Three independent constraints
Try privacy first. Tighten the budget to leave one candidate, then tighten the window: neither response fits both. These invented numbers describe one shared work package.
A local requirement needs assessment.No new observation → no added contract
Response work begins after European regulatory review; it cannot overlap it.Available window: 4 → 4 weeks
The regions fund the same analytics response.Shared allowance: 8 → 8 cost units
This is an explicit scenario decision, not a real approval. It takes effect only with the privacy observation. A regional law does not automatically apply to every region.
Observation → authorised scope → derived effects
| Response | Cost | Duration | Current bounds |
|---|
Two context views, with the original assumptions retained
C₀ · Baseline context
C₀ · Current context
What is formally defined here, and what is still a candidate?
The implemented base has eight objects: the binary triples (shared privacy contract, tighter time bound, tighter budget bound). There is one arrow Cᵦ → Cₐ when every active constraint in a is also active in b. Identity forgets nothing; composition is successive forgetting. The tests check identity and composition for this finite poset.
The diagram proposes plan objects with tasks, prerequisites, obligations and evidence attached to a context. Its horizontal comparison retains baseline identifiers and edges. A suitable category of plan morphisms, their composition, and the cartesian universal property are not yet constructed or checked. The projection label records which context a plan belongs to; it is not a verified functor on a total category.
A fibration would require appropriate cartesian lifts for every permitted base arrow and target. A cleavage chooses such lifts; different adaptation policies are not automatically cleavages. Reindexing coheres up to isomorphism, unless a suitable split construction supports strict equality. An empty feasible fibre can obstruct lifts; reporting a conflict does not fix that proof. See Stacks Project §4.33.
Local differences, named connections
Select a region with a pointer or keyboard. Impact and acceptance are separate: an unchanged task still has no completion evidence in this scenario.
The questions behind the example
Explain it to a project director
Imagine each regional plan on a transparency sheet. Shared analytics and launch commitments are the registration marks that align the sheets. A mark on Asia’s sheet appears elsewhere only when a declared shared connection carries it there.
The budget cut and late prerequisite come from different regions but constrain one shared response. With 5 units and 2 weeks, the cheaper option is too slow and the faster option is too expensive. The next step is an owner’s decision about scope, funding or time.
Does it actually work?
The app computes declared effects and checks a small response-choice problem. It makes the observation, scope decision and rules inspectable. The acceptance panel shows which evidence is missing. It does not infer real legal requirements or discover missing dependencies.
At the shared response, “candidate fits” means only cost ≤ allowance and duration ≤ available window. Regional task costs, resources, overlap, dates and real evidence are not supplied. No candidate is an accepted whole campaign plan.
So what does the fibration add?
Here, an ordinary dependency and constraint model produces the same task reviews and numerical result. The app’s useful extra discipline is visible context indexing: retained assumptions, local differences and a trace from decision to effect.
No exclusive mathematical benefit has been demonstrated. A next experiment would define plan morphisms and an actual lifting construction, then test reuse and successive changes. Adding terminology does not make a hand-written policy a theorem.
How does this compare with a schedule?
- WBS: what work belongs to a package or region.
- Dependencies: what constrains what; this app declares finish-to-start prerequisite edges without lags.
- Schedule: dates interpreted with dependency types, calendars and resources.
- Context-indexed plans: which assumptions each plan is interpreted under.
These views answer different questions. P6 already supports typed start/finish relationships, including across projects. The categorical proposal must be compared with that capability fairly.
Is a published baseline a total order?
No. Dates do not impose precedence between every pair of tasks. Let “creative” and “venue booking” have no dependency edge:
Creative: week 1–2
Venue booking: week 1–2
Creative: week 1–2
Venue booking: week 2–3
Both obey the same empty precedence relation between those activities. Sorting a schedule’s rows adds no dependency. A baseline is a saved comparison plan. An acyclic precedence graph gives a reachability partial order; typed endpoint relationships and lags contain more information than an unqualified activity poset.
What is float, and what does this not guarantee?
Total float is time computed from early and late dates with scheduling options. For example, early start at week 1 and late start at week 2 gives a start-based difference of one week. Float is not a distance or count of alternative total orderings. This app does not calculate schedule float.
Context indexing does not remove rebaselining, resource coupling or hidden dependencies. Checks here cover retained task identifiers, resolved prerequisite references, declared-edge propagation, policy deltas and the stated numerical predicates. They cannot show that the model includes every real connection.
Computed
Impact traversal, retained references, context bits, option inequalities, task deltas and current audit state.
Supplied by the author
Task dependencies, data-consumer tags, regional work templates, scope options, response durations/costs and acceptance predicates.
Unchecked in the world
Compliance, complete resource feasibility, completed work, human usefulness and a cartesian universal property.
Session audit
This is an ephemeral explanation in this browser tab. Reloading clears it. Export downloads a user-kept JSON receipt; it is not a saved approval or independently verified evidence.
Historical prompt and corrections
The two original prompt excerpts below are retained as historical text. Their automatic-propagation and guarantee claims are hypotheses, not results of this app. A local observation needs a scope decision; a valid fibration needs specified categories and cartesian lifts. Hierarchy alone establishes neither. “No orphaned tasks” is replaced here by bounded identifier/reference checks.