Problem Rule Generation based on Claude

[zazabap]

In .claude, we could design skill to automatically generating N rules and problems. Moreover, the new rules and models should better match the metrics considering the impact, which could be quantified by following standard:

0. Academia Publications: Quantification on the impact could be the number of papers in top journal like Journal of the ACM, SIAM Journal of Computing and famous textbook. How many papers study the specific problem/reduction rule?
1. . Industrial Application: In different industrial domains like Autocomplete in google search or VScode, Dijkstra in the Navigation for google map, Sequencing and Sliding window etc. By number of application scenarios, the impact should be high.
2. . Cross-Field Application: Some problem model which has potential to solve key problems in Condensed Matter Physics (since our group care) or Quantum Chemistry, the one applied in areas scientists care about should be considered.
3. . Top-Scientists: Whether the problems are top tier or planned in the list like Karp21, Scott Aaronson or other top computer scientist also interested in quantum computing and complexity theory.

Convention when adding new rule:

0. The new problems and rules added to the repository issue should follow the conventions of existing rule and model template. No repeated rules or problems should be mentioned in the issue list.
1. The addition should based on the interests of user. This should be a questionnaire or survey related to the above quantification. (Like rank the importance of the 0-1-2-3)

The skill should be a step by step guidance including, survey, search, rank, modification, evaluation and final file.

[zazabap]

After manually run the skill I found several issues related to the implementation.

1. The survey in the beginning give repeated options, please fix this when trying to select the options, Most important from 6 , second most important from 5 options, third most important from 4 options in such order.
2. Step 2 should first identify the (1) existing implemented lists and (2) already mentioned problem reduction rule in the issue lists. These should be excluded from new added problems and reduction rules.
3. The Final candidate rule should all be nontrivial, this is also shown in the previous issue here, [Contribution] 10 Reduction Rules  #127 Consider file rules over the models. If models exist but rule does not exist, file rule first. If both do not exist, file all of them.
4. The number of issues filed do not limited by 10, could be more than 10 but less than 20. If more than 10, it would be difficult and take to much time.
5. For filing the issue automatically, it might be better to use subagent to run add-issue-model and add-issue-rule SKILL.md file issues following the template. Double check the model or rule does not exist in the repo. May further define the format there for the example and the algorithm correctness.

[zazabap]

Notice the add-issue-model and add-issue-rule do not follow the template, modify.

[zazabap]

The filed issues should be the set for {filed-open} + {implemented}, new issues should exclude from this set. Format of the equation use latex for review purpose.