closure properties of large cardinals, reflection phenomena, indescribability behavior, combinatorial consequences (tree properties, stationary reflection). |
| Formal Sciences | Logic | Set Theory | Forcing & Independence Theory | Cardinal changes across forcing extensions, collapse phenomena, preservation or destruction of combinatorial principles, truth-value variation of statements (e.g., CH), behavior of generic filters, Boolean truth values, absoluteness patterns. |
| Formal Sciences | Logic | Set Theory | Descriptive Set Theory | Borel ranks, projective levels, Wadge degrees, definability behavior in Polish spaces, regularity properties (measurability, Baire property, perfect set property), game outcomes under determinacy. |
| Formal Sciences | Logic | Computability Theory | Models of Computation & Recursive Function Theory | Machine configurations (state, tape contents, head position), sequences of reductions in λ-calculus, recursion unfolding steps, halting vs. non-halting behavior, enumeration traces of partial computable functions, oracle query patterns, divergence patterns, step counts. |
| Formal Sciences | Logic | Computability Theory | Recursively Enumerable (r.e.) Sets & Degrees | Enumeration traces of r.e. sets, stage-by-stage limit approximations, oracle-query behavior, injury patterns in priority constructions, reducibility computations, convergence/divergence behavior, jump-operator outputs. |
| Formal Sciences | Logic | Computability Theory | Reducibility & Degrees of Unsolvability | Reducibility traces (Turing/m/tt/wtt), oracle-call patterns, stage-by-stage approximations to reductions, divergence or convergence of reduction attempts, behavior of jump operations, appearance of incomparable degrees in constructions. |
| Formal Sciences | Logic | Computability Theory | Arithmetical & Analytical Hierarchies | Quantifier-prefix patterns in formulas; stabilization of limit approximations; behavior of Turing jumps; oracle-call traces in relativized computations; definability changes under added quantifiers; emergence of completeness phenomena (e.g., Σ₁⁰-complete sets, Σ₁¹-complete sets). |
| Formal Sciences | Mathematics | Algebra | Group Theory | Multiplication behavior of elements; subgroup inclusions; coset decompositions; conjugacy patterns; element orders; orbit–stabilizer behavior under group actions; kernel/image under homomorphisms; eigenvalue structures for matrix groups. |
| Formal Sciences | Mathematics | Algebra | Ring Theory | Addition and multiplication behavior of elements; presence of units; zero-divisor interactions; ideal containment patterns; Gröbner basis reductions; factorization outcomes; matrix-ring multiplication patterns; behavior of evaluation homomorphisms; localization effects. |
| Formal Sciences | Mathematics | Algebra | Field Theory | Polynomial factorization patterns; behavior of roots under field extensions; splitting-field formation; separability/inseparability behavior; degree of extensions; automorphism structure; ramification behavior in valued fields; norm/trace computations; residue-field interactions. |
| Formal Sciences | Mathematics | Algebra | Module Theory | Submodule containment behavior; kernel and cokernel emergence under homomorphisms; decomposition into direct sums; torsion element behavior; rank or dimension changes (when defined); annihilator behavior; tensor-product transformations; presentation matrix reductions; exactness of sequences. |
| Formal Sciences | Mathematics | Algebra | Linear Algebra | Behavior of vectors under linear transformation; row/column dependencies; solvability of linear systems; matrix rank changes; eigenvalue/eigenvector structure; orthogonality patterns; projection behavior; determinant changes under operations; stability of decompositions (QR, SVD). |
| Formal Sciences | Mathematics | Algebra | Representation Theory | Matrix behavior under group/algebra actions; invariance of subspaces; decomposition into irreducibles; eigenvalues/eigenvectors of representing matrices; character values; multiplicity patterns; tensor-product decomposition outcomes; weight-space structure; branching rules. |
| Formal Sciences | Mathematics | Algebra | Universal Algebra | Operation outcomes; closure behavior; identity satisfaction/violation; homomorphism preservation patterns; congruence formation; subalgebra generation; product behavior; term-rewriting traces; free-algebra growth. |
