Appendix A — Glossary and Concept Reference

Glossary and Concept Reference

Status: In Progress

v0.3

A.1 Concept Reference Tables

This appendix has two roles. The glossary gives the book’s authoritative working definitions; the tables that follow provide a compact map of those definitions across the three strata (Structural, Dynamical, Observable) and the three levels of Reason (Association, Intervention, Counterfactual). The definitions below are CDCS modelling commitments. They draw on Whiteheadian and Proclean vocabulary where useful (Whitehead 1978; Proclus 1963), but do not claim that a modelling adaptation exhausts its philosophical source or establishes its metaphysical truth. As elsewhere, levels is the primary term, and rungs is reserved for the ladder metaphor. For how Parts I–IV relate to pedagogy and epistemology, see How to read this book.

The Introduction links here for the full concept tables (strata, levels, methods, package terminology).

Terminological convention. Define philosophical terms in the Introduction, Chapter 1, and this appendix, then use them selectively. Prefer ordinary causal and dynamical language when it is already unambiguous. Creative advance is not a name for \(\mathbf{u}\), organismal identity, or every residual; it is a limited interpretive gloss for declared novelty in actualisation. A Markov blanket is a conditional-independence partition, not a rule for deciding the system boundary. Identification and estimation retain Pearl/SciML names. Temporal identity uses the closed lexicon in Table 8.

A.2 Glossary

A.2.1 Entities, occurrences, and representation

Entity. Something distinguished as a unit within a description. Its individuation must be specified rather than inferred from the presence of a node. An entity may be represented by several variables; a variable may summarise several entities.

Occasion / occasional entity. A particular occurrence considered as a unit of becoming at the chosen descriptive scale. An occasion is not necessarily instantaneous and need not coincide with a measurement or computational time step. CDCS uses the term as a modelling adaptation of Whitehead’s actual occasion, not as a claim that every modelled event is metaphysically fundamental (Whitehead 1978).

Enduring object. In Whitehead’s account, a society of actual occasions whose social order takes the form of personal order: successive occasions form a historical route and inherit a defining character from their predecessors. More complex physical objects may be societies of such enduring objects. In CDCS, an enduring-object referent is a scale-specific continuity claim, supported by an explicit criterion such as causal inheritance, lineage, or organisational persistence rather than constancy of measured properties. Its graph representation does not by itself establish its Whiteheadian constitution (Whitehead 1978).

Identity through time. The criteria under which different temporal manifestations count as manifestations of the same enduring object. Identity is distinct from similarity, equality of state, and continuity of a plotted trajectory.

Individuation. The process through which a distinguishable unity is achieved and maintained. CDCS uses the term where an identity criterion requires both a constitution history and modes of causal inheritance, rather than a node boundary or a stable recorded value alone. Simondon’s language of metastability can illuminate continuing individuation, while a technical metastable state requires its own dynamical definition (Simondon 2020).

Repeatable pattern. An organisation, relation, or character that may be realised by different particulars or at different times. A pattern is distinct from its instances and from the mathematical expression used to describe it. CDCS structural patterns are declared modelling commitments. Whiteheadian eternal objects are definite potentialities, not model variables or efficient agents (Whitehead 1978).

Causal variable. A quantity whose possible values are distinguished by a causal model. Its definition specifies its referent, domain, descriptive scale, and temporal support. Introducing a variable does not automatically establish that it can be intervened upon independently.

Value / realisation. A particular member of a variable’s domain. Distinguish the variable \(X\), a realised value \(x\), and the entity or process represented by the variable.

Node. A graphical representation of a variable or another explicitly declared model object. In a causal graph, nodes represent causal variables; in a broader semantic diagram, they may represent entities, mechanisms, or repeatable patterns. These uses must not be silently interchanged.

Descriptive scale. The spatial, temporal, and organisational resolution at which entities, occurrences, and mechanisms are distinguished. What counts as one occasion, one enduring object, or a direct influence depends partly on this scale.

A.2.2 Time and temporal support

Temporal support. The time point or set of times a variable describes. It is distinct from the history that causes its value, the interval over which it has effects, and the time at which it is observed.

Point-supported variable. A quantity at a specified time, written \(X_i(t)\). It can describe an enduring object without representing that object’s entire history.

Interval-supported variable. A variable whose definition refers to an interval. It may represent a trajectory, an event within the interval, or a summary; its interpretation must be stated.

Trajectory. A realised path through time. \(X_i|_{[a,b]}\) denotes restriction to \([a,b]\). A trajectory describes temporal variation but does not by itself establish the identity of an enduring object.

Stochastic process. A family of random variables indexed by time, \(\{X_i(t):t\in\mathcal T\}\). A realisation of the process is a trajectory.

Interval summary. A variable obtained by aggregating a trajectory, \(Z_i := g(X_i|_{[a,b]})\). Distinct trajectories can share a summary while having different causal consequences.

Duration. The temporal extent of an occurrence or process. Duration is not endurance: how long something occurs does not specify what maintains its identity.

Temporal order. An ordering of times or occurrences. Precedence constrains causal interpretation but does not by itself establish causal influence.

A.2.3 Causal structure and dependence

Causal mechanism. A rule through which endogenous quantities are generated from direct causes and exogenous inputs. Its causal interpretation includes how it behaves when inputs or mechanisms are intervened upon. In open systems, the event pattern can reflect several concurrent generative mechanisms and their context; variable regularity therefore remains compatible with a mechanism whose operation is condition-dependent (Bhaskar 2008).

Mechanistic organisation. An organised arrangement of entities and activities productive of a regular change from specified start to termination conditions. A graph or structural equation can represent part of such an organisation; a mechanistic explanation also declares the relevant activities, organisation, boundary conditions, and intervention-sensitive components (Machamer et al. 2000).

