sci-council

name

sci-council

description

Three-persona mathematical research fan-out. Asks Gauss (algebraic / number-theoretic), Erdős (probabilistic / extremal), and Tao (harmonic / arithmetic-combinatorics) the same problem independently in parallel, then synthesises their 3×3 proposals into one ranked table with cross-persona consensus flags and composite scores. Use when a hard math problem needs breadth — stuck competitions, Einstein Arena openings, a new research question where a single frame is likely to miss something. Triggers "research council", "ask the council", "mathematician council", "3 personas", "gauss erdos tao", "fan out personas", "research fan-out". Does NOT trigger for literature search (use sci-literature-research) or single-author scientific writing (use sci-writing).

sci-council — 3-persona research fan-out

When to use

You have a hard math / optimisation problem where one frame is likely to miss the winning idea. Examples:

• Einstein Arena opening sessions where you haven't committed to an approach yet.
• A plateau on an active campaign where a fresh frame might surface a non-local move.
• Research-grade "how do I even think about this" questions.

Skip when:

• The problem is already well-routed (a specific arena submission polish — use sci-optimization or ops-ulp-polish instead).
• You need a literature search, not a research plan (use sci-literature-research).
• You're drafting prose, not proposing methods (use sci-writing).

Methodology

1. Fan out — spawn three persona sub-agents (Gauss / Erdős / Tao) in parallel with the same problem statement. Personas do not see each other's drafts.
2. Each persona returns exactly 3 ranked approaches using the schema in references/synthesis-protocol.md (approaches, dead ends, confidence).
3. Synthesise — union the 9 approaches, deduplicate by semantic equivalence, score by mean(P(BEAT)) / EFFORT_PENALTY[median_effort], rank descending, flag consensus (1/3, 2/3, 3/3).
4. Return one markdown synthesis: ranked table + dead ends consensus + dissenting views + council confidence.

Personas are opinionated by design (see references/personas.md). Do not blend them during the fan-out — adversarial diversity is the whole point.

API

from council import run_council, synthesize_responses, CouncilAllFailedError

# Fan-out + synthesis (happy path — 3 personas, default)
result = run_council("maximise the number of unit-distance pairs on n points in R^2")

# Custom persona list (e.g. add a sphere-packing specialist)
result = run_council(problem, personas=["Gauss", "Erdős", "Tao"], timeout_sec=120)

# Synthesis only (when you already have persona responses from elsewhere)
responses = {"Gauss": gauss_text, "Erdős": erdos_text, "Tao": tao_text}
result = synthesize_responses(responses)

Failure modes:

• ValueError — empty problem statement.
• CouncilAllFailedError — all personas failed or timed out.
• 1 or 2 persona failures are tolerated; the synthesis header is annotated with the degraded state ([WARNING: Erdős unavailable — 2/3 perspectives]).

Dependencies

Dependency	Required	Provides	Fallback
Python 3.10+	Yes	stdlib concurrent.futures, dataclasses, re	None
pytest	Dev-only	Test runner for tests/test_council.py	unittest

No external API keys. When wired into the Agent tool for real persona invocations, each persona call goes through the caller's configured LLM provider — _call_persona(persona_name, problem_statement) is the single monkey-patch point for testing and for swapping backends.

References

• references/personas.md — full Gauss / Erdős / Tao profiles + "when they activate" pattern triggers.
• references/synthesis-protocol.md — output schema, synthesis algorithm, dedup calibration, output format, failure handling.

Tests

python3 -m pytest .claude/skills/sci-council/tests/test_council.py -v

12 unit tests covering happy path, parallelism (max(t_i) not sum(t_i)), single-persona failure, all-fail → CouncilAllFailedError, duplicate approach dedup, no-consensus 9-row output, empty problem validation, persona override, deterministic synthesis, per-persona timeout, and parse_persona_response happy + malformed paths. All GREEN.

Triggers

Use when: "research council", "ask the council", "mathematician council", "3 personas", "gauss erdos tao", "gauss erdős tao", "fan out personas", "research fan-out", "council on", "persona fan-out".

Do NOT use for: literature search (use sci-literature-research), single-author scientific writing (use sci-writing), data analysis (use sci-data-analysis), one-liner optimisation queries.