Road × canal
The western and southern boundaries meet at a fixed corner. Their local coordinate accounts already agree.
Fixed by briefA different use of the original brief
The six early Tangled Triangle variants explore how well AI can make sense of interfaces, topology and system architecture. This later essay asks a different question: can declared local constraints compose into a compatible global account? Its checker evaluates those rules, not AI understanding.
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.
First try · Compare two sets of local rules
- Press Balanced. Read 91 global candidates and a best minimum margin of +44 units.
- Press No global fit. Now 0 samples pass. The selected strongest sample, (196, 456), still has a Canal margin of −11 units.
- Press Balanced again to restore the first comparison. Select another dot to inspect its five margins.
Interpretation: all five margins must be non-negative at the same sample. The preset changes several buffers; Canal identifies this selected point’s failure, not the sole cause of the whole result. Zero passing samples is not proof that every point between them is impossible.
Construction, named sources and limits · The separate early AI interpretation enquiry
Compatibility lab
Move the local boundaries
Global candidates—sampled locations satisfying all five rules
Best minimum margin—the tightest rule at the strongest candidate
Selected location—Select a dot on the plan
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.
Rail × road × canal
The viaduct crosses both ground features. Its construction clearance is compared with their usable site envelope.
Checking…Site × power
The overhead corridor restricts candidates on both sides of the line without changing the ground boundary.
Checking…Foundation × mine
The mine account removes a band from the otherwise two-dimensional site view.
Checking…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
- Extract. A language model can propose local objects, boundaries, units and candidate overlaps from briefs and package records.
- Declare. A human makes the cover, translations, tolerances and authority explicit.
- Check. Deterministic code compares the declared local assignments on their overlaps.
- Investigate. A failed patch names the boundary to revisit; it is not silently “resolved” by fluent synthesis.
From source question to this finite check
What is supplied, and what is computed?
The source question
Daniel Rosiak’s Sheaf Theory through Examples is part of the retained reading on local data, restriction to overlaps and gluing compatible sections. Choosing the cover and comparison maps matters; the vocabulary alone does not establish a sheaf.
Named sources, scenario provenance and the full interpretation
The construction here
The code supplies a triangular envelope, five illustrative exclusion rules and 462 sampled locations on a 16-unit grid. For each point it computes five margins and takes their minimum, M(x). A point passes when M(x) ≥ 0; the strongest sample maximises that minimum.
The boundary
The result concerns this grid and these declared rules. It neither proves continuous infeasibility nor establishes the full sheaf condition of unique gluing. Geometry, units and buffers are illustrative; there is no site survey, engineering validation or measured AI performance here.
To compare package disagreements with missing information, continue to Essay 001: Scope coherence.