Capacity / disposition. A mechanism’s or organisation’s ability to generate a characteristic response under specified enabling conditions. CDCS represents a capacity through a mechanism class together with its domain, context, and admissible interventions; a realised outcome supplies evidence about capacity without exhausting it. The distinction draws on the classical contrast between potentiality and actuality (Aristotle 1996).

Structural equation. An assignment expressing a causal mechanism, \(X_i := f_i(X_{\mathrm{pa}(i)},U_i)\). The assignment expresses causal generation, not merely algebraic equality or statistical association.

Structural causal model (SCM). A model specifying endogenous variables, exogenous variables, structural assignments, and a distribution over exogenous variables. Interventions replace selected assignments. An SCM need not be static or acyclic; cyclic models require appropriate solution conditions.

Endogenous variable. A variable generated by a mechanism within the model.

Exogenous variable. An input whose generating causes are not represented within the model. Exogeneity does not imply causelessness, independence from other exogenous variables, or lack of temporal variation.

Modularity. The assumption that specified mechanisms can be replaced while non-targeted mechanisms remain unchanged. It must be justified for the intervention and descriptive scale; it does not mean that components are physically isolated.

Causal graph. A graph representing direct causal dependencies among variables. What counts as direct is relative to the variables and resolution; the graph is not by itself a complete specification of mechanisms.

Causal production / influence. Dependence through mechanisms by which changing one quantity can change another under the model’s intervention semantics. Distinguish this from correlation, constitution, participation, and measurement.

Constitutive dependence. A relation in which components or activities make up an entity, state, or process. It is not automatically causal influence between independently variable objects and requires its own representation and admissibility conditions.

Participation. The relation through which a particular entity or process realises a repeatable pattern. In CDCS this is operationalised as organisational realisation or satisfaction of declared structural constraints; it does not automatically license an interventionist arrow (Proclus 1963).

Constraint. A restriction on admissible states, trajectories, or relations. A constraint is not necessarily a mechanism; treating it as causal requires an account of how it is imposed or maintained and what interventions can alter it.

A.2.4 Reception, becoming, and actuality

Prehension. Recipient-specific incorporation of a datum or influence into the constitution of an occurrence. In CDCS this may be represented by filtering, memory, sensitivity, or contextual transformation. These representations select one aspect of Whiteheadian prehension; they neither attribute conscious perception to the recipient nor reduce prehension to aggregation of graphical parents (Whitehead 1978).

Concrescence. Integration of multiple contributions into one determinate occurrence. In CDCS a differential-equation step or numerical update is not automatically a concrescence; a model using the term must identify what is integrated and what counts as completion (Whitehead 1978).

Genetic and temporal order. Genetic order concerns phases of an occurrence’s constitution; temporal order concerns earlier and later occurrences or states. Phases of constitution must not automatically be treated as successive physical-time intervals.

Satisfaction / completion. Completion of an occasion’s becoming, after which it is treated as a determinate occurrence available to subsequent processes. In CDCS, completion does not mean equilibrium, optimisation, or cessation of wider activity (Whitehead 1978).

Transition. Passage through which completed occurrences condition subsequent occurrences. It distinguishes succession between occasions from integration within an occasion.

Causal inheritance. Transmission or reproduction of relevant character from earlier occurrences to later ones. It can contribute to endurance without implying unchanged state, exact copying, or deterministic evolution.

Potentiality. Possibilities distinguished before or apart from a specified actualisation. CDCS distinguishes logically describable possibilities, dynamically reachable states, and outcomes admissible under intervention. A probability distribution represents uncertainty or variability without settling the metaphysical status of possibilities. Whiteheadian eternal objects name pure possibilities of definiteness; CDCS does not identify them with a state space, parameter, constraint, or probability law (Whitehead 1978; Segall 2026).

Actuality / actualisation. Actuality is the status of an occurrence treated as realised rather than merely possible; actualisation is its becoming realised. Sampling can represent a realisation in a stochastic model without being a complete metaphysical account of becoming.

A.2.4.1 Definiteness and determination

The following distinctions are stipulated for CDCS and are not claimed as a universally accepted division of philosophical terminology.

Term CDCS meaning
Definiteness Having a specific qualitative or structural character: being this way rather than another.
Determinateness Being settled with respect to specified alternatives in a realised occurrence.
Determination The process or constraints through which character or outcome becomes specified or settled.
Determinism Uniqueness of evolution given the complete conditions stipulated by the model.
Epistemic certainty An observer’s certainty about a character, outcome, or evolution.

A determinate outcome need not have been deterministically necessitated or be known. A definite probability law need not select one outcome in advance. In the Whiteheadian usage informing CDCS, definiteness belongs to potentiality, while determinateness is achieved in actualisation (Whitehead 1978; Segall 2026).

Remaining–procession–reversion — philosophical framework. The Proclean articulation of an effect’s remaining in its cause, proceeding as distinct, and reverting towards its source. CDCS may use it to frame questions about dependence, differentiation, and unity; it is not a synonym for persistence–evolution–feedback and supplies no dynamical equation without further interpretation (Proclus 1963).

A.2.5 Static and dynamical models

Static or time-abstracted SCM. An SCM that does not explicitly describe temporal evolution. Its variables may still refer to different times, interval outcomes, or equilibria. Static does not mean timeless.

Temporally explicit SCM. An SCM in which relevant variables have explicit temporal support. Time qualification alone does not supply an evolution law.

Dynamical structural causal model (DSCM). An SCM that explicitly represents causal evolution through transition rules, history-dependent mechanisms, or differential equations. Variables may represent point states, trajectory segments, or whole processes. Fixed background quantities may also be included.

