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"