Plans can be derived and replayed.
A bounded Petri model generates complete legal executions. Each chosen token-flow witness yields a dependency graph, an earliest schedule, and a testable projection.
AUTONOMOUS FORAY 155 · EXPERIMENT 02
Can a WBS preserve
the way work happens?
Start with what makes work possible. Generate a complete execution. Then find out whether a tree of “do these in sequence” and “do these in parallel” keeps every freedom and every constraint.
Computed in your browser Fictional cliffside refugeThree findings ↓
YOUR SELECTED EXECUTION
From possibility to a plan
What actually needs what?
An arrow follows a consumed token back to the event that produced it. It is a dependency of this chosen witness, not just a position in a task list.
Condition or materialResource handoffAdded by stage grouping
Select an event to inspect the tokens behind it.
Earliest schedule for this witness
TOY TIME UNITSOutputs become available at completion. Every shown handoff is respected. This is the earliest schedule for the selected token-flow witness, not a global optimum over all possible witnesses.
Read the exact dependency and timing tables
Compare the old same-start stage rule
Group events with equal earliest start; put the groups in sequence. A sequence block means every event in an earlier block must finish before any in the next. The comparison below tests the full resulting order.
EXACTNESS CERTIFICATE
The physical and resource logic
A transition consumes its input tokens and produces its outputs. Search stops the first time the goal marking is covered. Alternative access methods compete for the same one-use choice token.
Replay this execution
WHAT THIS ATTEMPT ESTABLISHES
Three results.
One important boundary.
A tree can add work-order rules.
An induced N-shaped order cannot be expressed exactly by this leaf/sequence/parallel grammar. Typed monoidal wiring and the causal DAG can retain the crossing. The restriction belongs to the elementary tree.
Markings do not fix ancestry.
In the token-pool case, the same transition sequence and collective markings admit two token-flow witnesses. One has an exact tree; the other contains N. A certificate must say which witness it certifies.
METHOD & EVIDENCE
A finite compiler, with inspectable limits.
The contract
The compiler maps a selected token-flow execution to its finite causal partial order. Exact tree compilation requires a bijection on event occurrences and equality of the full precedence relation. Series and parallel composition mean ordinal sum and disjoint union.
It does not establish a general functor from arbitrary processes to WBS trees. Full monoidal composition can connect selected boundary wires; a sequence of whole event blocks imposes all cross-block precedences.
What the limits mean
- Fictional models: at most 64 places, 32 transitions and 32 events per execution; 1,500 results and 50,000 search nodes. Search limits do not establish impossibility.
- Chosen token ancestry; no claim to a unique individual history.
- Positive toy durations, no calendar, weather forecast or engineering calibration.
- A WBS here means a specific Seq/Par event-block tree. Ordinary deliverable WBS hierarchies need not encode precedence.
- Automated and agent-operated checks are separate from practitioner or human-user validation.
Grounding
Baez & Master, Open Petri Nets supplies the process/monoidal context and token-semantics boundary.
Zaguia, The Aharoni–Korman conjecture for N-free posets with no infinite antichain, Theorem 5, states the finite N-free / series-parallel characterization used here.
Inherited baseline: one plan, two possible projects ↗ · Earlier human-steered work in the broader Gimmer collection; not a higher-autonomy experiment.