State. A collection of quantities sufficient within the model to determine future evolution, or its conditional distribution, given subsequent inputs. An observed snapshot need not contain the full state.

Evolution law. A rule specifying temporal change, for example \(X_{t+1}:=F(X_t,U_{t+1})\). Its causal interpretation requires specification of mechanisms and their behaviour under intervention.

Initial condition. A state or history from which modelled evolution begins. Whether it is fixed, random, endogenous, or externally imposed must be stated.

Non-anticipation. The requirement that a mechanism’s output up to time \(t\) does not depend on future inputs. Predictability of a future event is not causal influence from the future.

Time-invariant mechanism. A mechanism whose rule does not change with time. It may generate changing states.

Feedback. Causal influence that returns to a component through other components or later states. \(X_t\to Y_{t+1}\to X_{t+2}\) is feedback without a directed cycle among these point-supported nodes.

Time-unrolled graph. A graph with separate nodes for variables at distinct times. Strictly forward-in-time edges cannot form directed cycles. Same-time dependencies require additional assumptions.

Process graph. A graph whose nodes represent entire processes. It can contain cycles expressing feedback across time; DAG reasoning cannot automatically be transferred to it.

Equilibrium. A state remaining unchanged under specified fixed conditions. An equilibrium model abstracts from transients; intervention validity requires that the relevant equilibrium exists and is reached.

A.2.6 Interventions and counterfactuals

Intervention. A specified replacement of one or more causal mechanisms. In a dynamical model its definition includes target, timing, duration, and replacement rule.

Admissible intervention. An intervention permitted by the model’s domains, constraints, and solution conditions. Mathematical admissibility, physical feasibility, and practical availability are distinct.

Point intervention / reset. Assignment of a state at a specified time, after which evolution continues under remaining mechanisms. A reset is distinct from a brief input or impulse.

Sustained intervention / clamp. Imposition of a value or prescribed trajectory throughout an interval. Holding a variable fixed is different from setting it once.

Mechanism intervention. A change to a generating or evolution rule rather than direct prescription of its output.

Policy / adaptive intervention. A rule selecting actions from information available at each decision time. Its information set is part of its definition; future or unobserved information cannot silently be used.

Counterfactual trajectory. The trajectory generated under an alternative intervention while retaining the specified background circumstances of the comparison. It may remain uncertain when those circumstances are only partially known.

A.2.7 Observation and inference

Observation model. A rule relating underlying entities, states, or trajectories to recorded data. It specifies measurement error, sampling, detection, missingness, and aggregation as relevant. If measurement perturbs the system, that influence must also be represented.

Sign — Peircean adaptation. A recorded datum considered as materially produced evidence about a referent for a specified interpretive use. In CDCS, the observation model \(h\) specifies the record-producing relation, while the estimand and inference rule specify how the record bears on a question. This use holds the datum apart from both the process represented and the analyst’s subsequent interpretation (Peirce 1934).

Observation versus prehension. Observation concerns data production for an observer or instrument. Prehension, as used here, concerns incorporation into an occurrence’s constitution. A physical interaction may play both roles, but neither relation should be inferred from the other.

Sampling interval and aggregation window. The sampling interval is the spacing between observations; the aggregation window is the period an observation summarises. Neither necessarily matches the duration of a mechanism or occasion.

Temporal coarse-graining. Replacement of a detailed temporal representation with a less detailed one. It can obscure ordering, memory, and feedback; a model valid at one resolution does not automatically yield a valid SCM over arbitrary summaries.

Observability. Whether underlying states can be distinguished or reconstructed from available outputs under stated model conditions. Observability is distinct from causal identifiability.

Causal estimand. The precise causal quantity a study aims to learn, including intervention or policy contrast, target population or system, and temporal support of the outcome.

Identifiability. Whether an estimand is uniquely determined by available data distributions and stated assumptions. A model may support simulation while its causal effects remain unidentified from observational data.

Estimation. Use of finite data to approximate an estimand. Estimation error is distinct from non-identifiability and model misspecification.

Abduction — Peircean adaptation. The proposal of a candidate explanation worthy of investigation. In CDCS, abduction generates candidate variables, mechanisms, measurements, or interventions; identification and estimation assess their consequences under stated assumptions. This differs from SCM abduction, which infers exogenous context conditional on a specified model (Peirce 1934; Pearl 2009).

Operational closure / autonomy. A system-level claim that mutually enabling processes maintain the organisation through which they continue. CDCS requires a declared mechanism network, viable variables, external coupling, and perturbation evidence before using this description. A Markov blanket can contribute to the representation of an interface, while autonomy requires the further organisational evidence (Thompson 2007).

Requisite variety. A regulator must distinguish enough of the disturbance variety relevant to a stated viability condition to select an adequate response. CDCS uses this as a design heuristic for information, action, and policy support; adequacy remains a claim about the specified system and decision problem (Ashby 1956).

A.2.8 Mandatory semantic declarations

Before interpreting a model, declare the following for every variable or node:

  • Referent: the entity, occurrence, process, or relation it describes;
  • value type: state, event indicator, trajectory, summary, or other quantity;
  • temporal support: the point or interval it describes;
  • scale and individuation: what makes it one unit at that resolution;
  • identity criterion: if endurance is claimed, what establishes continuity; and
  • model role: endogenous quantity, exogenous input, observation, or parameter.

For every represented relation, declare whether it is causal influence, constitution, participation, measurement, or temporal order; the assignment, map, constraint, or other formal object that represents it; what can be changed independently; and which conclusions the relation licenses. For every intervention, declare its target and replacement rule, timing and duration, available information, admissibility and solution conditions, and the mechanisms assumed unchanged.

These declarations are not additional assumptions hidden behind terminology. They are the minimum metadata needed to prevent a timestamp from being mistaken for an occasion, an interval from being mistaken for endurance, a shared pattern from being mistaken for causal influence, or a philosophical interpretation from being mistaken for an empirical result.

