Essay 03 · worked scenario

The Tangled Triangle

Five local constraint views describe the same difficult site. Do they leave any locations that can exist in the global project account—or do their overlaps reveal an obstruction?

A different use of the original brief

The source scenario asks for a project and system architecture for a regional signalling control centre on a triangular site: canal to the south, road to the west, railway on a viaduct, an overhead high-voltage line and an old mine passage below. Here the aim is narrower. Each specialist supplies one local exclusion rule. The checker asks whether those rules can be patched into a candidate global location.

Model status: a finite, sheaf-shaped compatibility toy. It is not a full sheaf construction, site survey, design or safety assessment. Diagram units and clearances are illustrative.

Compatibility lab

Move the local boundaries

Global candidatessampled locations satisfying all five rules
Best minimum marginthe tightest rule at the strongest candidate
Selected locationSelect a dot on the plan
Tangled Triangle candidate compatibility plan A triangular site with road, canal, railway, power line and mine constraints. Dots show sampled candidate locations; filled circles satisfy all local rules.
compatiblenear obstructionblockedsubsurface

What is actually being patched?

Local views and their overlaps

The important modelling move is not to call a WBS a sheaf. It is to choose meaningful local views, say where they overlap, and define what agreement means there.

01 · Ground boundary

Road × canal

The western and southern boundaries meet at a fixed corner. Their local coordinate accounts already agree.

Fixed by brief
02 · Transport structure

Rail × road × canal

The viaduct crosses both ground features. Its construction clearance is compared with their usable site envelope.

Checking…
03 · Airspace

Site × power

The overhead corridor restricts candidates on both sides of the line without changing the ground boundary.

Checking…
04 · Subsurface

Foundation × mine

The mine account removes a band from the otherwise two-dimensional site view.

Checking…
05 · Global section

All five local views

A candidate survives only when every restriction returns a non-negative margin at the same location.

Checking…

Method boundary

Let the model propose; let the checker judge

  1. Extract. A language model can propose local objects, boundaries, units and candidate overlaps from briefs and package records.
  2. Declare. A human makes the cover, translations, tolerances and authority explicit.
  3. Check. Deterministic code compares the declared local assignments on their overlaps.
  4. Investigate. A failed patch names the boundary to revisit; it is not silently “resolved” by fluent synthesis.