RCHM × Hodge Research Round
R07 · The first closed-loop carrier reconstruction
A Closed-Loop Carrier Reconstruction Experiment with a Twisted Cubic on a Smooth Quartic Surface
On an explicit smooth quartic X containing the standard twisted cubic T, verifies exactly (SymPy) containment, smoothness and the determinantal form, and, using the Cifani–Pirola–Schlesinger equality I_{α(T,X),2} = I_{T,2} as an imported theorem, reconstructs T from its three quadrics.
In a known reconstructible case the carrier-inverse architecture has a theorem-bridged computational loop; it solves no new Hodge case.
The loop is closed by construction: the 'signature' given to the solver is the carrier's own ideal, and the Hodge side is the imported CPS theorem; periods and the Picard rank are not computed (stated in §18).