A.2.9 Classification Principles

Stratum structure: Many concepts are introduced first in one stratum and then reused in other strata with different semantics. The Primary Stratum listed in the tables is where a concept is introduced first.

Examples:

  • Graph Theory is introduced at Structural (structure/invariances), and appears in Dynamical (dynamic semantics) and Observable (data/estimation)
  • State-Space Models are introduced at Structural (latent structure and mechanisms), and used in Dynamical and Observable
  • ODEs come into being at Dynamical (time-dependent processes), and exist in Observable

Bridge concepts: Some concepts inherently span multiple strata because they address the relationship between strata. These are marked with both strata and a directional arrow to show the flow:

  • Centrifugal (→): Concepts that carry structural rules or assumptions into dynamical and observable analyses (e.g., Structural → Observable).
  • Centripetal (←): Methods that use observations to infer structural or dynamical possibilities (e.g., Observable → Structural).

The three modelling strata organise discussion by role; they are not nested ontological realms. Bridge concepts show how structural assumptions condition dynamical and observable analyses, and how observations can support inference about structural and dynamical possibilities. The Observable is not unreal, and the Structural is not directly visible.

Methods vs Concepts: Some entries distinguish between:

  • Concepts/theories (claims about the system): Distinctions and assumptions used in the model
  • Methods/computations (what we do): Practical operations that may span strata

This classification is purely organisational: it keeps separate what we assume structurally, what we model dynamically, and what we observe/estimate.

A.3 Table 1: Concepts by Stratum

Concept Primary Stratum Description
Dyad Structural Atom of causal structure: two nodes, one directed edge, local mechanism \(Y \coloneqq f(X, U)\); bivariate cause–effect before multivariate SCMs (Peters et al. 2017); Ch. 2
Graph Theory Structural Causal structure assumptions, DAGs, directed dependencies (includes network structure and properties)
d-Separation Structural Graph-theoretic conditional independence
Markov Boundary Structural Minimal sufficient set for causal reasoning
Identification Structural → Observable Centrifugal bridge: Structural question about what can be learned from observable data
Do-Calculus Structural → Observable Centrifugal bridge: Structural rules applied to compute interventional distributions from observable data
Counterfactuals (concept) Observable → Structural Centripetal bridge: Use observable data to reason about structural alternative possibilities
Transportability Structural → Observable Centrifugal bridge: Structural question about whether causal claims can be generalised across observable domains
State-Space Models (concept) Structural Latent process structure and mechanisms (often treated as time-invariant within a modelling context)
Filtering Observable → Structural Centripetal bridge: Method using observable data to infer current structural state
Smoothing Observable → Structural Centripetal bridge: Method using observable data to infer past structural states
Identifiability Structural → Observable Centrifugal bridge: Structural question about whether mechanisms are learnable from observable data
Model Criticism Observable → Structural Centripetal bridge: Method using observable data to test structural model validity
Free Energy Principle Structural → Dynamical Optional specialised interpretation under additional assumptions; not required for CDMs
Markov Blanket Structural/Dynamical Conditional-independence partition; it does not by itself individuate an organism or select variables; see Ch. 9
Formal constraint Structural Declared invariance, feasibility, viability, or cross-embodiment relation; constrains possibilities without becoming an event-like cause
Attractor / basin Dynamical Invariant set and its domain of attraction relative to specified dynamics; neither is automatically a goal or lure
Lure Structural → Dynamical Relevance of a possibility to a becoming; constraints, preferences, policies, and reachable-set geometry can provide empirical proxies for organised orientation without exhausting that relevance
Agency Dynamical Empirical claim about an integrated, self-maintaining process with adaptive action; not implied by a blanket, attractor, or pattern
ODEs Dynamical Deterministic dynamics, flows, equilibria
SDEs Dynamical Stochastic dynamics, process noise
Regime Switching Dynamical Tipping points, attractor transitions
Resilience Dynamical Recovery from perturbations
Robustness Dynamical Maintaining function under variation
CDMs Observable Unified causal-dynamical framework linking structure, dynamics, and data
Correlation Analysis Observable Method: Computing correlations from observed data
Conditional Forecasting Observable Method: Forecasting future observations given past data
Interventional Forecasting Observable → Structural Centripetal bridge: Method using observable data to reason about structural interventions
Counterfactual Simulation Observable Method: Computing unit-level alternative outcomes
G-Methods Observable Methods for time-varying confounding
TMLE Observable Method: Targeted maximum likelihood estimation
Policy Evaluation Observable Method: Evaluating dynamic treatment strategies
Experimental Design Observable Method: Optimal measurement strategies
Missingness / response indicators (\(R\)) Structural (+ Observable record) Mechanisms and MAR/MNAR claims for \(R\) (Structural); Julia missing as the recorded token and estimation policies (Observable); Dynamical when gaps are time-indexed

A.3.1 Incomplete-observation notation

Object Symbol Notes
Complete substantive value \(V\) (e.g. \(Y\), \(C\), \(W\)) Latent under missingness when \(R_V=0\); dashed outline in m-DAGs
Response / recording indicator \(R_V\in\{0,1\}\) \(R_V=1\) means recorded; Structural parents of \(R_V\) encode MCAR/MAR/MNAR
Recorded assay \(V^{\mathrm{rec}}\) Equals \(V\) when \(R_V=1\); Julia missing when \(R_V=0\)
Figure alias \(V^*\) Optional DAG label for \(V^{\mathrm{rec}}\) (McElreath-style); not a counterfactual
Imputed / filled value \(\tilde{V}\) or \(V^{\mathrm{imp}}\) Observable policy only; keep off the causal m-DAG
Counterfactual \(V^{do(\cdot)}(\mathbf{u})\) Requires a declared cross-world coupling; abduction need not identify a unique \(\mathbf{u}\)
Survival censoring \(C_t\) / \(\Delta\) Distinct from MAR missing terminal \(S_T\) or \(R_{S_T}\)

