Purpose

Coordinate the full mathematical modeling contest workflow from problem intake to final QA.

This skill is a gate-driven scheduler, not a stage-sequential scheduler. The difference matters: a stage scheduler answers "what stage are we in, what's the next stage?" — which lets work advance even when the current stage's outputs are unreliable. A gate-driven scheduler answers "does the current stage's gate pass — and if not, what's the fallback?" — which prevents drift from propagating downstream.

This skill does not solve models, write code, generate figures, or draft paper sections directly. Its role is to inspect the current project state across ALL subquestions, track per-question progress through a defined state machine, identify missing or blocked artifacts, evaluate each workflow gate against its enter_condition / pass_criteria / fail_fallback contract, route to the independent audit layer (consistency-auditor + completeness-auditor + quality-assurance-auditor) before final assembly, and decide the next appropriate skill to use.

This skill is the single source of truth for "what should we do next?"

Session-Start Environment Ping (MUST run first in any new session)

Before doing any orchestration work in a fresh session, ping the environment so downstream skills don't fail with surprises:

1. Working tree status: git status --short. If dirty (uncommitted changes, untracked files), surface the dirty files to the user before proceeding. Dirty working tree from a collaborator's in-progress work is the most common "git status looks weird" cause — flag it; do not silently work around it.
2. Python availability: python --version (or python3 --version). Flag if missing or wrong version.
3. MATLAB / 北太天元 availability: only when any Qx targets MATLAB. Check with which matlab or command -v matlab; if missing, report "MATLAB not in PATH — confirm 北太天元 will be used or switch implementation target to Python".
4. Required scientific packages (only when Python is the target): python -c "import numpy, pandas, matplotlib" — flag missing packages.
5. Workspace skeleton: verify planning/, methods/, code/, results/, robustness/, paper/, workspace/data_raw/ exist (or create them with a single mkdir -p if the user just initialized the project).