WHAT THE COMPARISON ESTABLISHES
A common challenge.
Different reasoning contracts.
The aim is to discover what each method can reveal, derive or rule out—and what disappears when one view becomes another.
Read the results at the right scale
All nine examples on this page now execute small calculations. Their scope is deliberately less than the fuller experiments linked below. The fictional refuge supplies the common question; it does not make every tab the same mathematical model.
The shared controls carry air-window availability, assumed permit evidence and lifting capacity. Other features are local to a question. Logical moves in the state model, abstract durations in the scheduling model, calendar windows in the sharing model and costs in the decision model are separate abstractions. No result here verifies the original ten-month target, the structure, the flight operation or a real permission.
Fixed scenario: a 7 m² reversible refuge, 160 km/h wind and −15 °C rating, £465k envelope. Model additions: two modules, explicit temporary rig, toy costs, durations, roles and probabilities. Structural and thermal ratings are supplied attributes, not calculated engineering performance.
Research progress, model correctness, successful use of the interface and usefulness to a human reader are separate questions. A clear demonstration can teach an existing result without advancing the underlying research. A failed construction or counterexample can advance the research.
110 · Process to plan
Six explicit facts feed a simple transformation. Four are retained as constraints; two narrative facts are omitted with a recorded reason. Two supplied process descriptions yield the same summary, but only one permits winch fallback when the air window disappears. Permission is never inferred from the existence of a plan.
This is a demonstrable loss of information under a projection, not a proof of functoriality or an inverse reconstruction algorithm. The broader investigation includes process/design artefacts beyond Petri nets.
Broader Gimmer collection · Current collection and comparison contract
120 · Dynamic project states
The state records rig presence, two module stages (absent, curing, ready, accepted), and removal. Explicit inputs produce new states; exhaustive breadth-first exploration finds a shortest completing continuation. With supplied evidence and air access, one lifting resource needs eight logical moves; two permit a joint lift and seven. Zero resources or unavailable air blocks completion under the air mechanism; selecting winch changes the mechanism.
Two states can both read “two modules installed” while only one permits inspection. Sufficiency belongs to the declared update law. This finite comparison uses dynamics; it does not reintroduce sheaves into the Myers dynamics/lens investigation. Cure moves have no inferred real duration.
140 · Local to global
Three accounts constrain month and delivery method; the access review also supplies or withholds permit evidence. The solver intersects every relevant domain and enumerates joint assignments. The pairwise trap uses {July, August}, {August, September} and {July, September}: every pair intersects, but the three-way intersection is empty.
These are finite constraint sets, not compatible sections of a declared sheaf for which a gluing theorem is being asserted. Missing evidence is not agreement; one fixed mismatch does not resolve another. Real review must also distinguish differing units, scope, versions and authority.
Local to Global experiments · Source and finite-model limits
150 · Mechanisms to possible plans
Eight once-only transitions model rig setup, fabrication of A/B, delivery of A/B, inspection of A/B, and rig removal. Read prerequisites preserve shared availability; delivery requires permit evidence, a method condition and one lifting resource. All 52 complete atomic execution orders are enumerated from this acyclic mechanism.
A separate event scheduler reserves lifting capacity throughout each delivery interval and credits completion at the end. Two earliest-start schedules finish in eight abstract units with one resource; one concurrent schedule finishes in six with two. These priority-generated schedules do not exhaust all possible deliberate waits. An independent replay checks duration, precedence, work coverage and aggregate capacity.
Typed signatures and sequential traces explain the resource reading of this small model. They do not implement a general Petri-to-SMC functor or guarantee a tree-shaped WBS can express all dependencies. Work grouping is separate from causal ordering. Main 150 retains its broad source-led method scope; the higher-autonomy investigations retain their separate identity.
Main processes-to-plans collection · Richer marking-to-plan lab · Current higher-autonomy collection
160 · Process wiring
The directed acyclic diagram checks four nominal interfaces. A mounted module cannot satisfy an accepted-module input. A separate simultaneous-use contract adds both lifting demands and checks the shared capacity, permit evidence and selected air input. Repairing an interface mismatch need not repair the resource failure.
The diagram expresses a small process composition with conditions. It is not a full wiring-diagram operad implementation, and the port types do not certify structural physics. Responsibilities and interfaces remain different useful views.