Assignment form (same in book and CausalDynamics):

\[ \begin{aligned} V &\coloneqq f_V\bigl(\mathrm{pa}_G(V),\, U^V\bigr), \\ R_V &\coloneqq f_{R_V}\bigl(\mathrm{pa}_G(R_V),\, U^{R_V}\bigr), \\ V^{\mathrm{rec}} &\coloneqq \begin{cases} V & R_V = 1, \\ \texttt{missing} & R_V = 0. \end{cases} \end{aligned} \]

Developed in Chapter 18 (m-DAG atlas) and Chapter 19.

A.4 Table 2: Concepts by Level of Reason

Concept Level 1 (Association) Level 2 (Intervention) Level 3 (Counterfactual)
Graph Theory Conditional independence (structural property) Intervention structure Counterfactual structure
d-Separation ✓ (tested on observable data) ✓ ✓
Markov Boundary ✓ (applied to observable models) ✓ ✓
Identification — ✓ ✓
Do-Calculus — ✓ ✓
Counterfactuals — — ✓
State-Space Inference ✓ (infer structural from observable) ✓ ✓
Filtering ✓ (infer current state) ✓ (infer under intervention) ✓ (infer for counterfactual)
Smoothing ✓ (infer past states) ✓ ✓
Conditional Forecasting ✓ — —
Interventional Forecasting — ✓ ✓
Counterfactual Simulation — — ✓
G-Methods — ✓ ✓
TMLE — ✓ ✓
Policy Evaluation — ✓ ✓
ODEs/SDEs (as mechanisms) ✓ (simulate dynamics) ✓ (simulate under intervention) ✓ (simulate counterfactual)
Resilience Analysis ✓ (measure from data) ✓ (test under intervention) ✓ (compare counterfactuals)
Experimental Design ✓ (design observational studies) ✓ (design interventions) ✓ (design for counterfactuals)
Correlation Analysis ✓ — —
Missingness / \(R\) Optional for prediction under MCAR/MAR Missingness DAG + ID of interventional targets with partial observation Shared \(\mathbf{u}\) / abduction when outcomes or paths were unobserved; else partial ID

Legend: ✓ = concept applies at this level; — = not the primary use at this level.

A.5 Table 3: Mathematical Methods by Stratum and Level

Method Stratum L1 (Association) L2 (Intervention) L3 (Counterfactual)
Graph algorithms Structural d-separation Backdoor criterion Counterfactual structure
Do-calculus Structural — ✓ ✓
Identification theory Structural — ✓ ✓
Kalman filter Observable ✓ ✓ ✓
Particle filter Observable ✓ ✓ ✓
Kalman smoother Observable ✓ ✓ ✓
Posterior predictive checks Observable ✓ ✓ ✓
G-computation Observable — ✓ ✓
IPTW Observable — ✓ ✓
TMLE Observable — ✓ ✓
Off-policy evaluation Observable — ✓ ✓
ODE integration Observable ✓ ✓ ✓
SDE simulation Observable ✓ ✓ ✓
Correlation analysis Observable ✓ — —
Missing-data policies (drop / IPCW / impute) Observable ✓ ✓ Posterior / shared-\(\mathbf{u}\) (opt-in)
Missingness identification (\(R\) on \(G\)) Structural (optional) ✓ ✓

A.6 Table 4: Process vocabulary in CDCS

These terms are interpretive aids, not replacements for causal, dynamical, or statistical definitions. The book uses them only where they clarify a distinction already made in the glossary. The brief notes below give the context of use; the glossary above remains authoritative.

Concept Use in CDCS Boundary
Prehension Recipient-specific incorporation of a datum or influence into an occurrence (Whitehead 1978) Not a claim of conscious perception; use “depends on”, “filters”, or “influences” where sufficient
Creative advance A philosophical gloss for novelty in actualisation (Whitehead 1929, 1978) Not identical to \(U\), process noise, measurement error, or a proof of non-physical input
Alternative concrescences A limited philosophical gloss for alternative modelled actualisations under different interventions and a declared cross-world coupling A completed occasion is not literally reconstituted; the coupling is a modelling assumption rather than an empirically known identity relation
Concrescence Integration of contributions into one determinate occurrence Not every solver step, update, equilibrium, or optimisation
Actual occasion Philosophical source of the modelling term “occasion” CDCS occasions are scale-dependent modelling units, not asserted metaphysical atoms
Individuation Constitution and maintained identity through transformation (Simondon 2020) Requires an explicit scale map, constitution history, and continuity criterion
Participation Realisation of a repeatable pattern in a particular process (Proclus 1963) Not automatically an interventionist arrow or efficient causation
Lure Relevance of a possibility to a becoming; CDCS can model empirical correlates of organised orientation through declared constraints, preferences, policies, and reachable-set geometry (Whitehead 1978; Segall 2025, 2026) Final rather than efficient causation; no basin, force, agent, or scalar proxy exhausts its intensive relevance
Society A nexus of actual occasions with social order, whose members inherit a defining character; a society with personal order is an enduring object (Whitehead 1978) A grouping or shared rule alone does not establish social order, identity, or a Markov blanket
Markov blanket A conditional-independence partition used to specify an interface in an optional FEP model Does not by itself individuate an entity or define the system boundary
Operational closure / autonomy Organisational maintenance through mutually enabling processes (Thompson 2007) Requires mechanism, viability, and perturbation evidence; a blanket alone remains insufficient
Peircean abduction Proposal of an explanatory candidate for inquiry (Peirce 1934) Distinct from SCM abduction and from identification or confirmation
Remaining–procession–reversion A philosophical framework for dependence, differentiation, and return Not a synonym for persistence–evolution–feedback and not a dynamical equation
Eternal objects / superject / causal efficacy Historical Whiteheadian or Proclean terms retained for philosophical reference (Whitehead 1978; Proclus 1963) Eternal objects are definite potentialities, not model variables or agents; prefer formal constraint, terminal state, and lagged influence in technical exposition

