A.3.3 - U.Dynamics: State-Space and Transition-Law Episteme

Type: Definitional pattern Status: Stable Normativity: Normative

A.3.3:1 - Problem frame

Use this pattern when you need a reusable account of how a particular subject’s state can change: which differences the state must retain, the law relating earlier and later state, and the conditions in which that law applies.

First useful move. Name the changing subject and what you want to find about its change. If the state and law are already available, state their meanings in one ordinary sentence; otherwise construct them through :4.4.1. For example: “In this two-substance mixture, the remaining masses in kilograms change from (a,b) to (a/2,b/4) after each treatment cycle; the instrument reports a+b.” The first question is whether the observed total contains enough information to predict the next total. Section 5.6 works out the answer.

If the ordinary statement is sufficient for the current comparison, stop. Add the observation, calibration or assurance account when the receiving use needs it. Before making a prediction, conformance or gate-use claim, name the exact applicability window and any observation relation that use requires; stop that use if a required condition is unavailable.

The practical gain is a model that supports the needed prediction or comparison, or identifies the missing distinction or rule. A model fitted to the wrong state can lose a difference that changes the answer.

This pattern identifies the episteme that states the model’s state space and transition law. Section 4.1 gives its membership rule. For a known model and a settled calculation, use the domain calculation directly. When the question instead concerns a procedure, an actual event or another receiving use, use the conditional contributions in :4.3.

A.3.3:2 - Problem

A time series describes observations but leaves the next state to be explained. A control instruction selects an action but may leave its physical effect unspecified. Even a declared law can give an inadequate prediction when its chosen state hides a consequential difference, as the two-substance case shows.

A usable account must therefore connect the changing subject, the state distinctions, the transition law and the observations. Its applicability and support must be sufficient for the particular prediction or decision, which may demand more than the initial model comparison.

A.3.3:3 - Forces

A.3.3:4 - Solution

A.3.3:4.1 - Definition

U.Dynamics is a same-individual dependent kind of U.Episteme. Membership holds when one already identified episteme has the changing subject as its exact C.2.1 EntityOfConcern and its ClaimGraph, interpreted under the effective U.ReferenceScheme, substantively declares both a state space and a state-transition law for that subject. The law may include exogenous inputs, constraints, disturbances, and an observation relation.

The C.2.1 ClaimGraph, exact EntityOfConcern, and effective U.ReferenceScheme remain the episteme’s identity discriminators. A.3.3 adds no context field or second dynamics identity. A U.ClaimScope, operating region, applicability window, qualification interval, parameter regime, or scale band enters only through the exact claim that uses it and its subject pattern; changing one can change claim content without becoming an ambient container.

U.Dynamics can declare a deterministic transition, permitted alternatives, a probability law over continuations, or a combination of these. Its time description can be continuous, discrete or hybrid. It can make state-change claims about physical systems, software services, organizations, epistemes, claim portfolios, resource states, architecture characteristics, or another exact EntityOfConcern. If several subjects are jointly modelled, the exact C.2.1 EntityOfConcern must itself be an independently identified collection, system, or other admitted subject.

If empirical grounding is claimed, state the exact C.2.1 EpistemeEmpiricalGroundingRelation.

A.3.3:4.2 - Dynamics statement

Use this compact aid only when the ordinary sentence is insufficient for the current decision:

Dynamics statement:
  CandidateEpisteme:
  EntityOfConcern:
  EffectiveReferenceScheme:
  StateSpace:
  TransitionLaw:
  TimeReference:
  TransitionChoices:
  ProbabilityLawIfSpecified:
  InputsOrDisturbances:
  ObservationRelation:
  ConstraintsOrInvariants:
  ClaimScopeIfReliedOn:
  OperatingRegionAndApplicabilityWindow:
  CalibrationOrParameterSourceIfReliedOn:
  PredictionUse:
  EvidenceOrAssurancePathIfReliedOn:
  StopCondition:

These rows are an optional aid for the minimum claim content and separately governed references needed by the current use. C.2.1 identifies the candidate episteme.

A.3.3:4.3 - Conditional contributions to the work

Use a contribution below when its question arises while constructing or using the state-law account.

