Count a rung
Count supported SU(7) bulk contents at selected moment coordinates without having to list every content individually.
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 understand how many discrete matter choices share a moment condition, especially when direct enumeration becomes expensive. A large count can reveal a large family of inputs, but many inputs may share the same potential or fail a later physical check. Compare this page with Same potential? to understand those different notions of sameness.
First steps
- Let the initial table finish, then read the selected gauge seed and coordinate range.
- Move the A₄ probe on the graph and compare counts across the displayed rungs.
- Use the extended range only when you need it; it increases memory use.
- Keep published-seed and candidate-seed counts separate when comparing results.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Gauge seed | Changes the admissible rungs and moment lattice. The candidate case has even rungs and half-integral A₄ coordinates. | Inspect the labels and counts after a seed change rather than reusing a previous row. |
| A₄ graph probe | Chooses a moment coordinate where the counting function is evaluated. | Move between neighbouring displayed points and read the integer counts. |
| Extended range / rebuild | Recomputes the counting table over the chosen range. The extended range is a larger memory task. | First understand a small-range result, then extend it if needed. |
Reading the results
| Result | Meaning |
|---|---|
| Counts by rung | The number of supported nonnegative integer contents satisfying the selected moment conditions. |
| Counting-function graph | Shows how the count changes with the moment coordinate. A large value is a combinatorial multiplicity, not a probability. |
| Archived enumeration comparisons | Specific independent totals against which the counting method has been checked. They do not certify every physical interpretation of a counted input. |
A count records distinct input contents in the stated arithmetic fibre. It does not count physically inequivalent theories or certify acceptable full-potential vacua. Archived enumeration totals validate specific counting cases.
Worked example
See why many inputs can share one coarse description
- Start with the default counting range.
- Select a point with several contributing contents and note its rung and A₄ coordinate.
- Move one coordinate step and compare the count.
- Open Same potential? to see why equality of a few moments is weaker than equality of the full potential.
What to expect: The counts are discrete and coordinate-dependent. They describe an arithmetic fibre, not a histogram of observed particles.
Scope and limitations
- The measured-mass fibre recorded for the published seed is not transferred automatically to the candidate seed.
- Counts do not impose all phenomenological requirements, anomaly completion or full-potential vacuum tests.
- A content count and an equivalence-class count answer different questions.
If something is unclear
The graph changes substantially after switching seed.
Read the new rung and coordinate conventions; the admissible lattice itself has changed.
The extended table is slow or uses substantial memory.
Return to the ordinary range and use a smaller question. A resource limit should not be interpreted as a zero count.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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