commit e7f7873fa8d81833c0f97dfd8e2e2b2dc3166696 Author: Yu Cong Date: Thu Mar 26 10:32:29 2026 +0800 first commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..d89697e --- /dev/null +++ b/.gitignore @@ -0,0 +1,314 @@ +_*/ + +.ds_store +.vscode/ +*.sage.py +*.pdf +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Generated if empty string is given at "Please type another file name for output:" +.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bbl-SAVE-ERROR +*.bcf +*.bcf-SAVE-ERROR +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync +*.rubbercache +rubber.cache + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs +*.lzo +*.lzs +*.slg +*.slo +*.sls + +# uncomment this for glossaries-extra (will ignore makeindex's style files!) +# *.ist + +# gnuplot +*.gnuplot +*.table + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.glog +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hypdoc +*.hd + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files +# *.tikz +*-tikzDictionary + +# listings +*.lol + +# luatexja-ruby +*.ltjruby + +# makeidx +*.idx +*.ilg +*.ind + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# newpax +*.newpax + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# svg +svg-inkscape/ + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# titletoc +*.ptc + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices and outlines +*.xyc +*.xyd + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# gummi +.*.swp + +# KBibTeX +*~[0-9]* + +# TeXnicCenter +*.tps + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + +# Makeindex log files +*.lpz + +# xwatermark package +*.xwm + +# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib +# option is specified. Footnotes are the stored in a file with suffix Notes.bib. +# Uncomment the next line to have this generated file ignored. +#*Notes.bib \ No newline at end of file diff --git a/AGENT.md b/AGENT.md new file mode 100644 index 0000000..7d89aa5 --- /dev/null +++ b/AGENT.md @@ -0,0 +1,16 @@ +You will be solving an extremely challenging mathematics question. The answer may not be known to anyone. + +Feel free to think out loud as much as you want. You also have a MacOS environment and some tools available to help you. + +Tips for solving: +* **Try your hardest to answer it.** Even if it seems impossible, spend some time thinking about it before giving up. +* **Create a plan.** I strongly recommend that you start by making a high-level plan for how you will tackle the problem. Revise your plan along the way if necessary. + +Ideas to try if you get stuck: +* Think about other, similar problems. +* Try first solving a simpler version of the problem. +* Pursue lines of investigation that might not seem like they will end up helping. +* Brainstorm new approaches and try each of them. + +Tips for writing: in markdown use `#` for sections and `##` for subsections. Write title in yaml section. + diff --git a/math-macros.md b/math-macros.md new file mode 100644 index 0000000..9b03263 --- /dev/null +++ b/math-macros.md @@ -0,0 +1,19 @@ +\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} +\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil} +\newcommand{\set}[1]{\left\{ #1 \right\}} +\newcommand{\norm}[1]{\left\| #1 \right\|} +\newcommand{\rm}[1]{\operatorname{#1}} + +\newcommand{\F}{\mathbb{F}} +\newcommand{\R}{\mathbb{R}} +\newcommand{\C}{\mathbb{C}} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\e}{\varepsilon} + +\newcommand{\mex}{\operatorname{mex}} +\newcommand{\lcm}{\operatorname{lcm}} +\newcommand{\dist}{\operatorname{dist}} +\newcommand{\poly}{\operatorname{poly}} +\newcommand{\polylog}{\operatorname{polylog}} +\newcommand{\span}{\operatorname{span}} \ No newline at end of file diff --git a/notes/main.md b/notes/main.md new file mode 100644 index 0000000..e69de29 diff --git a/paper-review.md b/paper-review.md new file mode 100644 index 0000000..263bc7f --- /dev/null +++ b/paper-review.md @@ -0,0 +1,68 @@ +``` +Act as a professional mathematician and journal referee in combinatorics/matroid theory. Review this paper draft carefully and critically. Your goal is to improve the paper’s exposition, intuition, and correctness. + +Read the entire draft, not just isolated local passages. Evaluate it as a serious research paper, not as lecture notes. + +Focus on three things: + +1. Correctness +- Check every theorem statement, proof strategy, and reduction for logical soundness. +- Identify false statements, hidden assumptions, unsupported inferences, ambiguous quantifiers, missing hypotheses, and places where a proof only sketches an argument but does not actually prove the claim. +- If a step looks suspicious but you are not fully sure it is wrong, say exactly that and isolate