A.3.3:4.4 - State-space and transition-law fields

The following optional view groups the claim content of one C.2.1 episteme:

U.Dynamics membership view {
  candidateEpisteme: U.Episteme
  entityOfConcern: EntityOfConcern
  effectiveReferenceScheme: U.ReferenceScheme
  claimGraph: {
    stateSpace: reference to an A.19 CharacteristicSpace with the admitted-state constraints
    transitionLaw: state-transition claim
    timeReference: continuous | discrete | hybrid
    transitionChoices: permitted continuations and conditions selecting among them
    probabilityLawIfSpecified?: conditional probability law over continuations
    inputsOrDisturbances?: CharacteristicSet
    observationRelation?: claim or exact relation reference
    constraintsOrInvariants?: claim content
    claimScopeIfReliedOn?: U.ClaimScope
    operatingRegionAndApplicabilityWindow?: ConditionSet
    calibrationOrParameterSourceIfReliedOn?: exact source or calibration-episteme reference
  }
}

stateSpace is claim content of this U.Dynamics episteme. It refers to an A.19 CharacteristicSpace: the product of declared characteristic value sets. The model states which combinations are admitted, through constraints or a predicate over that product. A.3.3.CC constructs such a configuration description; a predictive state can require additional information under :4.4.1. Characteristics retain their local meanings, units, Scales and comparability rules; C.16 supplies measurement construction when needed. A receiving evaluation may reuse this CharacteristicSpace; its scoring and judgement belong to that evaluation. Topology, geometry, aggregation or coordinate transformations are supplied over the domain where trajectories or comparisons use them; an independently selected organization of constituents and obtaining relations remains A.22 U.Structure.

transitionLaw is paradigm-agnostic. It can be an equation, relation, kernel, finite-state transition, queueing model, Bayesian update, Petri-net firing relation, simulation rule, learned predictor, or hybrid model, provided the state space, semantic basis, and applicability boundary are declared.

transitionLaw, observationRelation, constraintsOrInvariants, and calibrationOrParameterSourceIfReliedOn are ClaimGraph content or exact references inside the U.Dynamics episteme unless another governing pattern independently identifies one as an episteme, source, relation, or structure.

observationRelation specifies how the model connects its state to the observed quantity. For a deterministic observation, give the map y = h(x), where x is the model state and y the observed quantity. Identity observation (h(x) = x) is allowed only when the claim says the state coordinate is directly observed.

When proposing an exact deterministic one-step law on measured or aggregated coordinates, check whether two admitted states with the same current values of those coordinates, time and inputs can give different next coordinate values. Such a pair disproves that proposed law. Section 5.6 shows how to recover the missing predictive information or give a bounded answer.

For a proposed stochastic one-step law on aggregated coordinates, compare the next-observation distributions from the states it merges under the same time and inputs. If those distributions differ, the current aggregate omits predictive information. Retain a more informative state, condition a distribution over hidden states on the available history, or use a bound sufficient for the question. Equality for every merged group supports the aggregated one-step law under those conditions; longer use must preserve the later outputs and conditions it needs. Section :5.8 separates this question from long-run averaging.

A.3.3:4.4.1 - Construct the state and allowed continuations

1. Start with the question and participants. Name what can change, which result is needed and the conditions being considered. From the relevant subject account, identify the interacting participants and which of their differences can affect that result.
2. Describe allowed configurations. Use A.3.3.CC to select the participants’ retained differences, express compatible combinations, and choose independent coordinates, implicit constraints or finite enumeration for the receiving operation. Keep constraints on configurations separate from restrictions on rates or transitions. Sections :5.7 and A.3.3.CC:5 show how changed lengths, stock and job-order questions alter the description.
3. Recover the information needed for continuation. Separate changing state from parameters held fixed by the model and externally supplied inputs. Determine the initial data required by the proposed law. A position may also need its velocity; a computation may need its instruction position and saved local values. For a field, name its argument domain and value quantities, then obtain the needed initial and boundary data from its law and the modeled arrangement.
4. Construct the transition. Use the subject’s laws or operation rules to relate admitted states under the inputs. A.3.3.TR constructs that rule: state local effects, combine jointly active relations separately from alternative actions, and derive a small case. Check that the proposed continuation respects the constraints. If a constraint leaves the next state unresolved, supply the missing interaction or operation rule, or retain the alternatives it permits.
5. Interpret the alternatives. State who or what can select a continuation and under which conditions. Use a probability law when one is supplied or supported for that use. Counting possible continuations establishes their number; probabilities require a rule assigning them weights. The distinction changes the result in :5.9.
6. Test the description and choose the return. Apply the state-sufficiency comparison above to the prediction or observation needed now. A.3.3.PI constructs the retained state, usable history, predictive distribution or bound for that question and horizon. Return the state and transition account, a sufficient range or conditional conclusion, or the state distinction, law, input or observation still needed. Use C.11.DUA when choosing whether further information is worth obtaining.

