Design a scale
Search for integer bulk contents compatible with a target compactification scale and Higgs-mass window under the displayed SU(7) moment conventions.
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 when you have a desired scale and want to know whether the allowed integer matter choices can reach it. The reachable-set plot explains why a continuous target slider does not imply a continuous family of available theories. Some gaps can be certified arithmetically; other searches end because their computational budget is exhausted.
First steps
- Choose the gauge seed and enter the target scale and Higgs-mass window in the displayed units.
- Run the design search or inspect a rung separately.
- Read the named outcome and its assumptions. A budget stop leaves the question undecided.
- Load a returned content into the model and check its full potential in Hierarchy before using it.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Target 1/R₅ and Higgs-mass window | Define the requested region in the displayed scale and mass units. These are design assumptions; entering them does not turn them into experimental constraints. | Start from the prefilled target, then make a small change and compare the selected lattice points. |
| Rung buttons and lattice-point probe | Restrict the arithmetic problem to one rung or point so you can inspect its obstruction or construction. | Compare a successful point with a neighbouring refused point. |
| Require W > 0 | Applies the named preliminary screen before the full potential is asked. Passing this screen does not certify a global minimum. | Read the screen explanation before enabling it in a search. |
| Design and Load into the model | Run the bounded search, then transfer a returned content into the laboratory's SU(7) model. | Keep the search outcome and inspect the transferred content in Hierarchy. |
Reading the results
| Result | Meaning |
|---|---|
| Reachable-set clusters | Resolve a cluster into individual allowed points before interpreting its width as a continuous interval. |
| floor, cone, congruence, dual or exhaustion | Different reasons the specified arithmetic problem has no solution: a lower bound, a cone restriction, a modular condition, a separating rational certificate, or completed enumeration. Read the accompanying certificate. |
| budget | The permitted work ended before the question was decided. This is an incomplete search outcome. |
The search works on an arithmetic reduction of the model. An impossibility certificate is limited to the problem it states; a found content still needs its potential and vacuum checked. A stopped search supplies neither existence nor impossibility.
Worked example
Follow a design through to a physical calculation
- Run the prefilled design problem.
- If a content is returned, save its input values and use Load into the model.
- Open Hierarchy with the same seed and compare the approximate and full-potential outputs.
- If the search instead stops, read whether it supplied a certificate or only a budget message.
What to expect: The search and the potential check answer successive questions. A lattice solution alone is not a certificate of a physically viable model.
Scope and limitations
- Bounds and impossibility statements inherit the seed, mass window, coupling convention and arithmetic reduction used by the search.
- A positive preliminary screen does not establish a global vacuum or agreement with experimental data.
- The reachable set shown is for the stated search problem; changing the model family requires a new problem.
If something is unclear
The target lies between displayed points.
Expand the cluster into its individual points and inspect the certified gap before increasing a search budget.
The search reports budget.
Reduce the requested region or use the rung/point controls to isolate the question. Keep the result labelled undecided.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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