Details and Options
Rules can be specified in the following ways:
{"lhs_{1}">"rhs_{1}",…}

string substitution system

{{l_{11},l_{12},…}>{r_{11},r_{12},..},…}

list substitution system

SubstitutionSystem
[
rules
]

string or list substitution system

CellularAutomaton
[
rules
]

cellular automaton system

"type"→rules

system of the specified type

assoc

system with properties defined by assoc

Supported rule types include:
"StringSubstitutionSystem"

rules given as replacements on strings

"ListSubstitutionSystem"

rules given as replacements on lists

"CellularAutomaton"

rules given as a list of CellularAutomaton rule specifications

"WolframModel"

rules given as replacements on hypergraphs

When rules are specified by an explicit association, the following elements can be included:
"StateEvolutionFunction"

gives the list of successors to a given state

"StateEquivalenceFunction"

determines whether two states should be considered equivalent

"StateEventFunction"

gives the list of events applicable to a given state

"EventApplicationFunction"

applies an event to a given state

"EventDecompositionFunction"

decomposes an event into creator and destroyer events for individual elements

"SystemType"

system type name

"EventSelectionFunction"

determines which events should be applied to a given state

The event selection function sel in ResourceFunction["CausalInvariantQ"][rules→sel,…] can have the following special forms:
"Sequential"

applies the first possible replacement (sequential substitution system)

"Random"

applies a random replacement

{"Random",n}

applies n randomly chosen replacements

"MaxScan"

applies the maximal set of spatiallyseparated replacements (strings only)

The initial condition for ResourceFunction["CausalInvariantQ"] is a list of states appropriate for the type of system used.
ResourceFunction["CausalInvariantQ"][rules,"string",…] is interpreted as ResourceFunction["CausalInvariantQ"][rules,{"string"},…].
ResourceFunction["CausalInvariantQ"] accepts both individual rules and lists of rules, and likewise for initial conditions.
Options for ResourceFunction["CausalInvariantQ"] include:
"IncludeStepNumber"

False

whether to label states and events with their respective step numbers

"IncludeStateID"

False

whether to label states and events with unique IDs

Causal invariance is a property of multiway systems in which all branches of evolution history yield causal networks that are isomorphic as acyclic graphs.
In the case of an abstract rewrite system it is a sufficient condition for confluence (or the ChurchRosser property), and in the case of a WolframModel it is equivalent to Lorentz covariance.