Rediscover Before You Discover: A Recent Human Find as the Regression Target for an Agentic Geometry Pipeline

How do we validate a discovery pipeline that has never discovered anything? We propose rediscovery regression as an evaluation discipline for agentic mathematical-discovery systems. Before an agent's novel claims are accepted, its pipeline must re-derive a recent human discovery from a minimal, target-specific input and pass pre-specified verification gates against a separately archived prior record. We instantiate this for space-filling polyhedra. Our pipeline may not hunt until it re-derives the Josehedron (Bernhard, 2026), a 12-facet plesiohedron, from its 12-point generating orbit, its only target-specific input. After one recorded amendment it matched every pre-specified anchor, with the geometry in exact rational arithmetic and the polyform counts as exact integers. The same machinery then audited the discoverer's novelty claim. Our submitted audit settled the orbit's full space group, IT(220), which his paper does not state. It then recomputed the one cell in that group's survey table (Schmitt, 2016) with the Josehedron's vertex, edge, and facet counts and found a different type. A reviewer observed that the orbit is also a general-position orbit of subgroups of two types, P2₁3 and R3c. Rerun on their tables, the audit finds that the printed P2₁3 representative for those counts is combinatorially the Josehedron. The type sits, unnamed, in the 2016 survey, and the submitted audit had checked too few tables. The gates also caught a draft rule that would have rejected the target itself.