Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.
EnglishConstruct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.
EnglishGenerate 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, when you need simpler examples that satisfy both assumptions and conclusion, or when you want to see where the assumptions take effect and gain intuition.
EnglishScreen 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. Use when a decomposition plan is created.
EnglishSynthesize the common stuck points across failed decomposition plans and recursive sub-agent reports. Use when the current batch of decomposition plans has failed.
EnglishRetrieve previously saved immediate conclusions, toy examples, counterexamples, failed paths, or branch states from memory. Use when you want to check whether earlier conclusions, examples, counterexamples, failed paths, or brach states can bring insight to the current question, claim, subgoal, or branch decision, or when you want to test a claim against previously saved counterexamples.
EnglishLaunch one sub-agent per decomposition plan after direct screening has identified the key stuck points for each plan. Use when all current plans have been screened by direct proving, none fully solves the problem, and parallel recursive work is needed.
EnglishAggregate all detected errors and gaps into the final verification report, apply strict accept/reject logic, and produce repair hints when rejected.
EnglishVerify candidate proofs with the local proof verification MCP service. Use only when a full candidate proof of the entire problem has been assembled in markdown, and before publishing the final verified blueprint.
English
AGENT SKILLS ATLASIncludes Check Referenced Statements, Construct Counterexamples, Construct Toy Examples, and other workflows.
Claude Code
Codex
Cursor
GitHub Copilot
Gemini CLISupported by the Atlas install prompt. Skill-specific requirements vary.
Pack stats
What’s included
Check Referenced Statements
Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.
Construct Counterexamples
Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.
Construct Toy Examples
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, when you need simpler examples that satisfy both assumptions and conclusion, or when you want to see where the assumptions take effect and gain intuition.
Direct Proving
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. Use when a decomposition plan is created.
Identify Key Failures
Synthesize the common stuck points across failed decomposition plans and recursive sub-agent reports. Use when the current batch of decomposition plans has failed.
Query Memory
Retrieve previously saved immediate conclusions, toy examples, counterexamples, failed paths, or branch states from memory. Use when you want to check whether earlier conclusions, examples, counterexamples, failed paths, or brach states can bring insight to the current question, claim, subgoal, or branch decision, or when you want to test a claim against previously saved counterexamples.
Recursive Proving
Launch one sub-agent per decomposition plan after direct screening has identified the key stuck points for each plan. Use when all current plans have been screened by direct proving, none fully solves the problem, and parallel recursive work is needed.
Synthesize Verification Report
Aggregate all detected errors and gaps into the final verification report, apply strict accept/reject logic, and produce repair hints when rejected.
Verify Proof
Verify candidate proofs with the local proof verification MCP service. Use only when a full candidate proof of the entire problem has been assembled in markdown, and before publishing the final verified blueprint.
Quick start
- Choose your skills. Select individual skills above, or choose the entire pack.
- Copy the install prompt. Use Copy install prompt above the list.
- Send it to your agent. Paste into your coding agent’s chat. Your agent reviews the source and guides the setup.
Try it with your agent
After installation, start with a request like:
Use the Check Referenced Statements skill to help with my task.
Ask me for the context you need before getting started.Requirements & license
- A coding agent that can access your project files and install skills.
- Your agent checks each skill’s instructions, dependencies, and permissions during setup.
- Reported license for the skills shown: Apache-2.0. The author’s terms apply.