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.