Name the relations
Which equivalence relation on boundary conditions the literature already owns, and whether a proposed move set connects a class.
Control names are kept as they appear in the application. Start with a reference, change one input at a time, and retain the assumptions with your result.
What this tool is for
Use this to identify the existing mathematics behind a boundary-condition relation and test a proposed rewrite. A valid individual move must preserve the required data. A set of valid moves can still be incomplete if it leaves a class split into disconnected pieces.
First steps
- Pick an orbifold and a move.
- Read the attribution: whose relation this is and where.
- Run the walk to see whether the moves actually connect the class.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Orbifold, group and N | Choose the configuration whose relations are being inspected. | Start with a supplied small case. |
| Proposed relation and Judge it | Checks the entered move against the stated preserved data. | Read exactly which condition is tested before interpreting a successful verdict. |
| Walk a class | Explores reachability under the selected moves in the tested finite case. | Compare the number reached with the size of the class. |
Reading the results
| Result | Meaning |
|---|---|
| Attribution | Names the existing configuration, relation or result and its source. A known mathematical identification should retain that credit. |
| Move validity | Reports whether the specified rewrite preserves the tested data. |
| Connectivity and structural diagnostics | Separate finite-class reachability from broader claims about generating relations or complete intersections. |
The local/global distinction is the one that gets misquoted, and the page carries it explicitly.
Worked example
Distinguish a valid move from a complete move set
- Choose a supplied small configuration.
- Inspect a proposed relation and its preserved data.
- Run the class walk with the selected moves.
- Compare the reached component with the full class size and read the attribution.
What to expect: A move can be legitimate while its move set fails to reach the entire tested class.
Scope and limitations
- A finite connectivity experiment does not prove completeness at every rank.
- Local and global equivalence statements must retain their different hypotheses.
- A relation already identified in the literature should not be presented as a new discovery of the laboratory.
If something is unclear
A move is rejected.
Read which datum it changes; increasing the walk budget cannot repair a move that violates the required invariant.
A valid move set reaches only part of a class.
Keep the incompleteness result for that case and inspect which additional relations are needed.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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