The construction can finish before a complete dynamics model exists: a useful result may identify the missing physical interaction or computational rule. Section :4.1 admits U.Dynamics only when the episteme substantively states both the state space and the transition law.

A.3.3:4.5 - Evidence, prediction, conformance, drift, and calibration

Let D be a U.Dynamics about exact EntityOfConcern E. Let W denote only exact dated U.Work occurrences when Work is current, and let O denote separately identified observation, telemetry, source, or measurement records.

These expressions name claim-side calculations or questions. When an observation, conformance, drift, measurement, evaluation, gate, or assurance result is claimed, the applicable evaluation or measurement declaration states the criterion and result semantics, and the actual application and result are identified separately; C.2.1 identifies any persisted result episteme, and use A.10 or B.3 only for the separately claimed reliance or assurance use.

Calibration Work and its domain result may support a later dynamics episteme whose changed ClaimGraph receives its own C.2.1 identity; an EpistemeEditionRelation obtains only when C.2.1’s exact continuation predicate is separately established.

A.3.3:4.6 - Prediction use in comparison or gating

A prediction used for comparison, release, gate, assurance, or work preparation states the exact dynamics edition, predicted Coordinates, operating region, horizon, and relevant error or uncertainty. State any time step, parameter regime or source-currentness condition on which the prediction or receiving use depends. The direct consumer’s policy then states which observation, validation, sensitivity, robustness, stability, or normalization-composition conditions that use requires.

A fresh observation may replace or check the prediction when the policy calls for it. A non-expansive bound, another sensitivity bound, or commutation with a normalization step is required only when the named use relies on that property. If the required conditions are absent or fail, the prediction cannot carry that use. State a needed currentness claim through C.27.TA. Use C.27 when a separate authored temporal-claim adequacy question remains. Obtain a needed internal-constraint result through A.20; use A.21 for a gate decision or the applicable decision pattern for another decision.

A.3.3:4.7 - Apply or transfer a dynamics model

Stay in A.3.3 when the transition law or observation relation uses accepted local dynamics under one explicit semantic basis and applicability boundary.

Use C.29 when the law’s use depends on a contested transfer, cross-domain analogy, learned or speculative mathematical lens, scale change, abstraction, quotienting or reusable explanation across contexts. Establish the preserved and lost structure, operating region or scale window, applicable rival, lens-use boundary and stop condition. Then state the resulting dynamics law and its observation, constraint and calibration conditions here. The direct prediction consumer still determines reliance under :4.6.

A.3.3:4.8 - Recover an ambiguous source claim

When a source label such as “process” or “model” leaves the asserted relation unclear, recover one concrete claim before assigning a kind. Establish U.Dynamics membership on the episteme under :4.1 and a Method claim on the semantic way of doing under A.3.1. When an episteme is also claimed to describe that Method, apply A.3.2’s membership rule independently. Section 4.3 supplies the other conditional contributions; use E.10.ARCH if the represented relation remains unresolved.

A.3.3:5 - Archetypal Grounding

A.3.3:5.1 - Reactor control

A reactor team models temperature and concentration with a nonlinear ODE and disturbances. Identify the reactor as the changing subject, specify the two state coordinates, and declare the ODE, disturbances and applicable operating region. The resulting episteme meets :4.1 when those state-space and law claims are present under its reference scheme.

For a thermocouple comparison, the observation relation selects temperature from the modeled state. Align the observed and predicted temperatures over the comparison window, then use the tolerance and validation conditions required by :4.6. Changes to a control policy change the model’s input; selecting and describing that policy uses the Method contributions in :4.3.

If the question concerns an actual regeneration of the catalyst bed, recover that event’s boundary, observed bed conditions and continuity or reidentification under A.3.4. A proposed trajectory remains available for prediction; the actual-change claim needs the occurrence facts.

A.3.3:5.2 - Reliability and operations

A service platform models backlog, arrival rate and incident recovery with a queueing or birth-death model. Compare its predicted behavior with the stipulated service objective under the model’s operating assumptions. If that comparison is used for a release decision, apply :4.6.

A.3.3:5.3 - Evolutionary architecture

An architecture group tracks latency, coupling, operational cost, and change lead time across releases. An episteme about that architecture can be U.Dynamics when its ClaimGraph declares a state space over those characteristics and a discrete-time transition map as the transition law.

