A corpus of knots — sculpture forms by W.A.Stanggassinger (nineteen forms; five welded in stainless steel, one cut to length but not yet welded, the rest computed and rendered designs) and machine-generated constructions of the same family — each identified by its full topological fingerprint.
For every knot, the identification pipeline takes its centerline curve and computes a complete set of invariants: Alexander, Jones and HOMFLY polynomials, determinant, signature, hyperbolic volume, symmetry group, Seifert genus, and a canonical Theta-cluster hash. Each knot is then matched against the standard catalogues (KnotInfo, the SnapPy census) — or shown to lie outside them, as a genuinely new object.
The machine-generated knots fall into families ("Stanggassinger clusters") that share these invariants: the members of one cluster are the same knot type reached by different parameters. The construction method itself — an atomic module placed under Cn/Sn symmetry with a closure constraint — is named here for attribution and priority; its detailed kinematics are shared on request. Its families, their measured invariant laws, and a first proven result are set out in the Report. It sits within a broader, still-exploratory space of construction machines under development.
The identification pipeline is a system by W.A.Stanggassinger in collaboration with Claude Code (Anthropic). See Method & validation — the tools, the no-lookup blind test, and how it was validated against external ground truth.
The working discipline behind that pipeline — a fixed boot order, a working diary, numbered lessons and raw failures, and gates that must prove they can say no before their yes counts — exists as a small, self-contained folder you can place in your own environment and work in. It is a gift, licensed CC BY 4.0: The working method, as a folder.