refactor: make coordinator the main workflow agent

.codex/skills/fesa-formulation-spec/SKILL.md

@@ -13,9 +13,8 @@ Read these first:
 
 - `AGENTS.md`
 - `docs/SOLVER_AGENT_DESIGN.md`
-- `docs/formulations/README.md`
-- `docs/requirements/<feature-id>.md`
-- `docs/research/<feature-id>-research.md`
+- `docs/<feature-id>/requirements.md`
+- `docs/<feature-id>/research.md`
 
 ## Workflow
 
@@ -32,7 +31,7 @@ Read these first:
 
 ## Output Contract
 
-Produce or revise `docs/formulations/<feature-id>-formulation.md` with:
+Produce or revise `docs/<feature-id>/formulation.md` with:
 
 - Scope and Assumptions
 - Primary Variables and DOFs
@@ -63,7 +62,8 @@ Produce or revise `docs/formulations/<feature-id>-formulation.md` with:
 - Shape functions include partition of unity and Kronecker delta checks when applicable.
 - Jacobian, determinant validity, derivative transform, integration rule, and output location are explicit.
 - Missing research or requirements become open issues, not assumptions.
+- The document is `ready-for-numerical-review` only when all derivations, assumptions, output recovery rules, numerical risks, and open issues are explicit.
 
 ## Handoff
 
-Send the formulation to Numerical Review Agent first. After review, pass implementation-relevant pseudocode and acceptance quantities to Implementation Planning Agent, I/O needs to I/O Definition Agent, and benchmarkable checks to Reference Model Agent.
+Return `docs/<feature-id>/formulation.md`, status, evidence summary, blockers, and all review evidence to Numerical Review Agent through Coordinator Agent. Do not bypass the numerical/reference gate with a downstream handoff.