A.3.3:5.4 - Knowledge dynamics

A claim portfolio uses belief, evidence weight, source currentness, and contestability as state coordinates. An episteme declaring a Bayesian or likelihood update as the transition law over that claim-state space is U.Dynamics. Identify which incoming observation changes a belief coordinate under the update rule. Name the source content used to support or challenge the specified claim for that update.

A.3.3:5.5 - Natural physical evolution

A U.Dynamics episteme can model the Moon’s motion around Earth using an orbital state space and transition law.

A.3.3:5.6 - When the observed total is not enough to predict

A team wants to predict how much of two removable substances will remain after treatment. For this worked model, let a_n and b_n be their nonnegative remaining masses in kilograms after n cycles. Assume that each cycle leaves half of the first substance and a quarter of the second, with no new material added:

a_(n+1) = a_n/2, b_(n+1) = b_n/4.

The instrument reports only their total, y_n = a_n + b_n. The model’s state is (a_n, b_n); its observation relation maps that pair to the total. The states (1, 0) and (0, 1) both give y_0 = 1 kg, but their next totals are 1/2 kg and 1/4 kg. No deterministic law using only the current total can reproduce the next total for every admitted state.

Retain the two masses when they are available. If only totals are observed, two successive exact readings recover the composition in this model: solve a_0 + b_0 = y_0 and a_0/2 + b_0/4 = y_1, giving a_0 = 4y_1 - y_0 and b_0 = 2y_0 - 4y_1. These masses must be nonnegative. Substitution into the next-cycle law gives y_2 = (3/4)y_1 - (1/8)y_0; the same recurrence applies at every later cycle. The prediction now uses one previous total as well as the current one. Equivalently, take that pair of totals as the predictive state.

If only the initial total is available, the model still gives a range: for integer n ≥ 0, y_0/4^n ≤ y_n ≤ y_0/2^n. Each extreme is attained by putting all the initial mass in one substance. Use this range when it answers the working question; otherwise obtain information about the composition. If the two substances instead have the same known retention factor r with 0 ≤ r ≤ 1, the total alone obeys y_(n+1) = r y_n. Thus whether aggregation preserves the needed law depends on the modeled operations.

The calculation assumes exact readings and fixed retention factors. Applying it to treatment data requires accounting for measurement error and establishing the retention law over the intended operating range. Lin and Lu, §§2.1–2.2 explain the broader state/observation and model-reduction problem; the two-substance case here supplies an elementary construction.

A.3.3:5.7 - A constraint changes the state description

Two endpoints move in a plane and are connected by a rigid link of length l > 0. Four Cartesian coordinates obey (x2-x1)^2+(y2-y1)^2=l^2. One configuration description uses three coordinates: place the first endpoint at (X,Y) and the second at (X+l*cos(phi),Y+l*sin(phi)), with phi taken modulo a full turn. The construction makes the length constraint hold. To predict motion under an ordinary second-order mechanical law, also supply the required velocities and the forces or other interactions.

Change the question to longitudinal vibration of an elastic link. Fixed l has removed the extension that matters. Replace it with variable length r, keep its rate of change when required, and obtain the restoring interaction from the physical model. A rigid-link calculation remains useful for its earlier premise; the elastic question needs another state and law. Tong, Classical Dynamics, §2.3 supplies the generalized-coordinate method; the two-endpoint comparison here applies it.

In another practice, two queues share a fixed total of N items. Retain q1 and recover q2=N-q1, with 0<=q1<=N. If external arrivals are admitted, the state must retain the changing total or both queue sizes. The source of the constraint changes, while the construction still identifies which values can vary independently.

A.3.3:5.8 - A long-run average can coexist with predictive memory

Consider a three-state Markov model with this transition matrix. A readout reports 0 for A or B and 1 for C.

A present readout of 0 merges states with next-1 probabilities 0.1 and 0.7. The readout alone therefore leaves predictive information unresolved. The stationary distribution is (19/54,13/54,22/54). At stationarity, after readouts 1,0, the current A/B weights are 2/5,3/5, so the next-1 probability is 23/50. After 0,0, those weights are 73/105,32/105, giving 99/350. A decision that changes above probability 0.4 takes different actions after these histories. Keeping only the present 0 and the stationary A/B mixture gives 11/32 and loses that difference.

