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Derive immediate mathematical consequences from a theorem statement or subgoal. Use when starting a new problem, branch, or subgoal, or when cheap progress or a cleaner reformulation is needed before deeper proof search.
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SOC 職業分類に基づく
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.
Find relevant math results, constructions, examples, counterexamples, and background references for a statement. Use when you need context for a new problem, supporting references for constructing examples or counterexamples, or external results while proving subgoals.
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.
Verify a markdown proof in the order it is written. Use when the task is to check local correctness, theorem applicability, and reasoning gaps statement by statement through a paper-style proof.
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.
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.
| name | obtain-immediate-conclusions |
| description | Derive immediate mathematical consequences from a theorem statement or subgoal. Use when starting a new problem, branch, or subgoal, or when cheap progress or a cleaner reformulation is needed before deeper proof search. |
Extract direct implications before speculative reasoning.
Read from memory and current context:
problem_id$construct-counterexamples should be considered next.Append each conclusion to immediate_conclusions with JSON object payload:
{
"statement": "...",
"justification_type": "by_definition|calculation|known_fact|logical_equivalence",
"confidence": 0.0,
"is_fragile": false,
"fragility_reason": "",
"suggested_followup": "none|construct-counterexamples",
"scope": "global|branch|subgoal",
"branch_id": "optional",
"subgoal_id": "optional"
}
Rules:
is_fragile must always be present.is_fragile=true, then fragility_reason must explain the risk and suggested_followup should be construct-counterexamples.is_fragile=false, use fragility_reason="" and suggested_followup="none".memory_appendmemory_searchsearch_arxiv_theorems for nontrivial consequencesIf no meaningful consequence is found, append an events entry with:
event_type="immediate_conclusions_stalled"