Shared watersReading & provenance
A route back
to the ideas.
Three corrected drawings are a starting point for understanding. They preserve a route from the original question to a source concept, a visible construction and its limits.
Ends · ways · means
The End stays open.
Understand how one or another method for composing open systems works in a familiar SMR/depot and organisational context. Then explore how much it helps define useful chunks of work, capability, scope, resource or service.
Deriving useful project work through a sound formalisation remains the stretch ambition. Any such result must distinguish what was derived from the change patterns and assumptions we supplied.
These first means are deliberately small
Attempt01 constructs a finite graph join and a graph map. Attempt02 makes an explicit inventory correspondence. Attempt03 evaluates a finite compatibility and capacity relation.
They do not collectively establish a universal ontology or a single integrated theory. Each gives one part of the original exploration a precise, visible meaning.
The reading behind the attempts.
The ten records in the curated dynamics/sharing cluster were reread for this essai. A source can motivate a distinction without its full formal machinery being implemented. The per-attempt notes say exactly what is borrowed and where our small construction begins.
- Willems, The Behavioral Approach to Open and Interconnected Systems
Printed pp.46–54,60–64,70: behavior, local modules, interfaces and state as sufficient memory. Direction and institutional authority require care. - The Behavioral Approach to Systems Theory · n-Category Café
An accessible bridge to behavior and latent variables. Possible histories alone have no probability distribution; the primary paper qualifies the article’s directionality criticism. - Libkind, An Algebra of Resource Sharing Machines
§2.2: matching observations and possible deadlock; §5: the full construction and its hypotheses. Attempt03 uses only a finite snapshot compatibility relation. - Libkind & Fairbanks, Undirected composition
The common-pool and nested ecosystem examples distinguish shared variables from contributions to dynamics, and expose double counting. - Baez, Complex Adaptive System Design · part3
Typed composition syntax and its interpretation are different things. - Baez · part4
Distinguish network kinds and concrete instances; choose appropriate relation types. - Baez · part5
Refinement can require search; forgetting constraints need not preserve composition. - Baez · part6
A network model supplies actual assignments and combination rules, not merely arrows named “functor”. - Baez · part8
Agent/commitment networks differ from states and tasks for a specified team. A prerequisite join requires every input. - Baez · part9
Conserved catalysts and sequential reuse do not mean unlimited parallel availability.
Careful source reading and selected notation/figure checks are not an independent proof audit. The saved part4 capture has a page-count/extraction discrepancy; the substantive author text was checked against the original article.
Three source drawings, three corrections.
| 2022 GraphML | Corrected first attempt | Left unresolved |
|---|---|---|
| Open Graphs as a double category | Explicit boundary gluing; endpoint-preserving graph map | Double-category structure and semantic preservation |
| Basic functor setup for TOM | Typed organisational inventory and authored correspondence | Derivation of work, WBS product and functor laws |
| TOM open systems second attempt | Typed process surroundings; separate version and capacity conditions | Full dynamical transitions, SMC and schedule extraction |
The original source files are preserved. Nesting was read as structural evidence, not assumed to be a valid ontology. Unnamed arrows, duplicated labels and isolated nodes were not silently completed as facts.
Source hashes, model definitions and reading recordWhat could come next?
Give a local system enough state to remember the history that matters. Add a small transition model to the shared observations. Or ask whether a capability difference and a declared library of change operations can derive candidate project work. The next essai should follow whichever question the current examples make clearer.
These are possible directions, not claims that the three first attempts have already solved them.