A.7 Table 8: Package APIs and process terminology

Table 8 maps book concepts to the Julia APIs used in examples. Identification and estimation keep Pearl/SciML names. Temporal declarations are four orthogonal fields (Ch. 9): within a TimeUnrolledGraph, temporal_support fixes node multiplicity; graph_kind declares the represented graph and guards whether that unrolling is admissible; value_representation describes the value; ReferentSpec names what a variable concerns and may carry identity_criterion and, when taught or claimed, ontological_character. Whitehead glossary terms stay in Table 4 and running prose.

NoteMigration from temporal_mode

Pre-release drafts used temporal_mode = :occasion | :enduring to select construction patterns, conflating representation with ontology. Declare temporal_support and value_representation instead; the old flag never determined ontological character, and no default onset is inferred from it.

Published executable claims prefer released package versions (or a publicly accessible, pinned commit that the book environment tests). Local submodule tips are fine for development drafts; /dev/ documentation is not the sole reproducibility reference.

The book’s examples use CausalDynamics.jl (graphs, identification, SCMs, do(·)), CausalTargeted.jl (cross-fitted LMTP / MTP grids), CausalMediation.jl (interventional and related mediation), and DAGMakie.jl (DAG figures).

Causal terminology Typical API Process
Directed edge \(i \to j\) edge in DiGraph, dagplot Causal influence; optionally a limited prehension gloss
do(X=x) do_intervention, apply_intervention, do_surgery (display-only in DAGMakie), Intervention Intervention / graph surgery
Backdoor path find_backdoor_paths, backdoor_adjustment_set, identify / TotalEffectQuery Confounding path into treatment
Exogenous input \(U\) exogenous_values in simulate_scm Declared generative input; not an identity criterion
Counterfactual same unit compute_counterfactual (shared U) Alternative modelled actualisations under a declared coupling
SCM forward pass simulate_scm One unit evaluation given U
Discrete-time trajectory DiscreteTimeCDM, simulate, typed DoSequence / Policy, g_computation Time indices; book pedagogy often takes \(t = 0\) as baseline and \(t = 1\) as the first transition (Ch. 28)
Observational panel simulate_panel, CDMPanel, panel_column_name Wide baseline / timed / terminal columns → sequential LMTP
Static grid panel path plan_targeted_estimation, EstimationPlan, run_estimation_plan (CausalDynamics → CausalTargeted) Same-time arm contrast on wide panels; from-onset grid attributes (Ch. 23; Apodemus-style R/SS/SC)
Temporal declaration (Ch. 9) TemporalNodeSpec(; temporal_support = PointwiseSupport() \| PointSupport(t) \| IntervalSupport(a, b) \| FromOnsetSupport(t₀) \| GlobalSupport(), value_representation, referent = ReferentSpec(id; identity_criterion, ontological_character)); TemporalDAGSpec(; graph_kind) Within a TimeUnrolledGraph, support fixes node count; graph kind declares the representation and guards unrolling; representation describes the value; the referent carries identity and, only when claimed, occasion / enduring character. GlobalSupport is neither “unspecified” nor “time-invariant”
Temporal edge and its projection LaggedEdge(...; relation_kind), causal_projection, temporal_edge_records Declared :causal_influence edges are identified; declared constitution, participation, and measurement become constraints and provenance, never inferred from support pattern
Contract gates (teaching) validate_intervention_semantics, StructuralConstraintSpec / constraint_certificate, Policy(; information_set), mediation relation_kind refusal Check declared contracts (scalar do on interval summaries, feasibility, \mathcal{H}_t); they do not certify empirical truth
Temporal glyphs DAGMakie.dagplot_temporal, marker_for_value_representation Rounded rectangle means :interval_summary only; shape encodes neither endurance nor support
Nested units / hierarchy RandomEffectSpec, simulate_hierarchical_panel, unroll_hierarchical_dag, attach_hierarchy_assumptions (CausalDynamics); run_repeated_outcome_msm(...; cluster=) (CausalTargeted) Generative nest vs cluster-robust IF vs LMM (apps only)
Latent → observed ObservationBridge, panel_from_latent_series Filter/smoother outputs → panel (no Kalman in core)
Continuous functional ContinuousEffectFunctional, continuous g_computation Terminal / mean / integral of SciML solutions
Transport ID TransportQuery, domain_transport_weights Domain in adjustment; IPTW-style weights in CausalTargeted
Policy choice choose_policy, PolicyChoice Compare labelled estimands by estimated TE
Shared-U counterfactual path counterfactual L3 comparison under a declared shared-noise coupling
Time-indexed backdoor unroll_temporal_dag, temporal_backdoor_adjustment_set, TemporalEffectQuery Lagged confounding on pointwise nodes (Ch. 28); feeds sequential LMTP certificates
Discovered graph → ID infer_pc_graph, prepare_from_discovery (Associations.jl) Observable → Structural hypothesis (Ch. 05b)
Discovery as sensitivity merge_discovery_sensitivity! (CausalTargeted) Alternative adjustment set; never replaces user DAG silently
OCE → lag DAG infer_oce_temporal_spec, oce_parents_to_temporal_spec Time-series parent sets (Ch. 05b)
Latent vs observed node NodeType in DAGMakie Unmeasured vs measured
Continuous MTP / LMTP run_lmtp_grid, plot_mtp_curve, recommend_run_options, DEFAULT_SL_LEARNERS / RICH_SL_LEARNERS (includes :randomforest; opt-in :xgboost), ShiftPolicy, fold-stable mixed-type baselines (CovariateSchema) (CausalTargeted) Feasible shift of natural exposure (Ch. 23)
Factor-treatment MTP DiscreteTreatmentPolicy, run_discrete_lmtp, SequentialPolicy.policies, estimand_from_query (CausalTargeted) Recode of finite \(A\) / \(A_t\) (Ch. 23, 28); mixed sequential \(A\) rejected
Interventional mediation MediationSpec, run_mediation, run_mediation_grid, plot_mtp_curve, mediation_stability_summary (CausalMediation); MediationQuery / moc on certificates (CausalDynamics) Path-specific contrasts under MTP or factor recode of \(A\) (Ch. 20)
Binary Super Learner metalearner fit_super_learner(...; metalearner=:nnloglik) (CausalTargeted) Logit-scale ensemble for propensity / binary outcome nuisances
Positivity / support atlas positivity_report Overlap diagnostics before interpreting TE curves
Omitted-confounder sensitivity sensitivity_report, tipping_point_bias Partial-\(R^2\) / tipping-point diagnostics (Ch. 17, 29)
Multi-time sequential MTP SequentialPolicy, run_sequential_lmtp Recursive LMTP-style regression (Ch. 23, 28)
Count-outcome LMTP run_discrete_lmtp_contrast(...; family_outcome=:negbin), suggest_family_outcome, recommend_count_learners, COUNT_SL_LEARNERS Poisson / NB2 / ZINB Super Learner + log-link TMLE for overdispersed counts (Ch. 23)
Two-part hurdle LMTP run_two_part_discrete_lmtp_contrast, TwoPartInterventionalMean, NodeOutcomeSpec(hurdle, ...) Binomial presence + Gaussian intensity among positives; planner routes via :two_part_discrete_lmtp (Ch. 23)
Discrete-time survival / event-time MTP SurvivalPolicy, run_survival_lmtp, simulate_discrete_survival_mtp Event-free probability at a horizon under MTP (Ch. 23, 28); competing risks deferred (Díaz et al. 2024)
Incomplete observation (\(R_V\), \(V^{\mathrm{rec}}\)) MissingnessSpec, ObservationMask, handle_missing, impute_posterior Structural \(R\) / certificates (CausalDynamics); Observable policies (CausalTargeted); \(V^*\equiv V^{\mathrm{rec}}\) in figures only

