Shared watersCorrected attempt 03 / 03
A shared version.
A shared team.
Different rules.
The third drawing gives business processes their own input/output surroundings. We correct the boundary meanings, then examine a tiny question: do the local accounts agree, and is the same team being claimed twice?
Three local views of one power-link specification.
The service, design and installation processes each hold a local observation of the same specification identity. In this toy, version A must match A and version B must match B. Separately, design and installation may request one integration team in the same time slot.
Solid lines: shared version observations. Dashed lines from the separate square ports: requests for the integration team. Crossings without a junction do not identify the two relations.
These counts describe the finite toy relation. They are not probabilities, forecasts or counts of feasible project schedules. The diagram is an interface view of candidate process snapshots, not an execution trace.
Observation agreement
One identity, consistent values.
Repeating the word “Customers” or “Team” does not create a shared object. We name one interface—depot-barge.power-link.specification—and declare which local observations must agree.
Only (A,A,A) and (B,B,B) satisfy that equality. A shared value is not automatically a true or approved value: the rule establishes agreement within this model.
Exclusive allocation
A separate capacity rule.
The team is available to at most one of the two processes in this time slot. Valid request pairs are (no,no), (yes,no) and (no,yes).
All three versions can agree while both processes claim the team. Equality has not solved resource allocation; the separate rule exposes the conflict.
Correcting the original ports
Say what actually crosses a boundary.
| Original surrounding label | Corrected candidate interface | Keep the distinction |
|---|---|---|
| Customers → Sell | Service requirement supplied to “Agree service” | The customer is a participant; the requirement is the information used. |
| Operations capability → Design | Required service conditions plus available design capability | A capability condition and a specification value are different inputs. |
| Design → Regulators | A versioned submission sent to an independent authority | Design does not produce a regulator or guarantee a decision. This interaction is named, but not simulated here. |
| Site team → Build | A specific team allocation available to an installation process | Capacity needs identity and a time slot. A repeated label cannot duplicate people. |
| Customers → Market → Customers | A participant with a before/after information or engagement state | The intended transformation must be stated; this unresolved process is left out of the small model. |
From the 2022 drawing
What survives the correction?
2022 08 TOM open systems second attempt.graphml
Retained
Processes with exposed surroundings; the author’s question about artefacts versus teams; the need to identify common elements.
Corrected
Typed information/observation interfaces and one named team replace ambiguous actor ports. Equality and allocation are separate relations. Unconnected source elements do not become implied requirements.
Left out of this attempt: A full dynamical machine, SMC laws, a schedule functor, regulator decision dynamics and automatic generation of work. The implemented model checks finite snapshots only.
Source → concept → construction → limit
Libkind, An Algebra of Resource Sharing Machines, §2.2, uses compatible shared observations when composing automata. We borrow the finite compatibility idea; we have not supplied the transitions/readout/update structure needed for the full machine construction.
Libkind & Fairbanks, Undirected composition, helps distinguish identifying a common variable from combining its dynamics. Baez, part9, motivates distinguishing reusable resources from freely available parallel capacity. The same-slot allocation rule is explicitly supplied for this toy.
Original GraphML anchors: n0; n1; n2::n0; n2::n14; n2::n9. These identify the local source drawing; they are not mathematical claims. Original files remain unchanged. This site depicts the corrected construction.