Gimmer Crag · Essai 07 · Open systems
An open net joins work. What makes it a plan?
Open-net composition joins the resource logic of smaller work blocks. But how many tokens are present, which work occurrences are selected, and may a transition repeat? Two refuge lifts show where assembling a net stops and project planning begins.
One lift is available to both crews. Each crew borrows it and returns it. Either crew may go first; both cannot begin together. Give each crew its own lift, and a joint start becomes possible without changing the two serial orders.
Fictional project. Lifts, readiness and durations are declared modelling assumptions.The trial
Checking the connected process
A selected-work reading of the composed net
Places, work events and tokens
This is the earlier finite Gimmer model: circles are places and boxes are Petri-net transitions interpreted as selected project-work occurrences. Green arrows show the tokens each transition consumes; clay arrows show the tokens it returns or produces. The displayed atomic steps abstract from duration. The diagram and counts are computed from the chosen case. Its once-only rule is an added project contract; an ordinary transition in the structurally composed open net can fire again whenever enabled.
Ordinary Petri nets can also enforce once-only work: give each selected occurrence a ready place with one initial token, consumed without return when that occurrence fires. The small resource net drawn here omits those control places; the finite browser engine enforces the rule separately. Gluing does not infer which work should be selected once.
What can start together now?
The reference check
What open-net gluing leaves open
The earlier Boundary Contract Lab already established finite contract/direct-net agreement. The external package is useful here for a different question: what does assembling the open net give us before we add a project marking and a selected-work policy?
Complete serial orders of the selected work
All selected occurrences finish. These words alone cannot distinguish one shared lift from two independent lifts.
Bridge to the foray
Petri nets → monoidal executions → candidate plans
This advances the wider End of reusable smaller work blocks. The refuge is a test situation, not the future unit of reuse. What survives: the chosen ports, ownership, token counts, incomplete work and joint-step capacity. What does not follow: an automatically discovered WBS, an optimal schedule, or a universal theorem for arbitrary open nets.
Sources, construction and limits
Baez and Master, Open Petri Nets supplies the boundary-as-cospan and composition by gluing. Baez, Genovese, Master and Shulman, Categories of Nets supplies the choice of count-token execution semantics. AlgebraicPetri.jl is an independent implementation reference for structural open-net assembly. The bounded selected-work contract, its supply convention and checks belong to this experiment; the method note sets out their precise limits. The browser executes this repository’s finite engine, not Julia.