A.7.1 Book–package map

Book chapter Biological narrative Package surface
Causal discovery (Ch. 05b) Observational cohort + immune–parasite lags Associations.jl infer_pc_graph / infer_oce_temporal_spec → prepare_from_discovery; sensitivity via CausalTargeted
Ch. 28 confounded CDM Host immunity under confounded treatment; event-time under MTP DiscreteTimeCDM, typed do_sequence / policy, g_computation, simulate, counterfactual; simulate_panel → sequential_spec_from_identification → execute_estimand; SurvivalPolicy / run_survival_lmtp for event-free horizons
Ch. 28b case studies GRN, transmission, MIRS transport Full CDM pipeline + discovery bridge; small-\(n\) MTP stack for conservation-scale cohorts
Ch. 20 TMLE ATE of treatment on worm burden TMLE.jl + confounded_cohort_dgp; continuous MTP → CausalTargeted; mediation → CausalMediation (identify → spec_from_identification → run_mediation → plot_mtp_curve; factor \(A\) recode with continuous \(M\))
Ch. 23 policy evaluation Continuous exposure shifts; factor recodes; static grid panel path; count LMTP; hurdle two-part LMTP; event-time under MTP recommend_run_options → lean run_lmtp_grid → plot_mtp_curve with mixed baselines (String/Bool encoded); run_discrete_lmtp for string \(A\); plan_targeted_estimation → run_estimation_plan for wide grid arms; run_discrete_lmtp_contrast(...; family_outcome=:negbin) for count outcomes; run_two_part_discrete_lmtp_contrast for hurdle presence + intensity; SurvivalPolicy / run_survival_lmtp for discrete-time event-free probability; opt-in RICH_SL_LEARNERS (RF + EvoTrees; :xgboost explicit) + positivity; mediated contrasts in Ch. 20 / CausalMediation
Ch. 29 reporting Reviewer-proof causal claims Certificates, positivity, MC stability, Cinelli–Hazlett-style sensitivity; name the package that owns the estimand
Structural ID (Ch. 3–7) Toy pedagogical graphs identify, d_separated, backdoor_adjustment_set, dagplot_adjustment, GraphSCM, do_intervention (certificates feed Ch. 20/23 estimation)
Ch. 28 UDE / SciML bridge Continuous CDM + graph-constrained residuals CausalDynamics ContinuousCDMSpec / solve_cdm; Lux MechanismLibrary / build_ode_rhs (package recipe); UniversalDiffEq remains optional advanced trainer (not a core dep)
Ch. 28 / 30 high-dim assays Spectra / images → codes → ID / mediation / L3 RepresentationSpec / encode_to_panel; optional :generative L3 on codes; AgeSCM Flux CNN stays application-side
Ch. 20 mediation on codes High-dim mediator compressed before EIF CausalMediation on :z* columns; stress in CausalTargeted deep_scm_estimation_stress.qmd
Ch. 25 unit-level CF Shared-U abduction on mechanisms abduce_noise / mechanism_counterfactual (additive generative); twin-network compute_counterfactual
Ch. 30 software patterns — CausalDynamics + CausalTargeted + CausalMediation + DAGMakie layout; small-\(n\) checklist; optional MLJ / SciML extensions

