Optimal Control · Recursive (Econstellar v5)
turnpike
Turnpike + Saddle — Hamiltonian steady state (FRONTIERS V.2 · T3). Locates the interior turnpike (the activity-minimising adjustment speed) of the continuous-time Hamiltonian control problem, confirms it coincides with FRONTIERS V.1's static interior optimum (a convergence invariant — if the dynamic turnpike drifts from the static optimum the operator flags it), and reports the (state, costate) Jacobian eigenvalues that make the steady state a saddle (opposite-sign, one-dimensional stable manifold = the optimal path). Also maps the turnpike against the cascade-vs-activity cost ratio (monotone). Reproduces FRONTIERS V.2 Theorem 3: turnpike eta-bar = 0.9675, Jacobian eigenvalues -0.015 and +0.066. Bounded (n=26 fixture, sub-second). Gate: the turnpike and saddle are STRONG.
Identity
version 1.0.0 · capability control · min_obs 0 · runner r (turnpike.R)
Primitives
—
Composes with
not yet a catalog field — operator-composition metadata lands with Pathway F; nothing is invented here.
Parameters
| name | type | req | values / range |
|---|
| no parameters |
Returns
method,theorem,n,beta,eta_bar,trace_min,v1_interior_optimum,turnpike_matches_v1,ell_pp,rho_c,jacobian_eigs,is_saddle,stable_manifold_dim,cost_ratio_theta,cost_ratio_eta_bar,turnpike_monotone_in_cost_ratio,interpretation,gate,provenance
Paper
FRONTIERS V.2
Changelog
[object Object]
Run it
curl -s -X POST https://sys128-tower-1.tailac24de.ts.net/api/compute/run \
-H "Content-Type: application/json" \
-d '{"method":"turnpike","params":{}}'