Prioritize Assumptions
phuryn/pm-skills
Prioritize assumptions using an Impact × Risk matrix and suggest experiments for each.
Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal.
Apache-2.0Auto-check passed
Install Construct Toy Examples
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install frenzymath/Danus construct-toy-examples --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .claude/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .claude/skills/construct-toy-examples && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .claude/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examplesType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install frenzymath/Danus construct-toy-examples --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .agents/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .agents/skills/construct-toy-examples && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .agents/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install frenzymath/Danus construct-toy-examples --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .cursor/skills/construct-toy-examples && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .cursor/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/frenzymath/Danus.git --path agents/skills/worker/construct-toy-examples--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install frenzymath/Danus construct-toy-examples --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .gemini/skills/construct-toy-examples && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .gemini/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install frenzymath/Danus construct-toy-examplesInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .github/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .github/skills/construct-toy-examples && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .github/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add frenzymath/Danus --skill construct-toy-examples -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install frenzymath/Danus construct-toy-examples --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/frenzymath/Danus.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/agents/skills/worker/construct-toy-examples .opencode/skills/construct-toy-examples && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "construct-toy-examples" agent skill from https://github.com/frenzymath/Danus/tree/codex/agents/skills/worker/construct-toy-examples into .opencode/skills/construct-toy-examples/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "construct-toy-examples", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
Facts
- Skill name
construct-toy-examples- GitHub stars
- 475
- Token cost
- ~541 tokens
- SKILL.md length
- 199 words
- Files
- 2
- Skills in repo
- 16
- Repo updated
- First seen
- Licence
- Apache-2.0
At a glance
Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal.
- Works in 6 steps: Construct simpler cases (low degree,… → Ensure the toy example satisfies all… → Check that the conclusion also holds in… → …
- You are stuck in reasoning and need simpler examples to regain traction
- SKILL.md covers Input Contract, Procedure, Output Contract and Tools, plus 1 more section
- Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md
What it does
Construct Toy Examples is an agent skill from frenzymath/Danus. Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal. Use when you are stuck in reasoning and need simpler examples to regain traction, or when you want to see where the assumptions take effect and gain intuition.
Its SKILL.md is about 540 tokens, which your agent loads only when the skill is triggered. The skill folder holds 2 other files (for example `agents/openai.yaml`).
The repository describes itself as: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory. The licence is Apache-2.0.
When your agent uses it
- You are stuck in reasoning and need simpler examples to regain traction
- You want to see where the assumptions take effect and gain intuition
Example prompts
- “/construct-toy-examples”
Workflow steps
6 steps, taken from the first numbered list in SKILL.md.
- Construct simpler cases (low degree, small dimension, special forms, canonical objects).
- Ensure the toy example satisfies all assumptions of the target statement or subgoal.
- Check that the conclusion also holds in the toy example.
- Study where each assumption takes effect and what mechanism makes the conclusion true.
- Identify repeated patterns, invariants, or proof ideas suggested by the example.
- Use search/reasoning/decomposition as needed to find examples or simplify the situation.
What it can do on your machine
Read from SKILL.md and the folder at commit 6d92e8d. It shows what the files ask for, not the result of running them.
Tool permissions
Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.
From allowed-tools in the SKILL.md frontmatter.
Runs code
No scripts in the folder and no shell commands in SKILL.md (its code samples are json).
From the folder's file list and the shell code blocks in SKILL.md.
Network
No URLs in SKILL.md.
From URLs in SKILL.md, links to its own repository left out.
Credentials
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Context cost
Construct Toy Examples loads about 541 tokens when it runs. Until then it costs about 77 tokens; SKILL.md has 199 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
Safety
Auto-check passed
The automated check found no risky patterns in SKILL.md.
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
SKILL.md
The full file from frenzymath/Danus at commit 6d92e8d, republished under its Apache-2.0 licence (© frenzymath). 199 words, ~541 tokens.
Download SKILL.mdSave it as
.claude/skills/construct-toy-examples/SKILL.md (or your agent's skills folder). This skill also uses 1 other file; get the full folder from GitHub.- name
- construct-toy-examples
- description
- Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal. Use when you are stuck in reasoning and need simpler examples to regain traction, or when you want to see where the assumptions take effect and gain intuition.
Construct Toy Examples
Use this skill when the agent is stuck in reasoning and needs simpler examples that satisfy both the assumptions and the conclusion in order to understand why the statement works.
Input Contract
Read:
- current statement/subgoal
- relevant
immediate_conclusions - relevant
counterexamplesand failed branch notes - relevant background/results when available
Procedure
- Construct simpler cases (low degree, small dimension, special forms, canonical objects).
- Ensure the toy example satisfies all assumptions of the target statement or subgoal.
- Check that the conclusion also holds in the toy example.
