Representation and Possibility

Problem shape: the difficulty is not in solving but in stating — the symbols, categories, or enumerated options in play are the constraint. Symptoms: a problem that becomes trivial once renamed, a "complete" catalog nobody has bounded, a roadmap whose option space stops at the adjacent, a result that is intuitively obvious and formally unestablished.

Relevant geniuses

Agent	Use when
euler	the current notation or vocabulary obscures the solution — redesign the notation as infrastructure, delete what the abstraction does not need, enumerate exhaustively once the symbols carry their weight
borges	a system claims completeness or exhaustiveness — audit whether the space is actually searchable, keep the map distinct from the territory, detect the self-reference that makes the catalog contain itself
lem	the question is "what could this become?" and the standard forecast is too narrow — explore the possibility space systematically, push each principle to its logical extreme to see what breaks or emerges
archimedes	you need the result before you can prove it — find it by physical intuition, analogy, or simulation, then prove it rigorously by a second, independent method (the two-stage discipline; stage one alone is not a result)

Invocation

1. Pick the best-fit agent above. If two or more fit, run tools/genius-invoker.sh route "<problem>" and take the top ranked match.
2. Load it: tools/genius-invoker.sh invoke <agent> "<problem>", then read agents/genius/<agent>.md in full.
3. Apply the agent's <workflow> step by step and answer in its <output-format>. When archimedes is used, the heuristic stage and the proof stage are reported separately and labeled — an unproven heuristic presented as a result is the failure mode this shape exists to prevent.
4. Typical chain: euler renames until the structure is visible → borges bounds the space the new notation opens → lem pushes the surviving options to their extremes. Run via tools/genius-invoker.sh compose euler borges lem -- "<problem>".
5. If no shape above matches, do not force a genius — use a built-in agent with the closest GENIUS: pattern (rules/agent-routes.json, INDEX.md routing rule).

Refuse when

• The notation is fine and the problem is simply unsolved — renaming as displacement activity.
• The possibility exploration is asked to produce a prediction with a confidence attached: this shape maps what is possible, it does not forecast what is likely. Route probability to estimation or decision-bias-check.
• Only the heuristic stage is wanted and the proof stage is explicitly waived on a claim that will ship as established.