| Formal Sciences | Mathematics | Algebra | Algebraic Combinatorics | Enumeration sequences; symmetric-function expansions; tableau growth and behavior; eigenvalues/eigenvectors of combinatorial matrices; spectra of graphs in association schemes; permutation statistics (inversions, descents, major index); character values in symmetric-group representations; generating-function coefficients; Coxeter group actions. |
| Formal Sciences | Mathematics | Mathematical Analysis | Real Analysis | Limits approaching finite or infinite values; rates of convergence of sequences/series; continuity/discontinuity behavior; differentiability or nondifferentiability; oscillation of functions; integrability properties; measure of sets; variation of functions; norm changes in Lᵖ spaces; convergence behaviors under different modes (pointwise, uniform, almost everywhere). |
| Formal Sciences | Mathematics | Mathematical Analysis | Complex Analysis | Behavior of complex functions near singularities; convergence of power and Laurent series; contour integral values; residue contributions; argument/winding number changes; harmonic function behavior; modulus and argument variation; analytic continuation behavior across overlapping regions; uniform convergence on compact sets. |
| Formal Sciences | Mathematics | Mathematical Analysis | Functional Analysis | Convergence (strong, weak, weak-*); operator norms; spectral radii; compactness behavior; boundedness of linear maps; stability under perturbations; norm growth/decay; orthogonality relations; Fourier/Sobolev expansion coefficients; distributional action on test functions; resolvent behavior for operators. |
| Formal Sciences | Mathematics | Mathematical Analysis | Harmonic Analysis | Fourier coefficients; Fourier transform magnitudes/phases; decay rates in frequency domain; convolution outputs; oscillation patterns; singular-integral responses; maximal-function growth; wavelet coefficients; spectral distributions of operators; behavior of harmonic functions on domains. |
| Formal Sciences | Mathematics | Mathematical Analysis | Differential Equations (ODE/PDE) | Trajectories of ODE solutions; steady states; oscillations; blow-up events; diffusion and wave propagation; heat dissipation profiles; shock formation; boundary-layer behavior; PDE solution surfaces; eigenfunctions of differential operators; time-series evolution from numerical solvers. |
| Formal Sciences | Mathematics | Geometry & Topology | Differential Geometry | Curvature (sectional, Ricci, scalar), geodesic behavior, torsion, metric distances, volume elements, differential-form integrals, flow trajectories, local coordinate behavior. |
| Formal Sciences | Mathematics | Geometry & Topology | Algebraic Geometry | Zero-loci of polynomials, intersections, singularities, fiber behavior, divisor interactions, cohomology dimensions, deformation patterns under parameter changes. |
| Formal Sciences | Mathematics | Geometry & Topology | Metric Geometry | Distances, curve lengths, geodesic paths, triangle-comparison behavior, curvature bounds (CAT(k)), covering numbers, doubling properties, Gromov–Hausdorff convergence patterns. |
| Formal Sciences | Mathematics | Geometry & Topology | Point-Set Topology | Convergence (sequences, nets, filters), continuity behavior, compactness via open covers, connectedness patterns, separation-axiom effects, product and quotient behavior. |
| Formal Sciences | Mathematics | Geometry & Topology | Homotopy Theory | Behavior of paths, loops, homotopies, homotopy classes, fiber-sequence structure, long exact sequence patterns, suspension stability. |
| Formal Sciences | Mathematics | Geometry & Topology | Knot Theory | Crossing patterns, over/under information, Reidemeister-move behavior, linking behavior in links, chirality, Seifert-surface structure, polynomial invariant values, knot complement properties (e.g., hyperbolic volume). |
| Formal Sciences | Mathematics | Number Theory | Elementary Number Theory | Prime occurrence, divisibility patterns, modular residues, parity behavior, periodicity in congruences, factorization structure, arithmetic-function behavior (φ, μ, σ, τ), basic Diophantine solvability. |
