gcubed.projections.terminal_closure

The requested tail lacks a unique, economically compatible continuation.

Build u_t = K u_(t+1) + F_x x_t + F_c c_t from solved matrices.

u stacks the complete jump intercept (c2) and the expected-variable intercept passed backward (c4_lead). Constants stack state, jump and expected-variable reconciliation differences plus intertemporal constants. Static variables do not enter this dynamic boundary condition.

Prepared affine/geometric continuation, reusable across ITC perturbations.

For u_t = K u_(t+1) + f + (t-T) g + d**(t-T) c, solve for u_t = a + (t-T) b + d**(t-T) z. Consequently (I-K)b=g, (I-K)a=f+Kb and (I-dK)z=c. seed returns u_(T+1), which the existing backward loop requires.

A unit mode needs an explicitly justified level and, optionally, a drift. Constraints apply to recurrence intercepts; the caller must account for the state-dependent portion of any model normalization. All equations are checked, so inconsistent forcing is rejected rather than projected away.

Every non-unit mode of the backward recurrence must lie strictly inside the unit circle. Otherwise an algebraic particular solution does not establish a unique equilibrium continuation. Spectrum classification uses a 1e-8 tolerance around +1 and the unit circle, without changing any root. Undamped alternating or complex modes require another terminal method.