rank

The Rank-Reduction Engine

Input a domain, output its rank.

Use this when the user wants to find the "truly independent generators." Not for ordinary summaries, plain-language rewrites, or scenarios where you only need to list a few key points.

What Rank Is

Rank is not "key elements," not "core principles," not "summary points."

Rank is: how many truly independent generators exist in this domain? Can all phenomena be reverse-generated from them? Only if yes does it count as found.

If the user has not provided a list of phenomena, first supply a set of sufficiently representative phenomena, then begin rank reduction. The supplied list of phenomena must explicitly tell the user that this is a "working list / observational sample," not heaven-sent truth.

The Four Criteria

Only when all four pass does the rank stand. If any one fails, tear it down and start over.

1. Generativity——with the generators, every observed phenomenon can be derived back. Not one may be missed.
2. Minimality——turn off any one generator and some phenomenon can no longer be explained. No redundancy.
3. Independence——for every pair of generators, a real case can be found where one changes and the other does not.
4. Predictive Power——with the generators, phenomena beyond the original list can be derived, and they really do exist in reality.

How to Write It

Write an essay. Not fill out a table.

Your task is to take the reader on a journey: from "this domain looks pretty messy" to "so it was just these two or three threads pulling the strings all along." How that journey goes is up to you. No prescribed chapters, no prescribed format, no prescribed subheadings.

The only requirements are three:

• You want to read it in one sitting——even people who do not know the domain cannot stop
• Memorable——after reading, you can turn around and explain it clearly to a friend in one sentence
• Has contrast——the contrast from chaos to extreme simplicity is the beauty of rank reduction

Verification of the four criteria must be done and woven into the article. Verification itself is part of the narrative——"what would the world look like if one generator were removed" is a good story, and "using the generators to derive an unexpected phenomenon" is a good ending. Do not set up a separate appendix.

After the main text ends, you must give an extremely short conclusion section that clearly states:

• 秩：{N}, or when it cannot hold, write 秩：未定
• 一句话：{可复述的 takeaway}

If any generator fails any one of the four criteria, tear it down and start over. If in the end the four still cannot be satisfied, do not force a conclusion; write 秩：未定, and explain which criterion got stuck. Do not sacrifice verifiability just to compress the domain more beautifully.

Output

1. Read references/template.org。
2. When generating the timestamp, use the command corresponding to the current shell:
   • PowerShell：Get-Date -Format "yyyyMMddTHHmmss" and Get-Date -Format "yyyy-MM-dd ddd HH:mm"
   • POSIX shell：date +%Y%m%dT%H%M%S and date "+%Y-%m-%d %a %H:%M"
3. Make sure the output directory exists:
   • PowerShell：New-Item -ItemType Directory -Force ~/Documents/notes | Out-Null
   • POSIX shell：mkdir -p ~/Documents/notes
4. Write ~/Documents/notes/{时间戳}--{领域}的秩__rank.org
5. If creating the directory or writing the file fails, do not redirect the write to another directory; directly return the complete org-mode content in the conversation and clearly state that saving failed.
6. After saving succeeds, report the file path to the user.

If the user explicitly does not want it written to disk, only return the complete main text and conclusion section, and do not perform the file write.