| Formal Sciences | Mathematics | Number Theory | Algebraic Number Theory | Prime splitting in extensions, ramification patterns, discriminant size, ideal-factorization structure, residue-field behavior, norm/trace values, local–global solvability of equations. |
| Formal Sciences | Mathematics | Number Theory | Analytic Number Theory | Prime-counting behavior (\pi(x)); distribution of primes in progressions; oscillatory behavior of arithmetic functions (μ(n), Λ(n)); size/growth of L-functions; zero locations; exponential-sum cancellation. |
| Formal Sciences | Mathematics | Number Theory | Arithmetic Geometry | Rational and integral point patterns; reduction mod p behavior; splitting and ramification at primes; height growth; local solubility at completions; Galois action on torsion points; degeneration of fibers. |
| Formal Sciences | Mathematics | Number Theory | Modular and Automorphic Forms | Fourier coefficients (a_n); cusp growth/vanishing; Hecke eigenvalue patterns; q-expansion structure; spectral data of Maass forms; transformation behavior under modular groups; size and distribution of L-function values; local factors at primes. |
| Formal Sciences | Mathematics | Number Theory | Transcendental Number Theory | Failure of algebraic relations among special constants; nonzero linear forms in logarithms; size of transcendence measures; approximation quality of rationals to e, π, log α; growth of auxiliary polynomials at integer points; irrationality exponents. |
| Social Sciences | Anthropology | Human Evolutionary Anthropology | Fossil morphology; skeletal pathologies; tool assemblages; cut marks; locomotor traces; isotope signatures; hearths and habitation residues; genetic variation patterns; craniofacial metrics; limb proportions; developmental markers; geographic distribution of fossils; primate behavioral analogs; signs of dietary transition or ecological adaptation. | |
| Social Sciences | Anthropology | Kinship, Descent & Domestic Organization | Household composition; marriage patterns; residence shifts; inheritance transfers; genealogical relations; domestic labor distribution; caregiving arrangements; sibling sets; kinship terminology use; alliance formation; household fission/fusion events; birth and fertility patterns; lineage membership; fosterage or adoption practices. | |
| Social Sciences | Anthropology | Ritual, Cultural Practice & Symbolic Systems | Ritual sequences; participant roles and movements; spoken formulas; songs, chants, and narrative recitations; symbolic objects and their use; spatial layout of ritual spaces; emotional displays; sensory cues (sound, smell, color); repeated cultural practices; taboo observance; offerings/sacrifices; costume and body modification; art and iconography; mythic themes embedded in performance. | |
| Social Sciences | Anthropology | Subsistence Systems, Environment & Human Adaptation | Hunting returns; foraging yields; crop outputs; herd dynamics; seasonal mobility; tool-use patterns; burned or processed plant/animal remains; settlement and camp structures; water-source use; soil disturbance; storage features; midden composition; dietary isotopes; energetic expenditure; technological wear patterns; vegetation modification (niche construction). | |
| Social Sciences | Anthropology | Material Culture, Technology & Archaeological Interpretation | Artifact counts and distributions; tool morphology; wear and fracture patterns; residue traces (blood, starch, lipids); manufacturing debris (debitage patterns); ceramic temper and firing marks; metallurgical slag; architectural remains; hearths and ash layers; stratigraphic sequences; soil chemistry anomalies; microartifacts; 3D spatial clustering; refitting sequences; stylistic variation; taphonomic alterations. | |
| Social Sciences | Anthropology | Ethnographic Method & Comparative Analysis | Interaction patterns; conversational exchanges; ritual or daily practices; spatial use of homes or public areas; gestures, postures, and embodied behavior; work routines; kinship interactions; social-network ties; participation in events; linguistic forms; moral evaluations; narrative structures; culturally salient categories; variations in behavior across contexts. | |