Related formal project-transformation collection (related material, not claimed as the native implementation of this wiring example). The comparison implementation and its nominal contract are documented in models.js.
170 · Shared variables and review
The model enumerates placements of two lifts in August/September under accepted access windows, evidence and capacity. A shared resource contributes an aggregate demand: two simultaneous lifts need two units. With one resource and both windows, the two opposite orders remain feasible. Restricting access to one window removes both unless capacity also changes.
A reviewer proposes an access change; accepting it updates the local demonstration and its reproducible URL. A proposal is distinct from the accepted state. No remote message or real approval occurs. The behaviours are finite assignments across two windows, not physical differential dynamics or live collaboration.
The conceptual distinction is variable/resource sharing rather than only directed signal flow. See the finite shared-constraint implementation. No dedicated earlier public Gimmer sharing implementation is claimed.
180 · Feasible designs and their construction paths
Three hypothetical shells combine with two transport methods. Feasibility checks wind floor, load compatibility, shared access/evidence/capacity, temporary rig presence and full-path budget. The nondominated set minimises cost, delivery duration and site occupation without inventing a universal weighting.
The single cassette/air endpoint costs £440k, but its rig raises the path to £490k. Two split-module alternatives remain at the default £465k envelope: £430k with shorter air delivery and £400k with slower winch delivery. Low-rating light modules are rejected even when cheap. All thermal ratings and the rest of the engineering brief are supplied assumptions.
These six finite witnesses are a small adaptation of the staged-feasibility lesson. The separate package-backed power-loop experiment also shows why coupled component costs can reverse rankings; that feedback solver is not embedded here.
Project Co-design · Composition, finite implementations and model limits
210 · Meaning, goals and required work
The user supplies desired accepted modules and a clear site. Explicit method rules in a small local vocabulary compile to planning actions. Shared rig setup destroys “clear”; removal restores it only after the required acceptance records exist. The generated plan therefore includes work absent from the final product. Empty scope generates no work; unavailable inputs do not produce an invented method.
Necessity is checked by omitting each function and testing reachability again. A selected two-module method requires six functions; one module requires four. These are necessities of this catalogue, not all imaginable implementations. Product/process packaging changes the labels around the same action identities.
The semantic route searches sets of facts. The independently declared, parameter-free STRIPS domain is parsed into a separate bit-mask search. Both receive the same facts, goal and chosen method, and parity is computed. This local compiler does not implement full RDF/OWL or claim superior planning. The fuller Solway experiment supplies explicit foundational/domain alignment and a larger fair comparison.
The retained supplied-WBS validator checks a declared profile: a single-parent acyclic hierarchy and an output for every leaf. Summary nodes are exempt. It computes violations from actual edges and node types.
220 · Evidence before commitment
Three decision windows, a hidden favourable/adverse regime, conditional flight probabilities and one possible survey define a finite belief model. Failed lifts and survey signals update the posterior. Decisions use only that belief and the time remaining. Waiting does not secretly supply information.
Dynamic programming compares commit, wait, winch fallback, decline delivery and buy evidence. The default informative early survey has positive net value and can change the action. An uninformative survey costs money without changing the posterior; evidence arriving after the final window cannot save the decision. The 0.6 threshold policy is evaluated under the same probability and cost rules.
Figures are fictional delivery-decision costs, not the whole £465k refuge budget. Optimality is exact for the declared finite model, not actual operations. Tests independently enumerate complete deterministic policy cost possibilities and compare their minimum with the displayed policy.
How this comparison should evolve
Use the same question, a controlled change and explicit outcomes to reveal the strengths and losses of each view. A useful next case may disconfirm a claim, expose a missing state or method, or show that a simpler baseline does the same job. Keep the nine investigations independent unless a justified translation or composition is itself the research question.
Update the relevant tab when its source experiment, method, assumptions or evidence changes. Preserve useful interaction and explanation when replacing an old implementation. Compare research contribution separately from reader comprehension, and do not claim human learning value from automated checks.
The July 2026 comparison has been superseded here. Its illustrative animations have been replaced by explicit finite models, clear constraints and reproducible links. Private source history remains with the working project; this public page contains only the fictional example and public references.