A.8 Table 5: Methods for Each Level of Reason

A.8.1 Level 1: Association (Seeing)

Method Stratum Purpose
Conditional forecasting Observable Predict future given past observations
Filtering Observable Infer current structural state from observations
Smoothing Observable Infer past structural states from all observations
Correlation analysis Observable Find associations in observed data
d-separation Structural Graph-theoretic conditional independence
Model criticism Observable Validate structural model fit using observable data

A.8.2 Level 2: Intervention (Doing)

Method Stratum Purpose
Do-calculus Structural Rules for computing interventional distributions
Interventional forecasting Observable Forecast under interventions
G-methods Observable Handle time-varying confounding
TMLE Observable Robust causal effect estimation
LMTP / continuous MTP Observable Feasible shifts of continuous exposures (Díaz et al. 2023)
Count-outcome LMTP Observable NB2 / Poisson / ZINB nuisances + log-link TMLE for count endpoints
Two-part hurdle LMTP Observable Binomial presence + conditional intensity (zero-inflated ecological counts)
Survival / event-time LMTP Observable Event-free probability under longitudinal MTP (Díaz et al. 2024)
Interventional mediation Observable Path-specific effects under MTP (Díaz and Hejazi 2020; Liu et al. 2024)
Policy evaluation Observable Evaluate treatment strategies
Structural interventions Structural Concept of modifying mechanisms

A.8.3 Level 3: Counterfactual (Imagining)

Method Stratum Purpose
Counterfactual simulation Observable Unit-level alternative outcomes
Shared exogenous values Structural Declared cross-world coupling; does not identify an organism
Alternative modelled actualisations Structural Counterfactual possibilities under a declared coupling
Bounds Observable Partial identification
Sensitivity analysis Observable Test counterfactual assumptions

A.9 Table 6: Cross-Stratum Concepts

Some concepts span multiple strata, showing how the framework unifies:

Concept Strata Description
Represented relations Structural, Dynamical, Observable Influence, constitution, participation, measurement, or temporal order; the relation type must be declared
Attractors Dynamical Defined only for specified dynamics; distinct from structural assumptions and observed states
State Variables Structural, Dynamical, Observable \(X_t\) exists across these strata
Observations Observable \(Y_t\) manifests from inner strata
Interventions Structural, Observable \(do(\cdot)\) applies across strata
Exogenous inputs Structural, Dynamical, Observable Declared process, action, context, or observation inputs; cross-world coupling must be stated separately
Graph Structure Structural, Dynamical \(G\) constrains all strata
CDMs All Unified framework across all strata
Model-development loop All Build, fit, criticise, expand or repair, compare, and decide; the loop may reopen earlier declarations
Workflow provenance All Record which checks were run, what they tested, which failures changed the model, and which claim remains supported

A.10 Table 7: Practical Workflows by Stratum and Level

A.10.1 Structural Stratum

Workflow Level Steps
Causal Discovery L1 1. Test conditional independences
2. Apply d-separation
3. Infer graph structure
Identification L2 1. Specify estimand
2. Check identifiability
3. Apply do-calculus
Counterfactual Reasoning L3 1. Declare and, where needed, abduct a cross-world coupling
2. Compute alternative outcomes
3. Compare outcomes

A.10.2 Structural Stratum (continued)

Workflow Level Steps
State Inference L1 1. Filter
2. Smooth
3. Validate with PPCs
Interventional Inference L2 1. Infer state under intervention
2. Propagate through mechanism
3. Compare to baseline
Counterfactual Inference L3 1. Infer unit-specific noise
2. Simulate alternative mechanism
3. Compare trajectories

A.10.3 Dynamical Stratum

Workflow Level Steps
Dynamics Simulation L1 1. Specify ODE/SDE
2. Integrate forward
3. Analyse trajectories
Intervention Simulation L2 1. Modify mechanism
2. Integrate under intervention
3. Compare attractors
Counterfactual Dynamics L3 1. Declare or infer a coupling
2. Simulate alternative dynamics
3. Compare system evolution

A.10.4 Observable Stratum

Workflow Level Steps
Forecasting L1 1. Fit CDM
2. Condition on history
3. Predict future
Policy Evaluation L2 1. Identify adjustment
2. Choose MTP / policy
3. Estimate with positivity + sensitivity diagnostics
Counterfactual Analysis L3 1. Infer unit-specific noise
2. Simulate counterfactual
3. Compare to observed
Model criticism L1–L3 1. Simulate and recover known quantities
2. Fit the declared component
3. Check calibration, PPCs, trajectories, and computation
4. Expand or repair and re-check
Causal-dynamical validation L2–L3 1. Retain the identification certificate
2. Validate dynamics and observation separately
3. Probe positivity, sensitivity, and transport
4. Report the supported claim and its limits

A.11 How to Use These Tables

  1. Finding concepts by stratum: Use Table 1 to see which concepts belong to which stratum(s)
  2. Finding concepts by level: Use Table 2 to see which concepts apply at each level of Reason
  3. Finding methods: Use Table 3 for mathematical methods, Table 5 for methods by level
  4. Understanding philosophy: Use Table 4 for Whiteheadian/process philosophy concepts
  5. API map: Use Table 8 to map book concepts to the Julia APIs used in examples (Pearl/SciML for identification and estimation; closed temporal lexicon on existing types; Whitehead glossary remains book-side in Table 4)
  6. Cross-stratum connections: Use Table 6 to see how concepts span multiple strata
  7. Practical workflows: Use Table 7 to see step-by-step procedures

These tables complement the book’s structure by providing a cross-cutting view of how concepts relate to the three modelling strata and three levels of Reason.