| Social Sciences | Economics | Choice (Microeconomic Foundations) | Consumption choices; labor–leisure allocations; price responses; revealed preference patterns; savings and investment behavior; risk-taking decisions; intertemporal tradeoffs; substitution vs. income effects; cost minimization patterns; firm production adjustments; reaction to information changes. | |
| Social Sciences | Economics | Interaction (Markets, Strategy & Mechanisms) | Price changes; quantity traded; market-clearing outcomes; bidding behavior in auctions; strategic choices in games; coordination or miscoordination; market entry/exit; bargaining outcomes; matching results (e.g., stable matches); signaling and screening patterns; welfare changes; evidence of externalities or market failures. | |
| Social Sciences | Economics | Aggregation & Dynamics (Macroeconomic Systems) | GDP growth; inflation rates; unemployment; interest rates; investment cycles; consumption smoothing; productivity trends; business-cycle fluctuations; fiscal/monetary responses; credit booms and busts; asset-price dynamics; wage rigidity; propagation of shocks through sectors; long-run capital accumulation paths. | |
| Social Sciences | Geography (Human) | Spatial Patterns & Spatial Analysis | Spatial clustering and dispersion of population or activity; density gradients; flows of people, goods, or information; spatial boundaries; land-use mosaics; accessibility surfaces; distance-decay behavior; spatial autocorrelation patterns; regional differentiation; network connectivity structures; spatial inequality; travel-time contours; urban form and sprawl; location patterns of facilities or hazards. | |
| Social Sciences | Geography (Human) | Mobility, Flows & Connectivity | Commuting flows; migration streams; freight or supply-chain movements; pedestrian trajectories; vehicle traffic counts; airline, rail, or maritime flows; digital communication pathways; network bottlenecks; congestion patterns; temporal flow spikes; modal shifts; accessibility changes; mobility inequalities; diffusion of innovations, diseases, or information across networks; disruption cascades in transport systems. | |
| Social Sciences | Geography (Human) | Human–Environment Interaction & Landscape Modification | Deforestation fronts; terracing; irrigation canals; soil erosion features; sediment accumulation; vegetation die-off; urban sprawl; agricultural field boundaries; land-use transitions; water diversions; pollution plumes; mining scars; fire regimes; infrastructural imprints (roads, dams, levees); settlement expansion; ecosystem fragmentation; reforestation or restoration signs. | |
| Social Sciences | Geography (Human) | Place, Territory & Spatial Experience | Expressions of place attachment; boundary-marking behaviors; territorial signage (flags, fences, murals); patterns of movement and dwelling; use of public vs private space; avoidance zones; symbolic landscapes (memorials, sacred sites); conflict or contestation over spatial claims; ritualized occupation of space; sensory engagement (sound, smell, visibility); narrative descriptions of place; emotional responses to landscapes; social mapping of safe or unsafe areas. | |
| Social Sciences | Linguistics | Phonetics & Phonology | Articulatory movements, airflow patterns, vocal-fold vibration, formant frequencies, pitch contours, amplitude envelopes, spectral shape, duration contrasts, syllable boundaries, tone/intonation patterns, assimilation and coarticulation effects. | |
| Social Sciences | Linguistics | Morphology | Surface word forms; morpheme boundaries; inflectional endings; derivational affixes; stem alternations; allomorph distribution; paradigm gaps or irregularities; productivity of morphological rules; frequency of morphological patterns in corpora. | |
| Social Sciences | Linguistics | Syntax | Grammaticality judgments, constituent ordering patterns, agreement patterns, case-marking distributions, dependency distances, movement effects (gaps, traces), word-order alternations, sentence-processing times, acceptability gradients, corpus frequency of constructions. | |
| Social Sciences | Linguistics | Semantics | Truth-value judgments, entailment patterns, paraphrase judgments, ambiguity detection, scope preference data, acceptability tied to semantic constraints, lexical-relatedness ratings, presupposition projection behavior, quantifier interaction patterns, event-structure interpretations. | |
