Lean gateway
APM-installable agent skills for Lean 4 and Mathlib4 — proof tactics, math domains, review and research workflows, generic tooling.
npx -y skills add r-irbe/proof-skills --skill lean-gatewayAssembled from the repository path, not quoted from the project. Check it against their README if it does not work.
One thing to look at
- 2 stars2 stars. Stars are a popularity signal and not a quality one, but at this level it is likely that nobody has read this closely except its author, and you would be relying on your own review.
What its author says it does
Copied from the file, not written here
USE FOR: routing the top-level entry-point for a complex Lean 4 task; selecting which downstream skill(s) own each phase; preventing context collapse across long sessions; maintaining feedback / feedforward loops; fan-in / fan-out coordination; system-wide health monitoring. DO NOT USE FOR: doing any actual work (always delegate to a domain skill); single-file editing (use @lean-proof or @lean-doc-improvement); script-level enforcement (use @lean-enforcement). TRIGGERS: gateway, orchestrate, route, dispatch, top-level, context collapse, fan-out, fan-in, ecosystem health.
SKILL.md
5.8 KB, as published. Nobody here has run it
lean-gateway
⚠️ MANDATORY (hot-tier): the gateway NEVER does substantive proof or documentation work — every operation is a delegation. Skipping Persist (the global task tracker) = incomplete.
Routing
- USE FOR: receiving a Lean 4 task at session start, decomposing it into phases, routing each phase to the appropriate skill in
REFERENCE.mdPart 1's registry; deciding fan-in vs fan-out vs sequential topology; maintaining the per-task state document; detecting context-collapse signals and prescribing a fresh session. - DO NOT USE FOR: writing a proof (delegate to
@lean-proof); reviewing a proof (delegate to@lean-proof-review); editing docs (delegate to@lean-doc-improvement); running scripts (delegate to@lean-enforcement). - TRIGGERS: gateway, orchestrate, route, dispatch, top-level, context collapse, fan-out, fan-in, ecosystem health.
Behavioural rules (G-*)
- G-1 (MUST NOT): The gateway MUST NOT execute substantive proof, doc, or research work itself; every such operation MUST be a delegation. [Trace: AC-01]
- G-2 (MUST): Each phase MUST be routed to exactly one owning skill from the registry; if no clear owner exists, the gateway MUST escalate per §Recovery & STOP. [Trace: AC-02]
- G-3 (MUST): Fan-out topology (parallel skills) MUST converge through a documented fan-in (a single skill that integrates the results). [Trace: AC-03]
- G-4 (SHOULD): The gateway SHOULD prefer the most specific skill in the registry over a broader one (e.g.
@lean-blueprintover@lean-doc-improvementfor blueprint work). [Trace: AC-04] - G-5 (MUST): On any of the documented context-collapse signals (≥ 2 from
AGENT.md), the gateway MUST recommend a fresh session before continuing. [Trace: AC-05] - G-6 (MUST): The gateway MUST maintain the per-task tracker (phase status, owner, predecessors, successors, sign-offs); a missing tracker entry = a missing delegation. [Trace: AC-06]
- G-7 (SHOULD NOT): The gateway SHOULD NOT silently retry a failed downstream delegation; it MUST escalate per §Recovery & STOP. [Trace: AC-07]
- G-8 (MUST): On any guard failure the skill MUST escalate per §Recovery & STOP. [Trace: AC-08]
Workflow
- Discover [discover] — receive the task, locate prior tracker for this scope (if any), enumerate the candidate skills from the registry.
- Plan [discover] — partition the task into phases; for each phase, pick the owning skill; choose topology (sequential / fan-out / fan-in / hybrid); STOP if confidence < 90 %.
- Delegate [execute] — invoke each phase's owning skill in the chosen order; capture the returned artefact reference + sign-off state.
- Integrate [validate] — when fanning in, confirm every parallel branch returned a sign-off; halt on any unsigned branch.
- Health-check [validate] — sweep for context-collapse signals; recommend a fresh session if ≥ 2 are present.
- Persist [persist] (MANDATORY) — update the per-task tracker (phase status, owner, artefact links, sign-offs); update the ecosystem-health dashboard; tick the global tasks list. Skipping Persist = incomplete.
Recovery & STOP
- No clear owning skill for a phase → STOP, ask which skill to add or extend.
- A downstream skill returns a hard failure → STOP, do NOT silently retry; escalate to that skill's owner.
- Fan-in fails because a parallel branch is unsigned → STOP, complete the missing branch before integrating.
- ≥ 2 context-collapse signals from
AGENT.md→ STOP, recommend a fresh session. - Confidence < 90 % on phase decomposition or topology → STOP, ask.
Handoffs
- Predecessors / successors: see FM
handoffs(grammar from ADR-0080). - Dispatch targets: see FM
dispatch_targetsfor the full set of downstream skills the gateway may delegate to. - Source spec:
specs/lean/gateway/requirements.md— every G-rule traces to an AC there. - Related ADRs: ADR-0076, ADR-0080.
- Reference: see
REFERENCE.mdfor the full skill registry, context-collapse signal list, feedback-loop topology, fan-in/fan-out patterns, health dashboard schema, hierarchy management, enforcement-script orchestration, and ecosystem topology diagram (original v1 content, preserved verbatim).
Common failure modes
AI agents commonly: do the work themselves "to save a delegation"; pick a broad skill when a specific one exists; retry a failed delegation instead of escalating; ignore context-collapse signals; skip the per-task tracker update. Full registry: GUARDRAILS.md §Agent failure taxonomy.