Condition on the available history or retain the resulting predictive distribution. With no information beyond the current 0, the range [0.1,0.7] may already answer a weaker question. The full finite chain is irreducible and aperiodic, and its long-run proportion of readout 1 converges to 22/54. That long-run result leaves the history-dependent prediction above intact. The finite-chain results are given in Cambridge’s Markov Chains notes, §§9-10; the matrix and conditional calculations here are an authored example.

A.3.3:5.9 - Possible execution orders do not supply a probability law

Two participants A and B each read shared integer x into a local saved value, then write that saved value plus one. Each read or write is atomic, and each participant’s read precedes its write. Initially x=0. To follow the permitted reads and writes, use x, each participant’s position in its two-step procedure and any value already read.

There are six interleavings that preserve those local orders. Only readA,writeA,readB,writeB and its A/B reversal finish at 2. The other four finish at 1: both reads occur before either write, so each participant later writes 1. This enumeration identifies allowed histories that defeat the intended two-increment result.

The six histories have no assigned execution probabilities. Inferring a probability of 2/3 for a lost increment from these counts requires a scheduler model that justifies equal likelihood for the six histories. To obtain the intended result for every allowed history, serialize the read-and-write pairs or supply an indivisible increment operation. If that repair introduces waiting, separately check the progress condition required by the use.

A.3.3:6 - Bias-Annotation

Available measurements can determine the chosen state too early. In :5.6, a convenient total conceals the composition that determines the next total. Compare states that share the proposed observation before treating it as sufficient for prediction.

A familiar equation or a well-fitting simulation can also encourage extrapolation beyond its established conditions. Keep the observation relation and applicable region visible when interpreting its result. The physical and organizational examples require their own domain laws and validation.

A.3.3:7 - Conformance Checklist

CC-A3.3-1 (Membership and identity). A.3.3 judges one already identified U.Episteme. That same individual is U.Dynamics only when its exact C.2.1 EntityOfConcern is the changing subject and its ClaimGraph, under its effective U.ReferenceScheme, declares both a state space and a transition law. A.3.3 adds no second identity.

CC-A3.3-2 (Local meanings and applicability). Interpret characteristic names under the effective U.ReferenceScheme. State units, operating region, time base, approximation regime, claim scope when needed, qualification window and source-currentness condition as claim content or their separately governed values.

CC-A3.3-3 (EntityOfConcern). Name the changing EntityOfConcern. Joint modeling uses the independently identified joint subject required by :4.1.

CC-A3.3-4 (State space). The state description names the A.19 CharacteristicSpace, the combinations admitted by the model, and the information required by its law. Characteristics retain their meanings, units, Scales and comparability rules; topology, geometry or coordinate transformations are supplied when the use needs them. Use A.3.3.CC to construct the configuration description and :4.4.1 to complete the state-and-transition account.

CC-A3.3-5 (Transition law). The law states a relation, map, kernel, equation, rule, learned predictor or simulation rule for the declared time base. Its permitted alternatives, conditions selecting among them and any supplied probability law remain recoverable under :4.4.1.

CC-A3.3-6 (Observation relation). Evidence use states how exact Work-side facts when present and separately identified work records, telemetry, measurements, observation records, or source records become observed coordinates. Direct observation is declared rather than assumed.

CC-A3.3-7 (Constraints and applicability). Constraints, invariants, operating region, approximation regime, parameter range, horizon, and scale window are stated before prediction or gate use.

CC-A3.3-8 (Control or planning procedure). When a reusable planning or control way uses the dynamics, identify that Method under A.3.1. Apply A.3.2 to an episteme claimed to describe it; the dynamics membership test remains :4.1.

CC-A3.3-9 (Observed facts and calibration). Attach resource actuals, timestamps and observations to the Work, measurement or source they describe. Relate them to the dynamics through :4.5. Apply its C.2.1 identity and edition conditions when calibration changes the model.

CC-A3.3-10 (Prediction use). Predicted Coordinates used for comparison or gating state the exact model edition, domain, horizon, currentness, error or uncertainty, and every observation, validation, sensitivity, stability, or normalization-composition condition required by that consumer’s policy. No universal non-expansiveness or commutation test substitutes for the direct decision rule.

CC-A3.3-11 (Temporal use). State temporal aspects through C.27.TA and establish the adequacy required of an authored temporal claim through C.27, as specified in :4.3.

CC-A3.3-12 (Representation transfer). Apply :4.7 when representation transfer changes the law’s permitted use, and carry the resulting conditions into the dynamics account.

CC-A3.3-13 (Source-label repair). Recover the relation asserted by an ambiguous source label under :4.8 before applying a membership predicate.