- Study where each assumption takes effect and what mechanism makes the conclusion true.
- Identify repeated patterns, invariants, or proof ideas suggested by the example.
- Use search/reasoning/decomposition as needed to find examples or simplify the situation.
Output Contract
Publish each toy example to global memory with gm_add (kind example):
claim = what the example shows, evidence = the construction, plus these fields:
{
"example": "...",
"why_relevant": "...",
"assumptions_satisfied": ["..."],
"conclusion_verified": true,
"where_assumptions_take_effect": "...",
"observed_pattern": "...",
"supports_branch_ids": ["optional"],
"subgoal_id": "optional"
}Tools
gm_add(publish the example finding)gm_search(recall related findings)search_arxiv_theoremsfor matching examples/known motifs- Codex built-in web search for known example families and standard constructions
- use
$search-math-resultswhen broader retrieval is needed
Failure Logging
If generated examples are inconclusive, append an events record:
event_type="toy_examples_inconclusive"- include attempted example families
© frenzymath, Apache-2.0. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
Files
SKILL.md and 1 other file in agents/skills/worker/construct-toy-examples of frenzymath/Danus.
- SKILL.md
- agents/openai.yaml
Open the folder on GitHubat commit 6d92e8d
Compare with similar skills
Construct Toy Examples next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Construct Toy Examples this skillfrenzymath/Danus | 475 | — | ~541 | Automated safety check: Pass | Apache-2.0 | |
| Prioritize Assumptionsphuryn/pm-skills | 27k | — | ~571 | Automated safety check: Pass | MIT | |
| Nexrad Mosaic Constructionsickn33/agentic-awesome-skills | 47k | 1 repos | ~3.1k | Automated safety check: Pass | MIT | |
| Agent Harness Constructionaffaan-m/ECC | 275k | 2 repos | ~222 | Automated safety check: Pass | MIT | |
| Agent Harness Constructionaffaan-m/ECC | 275k | — | ~297 | Automated safety check: Pass | MIT | |
| Identify Assumptions Existingphuryn/pm-skills | 27k | — | ~525 | Automated safety check: Pass | MIT |
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More from frenzymath/Danus
All 16 skills in this repoCheck Referenced Statements
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Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second.
Construct Counterexamples
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Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail.
Direct Proving
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Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through.
Identify Key Failures
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Obtain Immediate Conclusions
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Questions about Construct Toy Examples
What does Construct Toy Examples do?
Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal. Construct Toy Examples is an agent skill from frenzymath/Danus. Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal.
When should I use Construct Toy Examples?
Construct Toy Examples fits situations like: you are stuck in reasoning and need simpler examples to regain traction; you want to see where the assumptions take effect and gain intuition.
How do I install Construct Toy Examples in Claude Code?
Run `npx skills add frenzymath/Danus --skill construct-toy-examples -a claude-code`. Or copy the skill folder (agents/skills/worker/construct-toy-examples in frenzymath/Danus) into .claude/skills/construct-toy-examples in your project. Claude Code loads it when a task matches its description.
How do I install Construct Toy Examples in Codex?
Run `npx skills add frenzymath/Danus --skill construct-toy-examples -a codex`. Or copy the skill folder (agents/skills/worker/construct-toy-examples in frenzymath/Danus) into .agents/skills/construct-toy-examples in your project. Codex loads it when a task matches its description.
Can I use Construct Toy Examples in Cursor, Gemini CLI or GitHub Copilot?
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add frenzymath/Danus --skill construct-toy-examples -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/construct-toy-examples, .gemini/skills/construct-toy-examples, .github/skills/construct-toy-examples and .opencode/skills/construct-toy-examples in your project.
What does Construct Toy Examples need to run?
SKILL.md names no scripts, command-line tools or credentials: Construct Toy Examples is instructions for the agent only.
Does Construct Toy Examples access the network?
SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.
Is Construct Toy Examples safe to install?
Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.
What licence does Construct Toy Examples use?
Construct Toy Examples is published under the Apache-2.0 licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
How many tokens does Construct Toy Examples use?
About 541 tokens (SKILL.md is roughly 2.2k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.
What are the alternatives to Construct Toy Examples?
Skills that share tags, products or a category with Construct Toy Examples: Prioritize Assumptions (phuryn/pm-skills, 27k stars), Nexrad Mosaic Construction (sickn33/agentic-awesome-skills, 47k stars), Agent Harness Construction (affaan-m/ECC, 275k stars) and Agent Harness Construction (affaan-m/ECC, 275k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
Who maintains Construct Toy Examples?
frenzymath (a GitHub organization) maintains it in frenzymath/Danus, which has 475 GitHub stars. The repository holds 16 skills in this directory. The repository was last updated on August 27, 2026.
Source: frenzymath/Danus on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.