the first place where the proof stops being convincing. +- Distinguish clearly between: + - definitely incorrect, + - likely incorrect / unsupported, + - probably correct but poorly explained. + +2. Exposition +- Judge whether the paper is readable by a professional mathematician outside the immediate subsubarea. +- Flag notation overload, repeated definitions, unclear theorem statements, badly placed lemmas, poor section order, and proofs that mix setup, bookkeeping, and ideas in a confusing way. +- Pay special attention to whether lemmas are self-contained, whether they use standard notation, and whether proof-local notation is introduced too early or too heavily. +- Point out places where a result should be split into separate lemmas, and places where the paper introduces unnecessary lemmas instead of giving a short direct proof. + +3. Intuition +- Identify places where the paper needs more explanation of why a definition is natural, why a theorem should be expected, or what the proof is trying to do. +- Flag sections where the paper becomes technically correct but conceptually opaque. +- Suggest where a short roadmap paragraph, example, or conceptual remark would make the biggest difference. +- Explain what the “main idea” of each major proof seems to be, and say when that idea is currently buried. + +Reviewing standards: +- Do not praise generically. +- Be direct, concrete, and technically precise. +- Quote specific statements, notation, or proof steps when useful. +- Refer to exact section / theorem / lemma names or line ranges when possible. +- Prefer high-signal comments over broad vague advice. +- Do not rewrite the whole paper; focus on the most important improvements. + +Output format: + +A. Major correctness findings +- List the most serious mathematical issues first. +- For each one: + - location, + - problem, + - why it is a problem, + - what would be needed to fix it. + +B. Major exposition findings +- List the most serious writing/structure issues. +- Focus on theorem statements, proof organization, notation, and section flow. + +C. Missing intuition +- List the main places where the paper needs motivation, conceptual framing, or examples. + +D. Section-by-section brief assessment +For each major section, give: +- what the section is trying to do, +- whether it succeeds, +- what its biggest weakness is. + +E. Top revision priorities +- Give the 5 to 10 highest-value changes that would most improve the paper. + +Important: +- If a theorem appears correct but the proof is not publication-ready, say so explicitly. +- If a lemma should be self-contained but is not, point that out. +- If notation is repeatedly redefined or recalled unnecessarily, point that out. +- If a proof should be split into a structural lemma and a bookkeeping lemma, say that explicitly. +``` \ No newline at end of file diff --git a/proof-review.md b/proof-review.md new file mode 100644 index 0000000..3807673 --- /dev/null +++ b/proof-review.md @@ -0,0 +1,41 @@ +Be concise but rigorous. Do not invent objections. Only report an issue if you can explain exactly why the step fails or is insufficiently justified. +Act as a careful mathematical referee. Review the proof below for correctness, not for style. + +Your task: +- Find actual logical gaps, unjustified inferences, hidden assumptions, undefined objects, notation conflicts, or uses of results stronger than what was stated. +- Be skeptical and precise. +- Do not give a general summary first. + +Instructions: +1. Read the input line by line. +2. List findings first, ordered by severity. +3. For each finding, include: + - the exact step or sentence, + - why it does not follow, + - whether it is a fatal gap or a fixable omission, + - what additional argument, lemma, or hypothesis would fix it. +4. Distinguish clearly among: + - Fatal gap + - Fixable omission + - Notation problem + - Exposition issue only +5. Check specifically: + - whether every object is well-defined, + - whether quantifiers are correct, + - whether induction hypotheses are applied legally, + - whether extremal choices are justified, + - whether cited theorems are used in a form strong enough for the conclusion, + - whether any notation changes meaning during the proof. +6. If a step is correct but nontrivial, say what theorem or standard fact is being used there. +7. If you do not find a logical gap, say exactly: + “I do not see a logical gap.” + Then list all nontrivial dependencies and any places where the exposition could mislead a reader. + +Output format: +- Findings +- Nontrivial dependencies +- Minor issues +- Verdict + +Input: +[paste proof] \ No newline at end of file diff --git a/reference.bib b/reference.bib new file mode 100644 index 0000000..e69de29