| Social Sciences | Linguistics | Pragmatics | Conversational implicatures; discourse coherence patterns; presupposition accommodation; reference resolution; deixis interpretation; politeness strategies; indirect speech acts; context-driven meaning shifts; repair sequences; turn-taking influenced by meaning. | |
| Social Sciences | Political Science | Political Institutions & Formal Political Order | Constitutional amendments; legislative voting patterns; executive decrees; judicial rulings; vetoes and overrides; bureaucratic performance metrics; regime transitions; institutional crises; party-system fragmentation; electoral-system effects on seat allocation; agenda control; policy gridlock; intergovernmental conflict in federal systems. | |
| Social Sciences | Political Science | Political Behavior, Mobilization & Collective Action | Voting turnout; partisan vote share; protest size/frequency; petition signatures; activist participation; political donations; social media political engagement; mobilization waves; polarization indicators; violence levels; coordination failures; cascades and tipping-point events; diffusion of protest across regions or networks. | |
| Social Sciences | Political Science | Governance, Policy Formation & State Capacity | Policy outputs (laws, regulations, decrees); implementation success/failure; bureaucratic efficiency; corruption incidents; service-delivery metrics; fiscal extraction performance; regulatory enforcement outcomes; crisis-response timelines; administrative bottlenecks; interagency coordination failures; policy reversals; institutional drift; state collapse or consolidation. | |
| Social Sciences | Political Science | International Relations & Global Order | Military mobilizations; treaty formation; alliance behavior; conflict onset and escalation; sanctions implementation; trade flows; IO voting patterns; diplomatic visits and statements; arms transfers; border disputes; cyber operations; humanitarian interventions; peacekeeping deployments; compliance or defection from international agreements. | |
| Social Sciences | Psychology | Cognitive Processes & Mental Architecture | Reaction times, error rates, gaze patterns, fixations, attention shifts, memory recall accuracy, recognition curves, categorization choices, reasoning steps, neural activation patterns (as indirect evidence), decision-response distributions. | |
| Social Sciences | Psychology | Learning, Conditioning & Behavioral Mechanisms | Response latency, response frequency, acquisition curves, extinction curves, reinforcement-response patterns, generalization gradients, discrimination performance, shaping progressions, reward-seeking/punishment-avoidance behaviors. | |
| Social Sciences | Psychology | Emotion, Motivation & Affect Regulation | Facial expressions, vocal tone, posture and gesture changes, autonomic arousal (heart rate, GSR), cortisol levels, pupil dilation, approach/avoidance behaviors, self-reported emotion states, motivational persistence, regulation attempts (reappraisal, suppression). | |
| Social Sciences | Psychology | Development, Individual Differences & Psychometrics | Behavioral performance differences, developmental milestone attainment, stability/change in trait scores, inter-individual response variability, cognitive ability profiles, reaction-time distributions, item-response patterns, age-related growth curves. | |
| Social Sciences | Sociology | Social Interaction Mechanisms | Facial expressions, tone of voice, body language, gaze patterns, turn-taking sequences, norm enforcement behaviors, impression-management moves, conformity/deviance signals, emotional displays, role-taking cues, situated definitions of reality. | |
| Social Sciences | Sociology | Social Structure Mechanisms | Income distribution patterns; occupational hierarchies; institutional access levels; demographic segregation; mobility flows; inequality indices; boundary-maintenance behaviors; rule-application consistency; organizational authority patterns. | |
| Social Sciences | Sociology | Social Network & Relational Dynamics | Tie formation and dissolution; interaction frequency; clustering and subgroup formation; information diffusion; influence cascades; reciprocity patterns; triadic closure; homophily signals; network centralization; bridging and brokerage behavior. |