CC-A3.3-14 (Actual change). When an actual transformation is claimed, establish A.3.4’s occurrence basis specified in :4.3. A predicted or simulated trajectory describes change under the model’s premises.

A.3.3:8 - Common Anti-Patterns and How to Avoid Them

A.3.3:9 - Consequences

An explicit state and transition law lets the practitioner calculate a possible trajectory and compare it with observations through a declared relation. A failed comparison can then change a particular state choice, parameter, observation account or applicability condition.

The work costs more than collecting measurements: the model needs interpretable characteristics and a supported law. A bounded prediction may be sufficient; a more consequential use may require additional observation, calibration or validation under :4.6.

A.3.3:10 - Rationale

The needed prediction determines which state distinctions have to remain recoverable. The transition law expresses how those distinctions evolve, while the observation relation says which part of that state the available measurements reveal. Keeping these contributions explicit makes both successful prediction and a failure caused by lost information explainable, across different domain laws.

A.3.3:11 - SoTA-Echoing

Choose a predictive description for the question being asked. In :5.6 the available observation is the total mass, but the next total depends on its hidden composition. Compare the descriptions under the same fixed retention law and exact-reading premises:

For a present total of 1 kg, the interval [0.25, 0.5] kg already settles whether the next total is at most 0.6 kg. It leaves an at-most-0.4 kg question unresolved. Acquire composition or a sufficiently informative history only when that remaining uncertainty matters. Equal retention restores a one-total transition law, so the extra state or reading becomes unnecessary.

Lin and Lu, §§2.1–2.2 supplies the methodological comparison line: selected observables can discard information that reappears as memory in a reduced description. Its exact projection identity still requires closure choices for a usable reduced model; its statistical treatment uses a stationary-process setting. The elementary calculation above is an authored construction. It selects the state–observation distinction in :4.1–:4.2 and the question-dependent choice in :5.6, with a measurable cost: additional coordinates or observations only when the cheaper description is insufficient.

Strengthen support when the use changes. For data-driven predictive control, de Jong and colleagues, §§I–IV, especially III and Theorem IV.2, compare iterated one-step lifted models with directly learned multi-step predictors. They choose the latter to avoid propagating one-step prediction errors across the horizon, at the cost of learning horizon-dependent prediction matrices and observables. Their constrained controller adds an interpolated initial state and terminal ingredients; recursive feasibility depends on the stated terminal-set assumption and a feasible preceding problem. These are contributions to a particular control problem.

Accordingly, :4.6 makes the intended consumer specify the prediction conditions and properties it relies on. A control decision that relies on recursive feasibility must establish the relevant model, constraints and feasibility conditions. An ordinary comparison can finish with the state, law, observation and applicability information sufficient for its question. The extra cost of a stronger guarantee is incurred by the use that needs it.

Reopen the chosen description when the observation error, retention law, horizon or question changes enough to defeat its information or error bound. Reopen a control use when its measured prediction errors or operating conditions defeat the assumptions supporting its selected guarantee.

Construct before reducing. Tong’s generalized-coordinate construction, §2.3 supplies a way to represent configurations satisfying constraints. His field-theory discussion, §1.1.2 shows that the interpretation and time order of a field law determine its initial data. Section :4.4.1 adopts the common sequence from participants and constraints to predictive information; the particular forces, field equations and solving Methods remain subject contributions. Retaining an implicit constraint can be preferable to eliminating it when the elimination obscures the relation being investigated.

The deterministic comparison in :5.6 and stochastic comparison in :5.8 ask which distinctions prediction needs. Long-run averaging answers a separate question about repeated evolution. In :5.9, a range over allowed executions is available before their probabilities are known. Choose the transition representation that answers the present question with the information available.

A.3.3:12 - Relations

C.2.1 supplies episteme identity, empirical-grounding and edition conditions. A.19 and C.16 supply characteristic and measurement construction; A.2.6 supplies a claim scope when the use relies on one.

A.3.3.CC constructs a description of configurations under constraints. It can return that result before a transition law is available; :4.4.1 then connects the configuration, additional state information and allowed continuations. A.3.3.TR constructs the rule relating states from the supplied interactions, operations and inputs. A.3.3.PI retains the information needed for a prediction, using additional state, history, uncertainty or a sufficient bound.

When an independently selected bounded-model-use structure or obtaining model-use relation changes the receiving use, A.1.1 supplies that account. The other conditional contributions are specified at :4.3; :4.7 governs mathematical transfer into a dynamics use.

A.3.3:End