Immutable. This exact content is served forever at /api/v1/blob/d7c1a4ee6b9c5bca.
--- name: representation-and-possibility description: > When the notation is the obstacle and the option space was never enumerated. Use when the current vocabulary hides the solution, when a system claims to be exhaustive but nobody checked whether the space is searchable, when a forecast is too narrow because no one pushed the principle to its limit, or when you need the answer now and the proof afterwards. --- # 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](../../agents/genius/euler.md) | 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](../../agents/genius/borges.md) | 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](../../agents/genius/lem.md) | 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](../../agents/genius/archimedes.md) | 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 standard team agent (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.